Embed Size (px)
DESCRIPTION
Решебник (ГДЗ) Алгебра і початки аналізу 10 клас Мерзляк
Citation preview
$iill:i:ii::j
liitii
s 1 . MHox,lHA. onEpAqti HAA MHo)KHHAMl,l
1. MHoxnHa raiie,|eMeHTtn
1. Bicexrpnca.
2. Craa.
3. I]onllj corlls.
4. neaa.oriqErn llo,'lexluB.
"s./s2) 4x: 5=0: r=.: x=lj.
Bianoaiat: x&.2
3) x, 12r + 21 = o: , = a t ulaa zt=sx"Ei=atzJa.Bilno.tiAb: 6l:2.15.
4) :r' 8,+I=0ir.'9+8r. 9=0; t= 9a6ot=1.BiAnoqiAb: g;1.
.,1...,512.r _5, a 0,, 5_Jh Z.r
"t, l.__ ,
BiAno6i0b: 1.1,5.
6) 16,:+ 24jr + 9 = 0; 1=n" rc's=t+4 144-o; ,=#= ir.4pyrxt cno.i6: l6' 24r I g O: (,1.r - 31 0: r I 0: x -3 t.
Bionoai,.io: 3 .
4
14. rr6,,r.r 7 6r.i 6x 4r.7-6i2, ttx tt..(1, -l
Bidnoqidb: \t: + -).
2\12-tu<3 2x; 5x+2t<3 12; 8jr < 9; J.>3.BiAnoBiAb: Gi +-t.4\ 7a - 3>7(a+ 1): 7a 3> 7d + 7i 0 o> 10.
Ue HepiBHicrb dF B/{oryr rB.s 4,1t )l{onHoi'o 3Hrqe".q rviHrroi d.Bldno8labr po3B'fl sriir EeMa€.
5) 4(2 + 3b) 3(4b-3)> o:a+ 12b 12b +9>0;0 b:- 17. IIs EepiBHicr!-npaBE,1lsa, BrKoHy€rr,c€ ans 6yAL.tHoro 3HaqeHHn b.BiAnoBiA': ( -; +-). '
6r 12 - 9'r ?. 12 . 9r r 49: Lr:37 37
I i x''-'
Bilnoeidb: ) -:I el7)x'J-8x+7>0.Po3B'nriieMo piBE'EE.s x' 8:. + 7 = 0,r=7 a6o r= l qrcna 7 i 1 xopeHirpnureua;r'?- 8x + 7t ! E ( -; 1) L, (7; +-).BiAnosiAb: ( -; 1) u (7; +*).8)n:+i. 2<0. qnc.ra (-2) i 1e EopeHsMr.Irpr.r.ineHa n':+ jr 2: x e l-2;11.BiAnBiAb: L 2; 11.9) 9 - r'?> 0; (3 irx3 + r) > 0; .]' € [-3j 3].BiAno6iAb: I_Bi 31.
5. 1)5€N; 2)0eN;14t ;q/t 5)3.14 01
!:ri:!iil ,tr 1e Ri q "E
e a.i.i!:.il!:!:::*:::J: 6. D(n = fi. E(l) = t1; -).i:::::::::i:: 1)B- Dtn; Uo D(l)l
:::.:::::::::. 4) -e Ell)t 5) l.0l - E(0.ii::ii:. 2
3)-5€Q;6\ne Qt
3) o q E(f)l
7. npaBrnbFi rBepAncenst: 1). vci iHlni - HerpaBItnLHi
8. 1) {o; 1}; 2) I 2; 2lt 3\ \21; q a.
s. r, 1,2,3,a,5,61, ,, I',',t,','1,l7 7 7 7 7 7i 14 3 2 3 4l3) {M; a; r; e; M; a; r; rr; K; a} = {M; aj r; e; ir; I(};4) lD; 5; 5; 5t - l5).
1O. PiBHi MHor{r.rHr.r npeacraBneHi B nep o}ry BtrnaAny,60 Rox(eH e,!eMeHrnepuloi MHo-
xcrErr € eneMeHroM apyroi MHojrtlrrr i, ereMuHr Apyroi MHoxrrHt€ €,leMeHroM nepuoi MEoritrEr. v ApyroMy BrraAKy € piBH Mt{, 6()
ereMenroM MsonirHr A € Eapa (1; 0), a e,leMesroM MHonitrEtrBenr anapa(0; 1).y rpe1r,oMy Bsnaany eneMenroM MEoJ{rulIl A e qficno 1, a eneMeEroM MIIori{IjHII B
_/.no t. . ^\ y
1 1 . 1) Hi, 60 eneMeH" ( 1) MlroJnx rdHe€eneMeHroMMqo}l{ Irr B, a eneMeEr 2 Mqo-x{sx B se e eieMesroM MEoJrtnHu A.2) Ta!{,A=R,60 nopensmu piesssgs lrl = :c e jr > 0, a r> 0 €saqae, rqo jr € [0; +-),ro6ro MEor{t{sa B.3) Hi, 60,4. c B.
12. 1) O, 60 cvMa r.yriB rprICyrHLIRa AopiBHBe 180";
2) He € nopor$sLoro MHonir.rHoro, 60 € ropr saBsnukIr tronaA8800 M;
3) nopo)nHs MHox{,1Ha.60 ve.airH, ropis'n. no loBH H i
cropolrx, Ao nl{oi Bosa npoBeaeira, ,'Islne B npsMol{yr- AEOMY TP]II{YTHI'II{Y; D4J Z, 60 lio]ro ae rpaoi( piBHrrnH.s (r - a)'z + (r b)' = R'.
BnpaBx Arq noBropeHH9
13. 1).r'g 1jr=0; alr 7)=O;x=Oa6ox=7.BiAnoqiAb: O. 7.
230 ii! AnrEEPA Mep3nrK A. r. ra iH. aKaaeMi'{H4i piBeHh ;:!ii;i:ii:::!;i:il:::.x
lO) 612 2r < 0; 2r(3r - 1) < 0;
ut"""ru,, (.otl).
+=-t--=-)].'-+.01
3
"[''f
;ii::iiilliiti::: AI f EEPA Mep3ncK A. f . ra iH. AKaAeMiqHui piseHb l::.:; 23 1
11) r'+ 3i. + 4 > 0; r, - 8rc - 4 < 0.r{icna ( 1) i 4 e xopeHnMn rplrqnelrax'z-3x-4, re (-1;4).Bi0no6iAb: ( li 1).
12, O,2t'> 1,8r; 0,2r'.- 1,8x > 0;O,2t(t 9') > 0i .jr € (--; 0) u (0; +-).Bi)noqi'b: (--i 0) u (9; +-).
2. niAMHoxrHa, Onepaqil HaA MHoxnHaM!l
15. AiBqara niAMHonnsa l.r$iB Knacy.Xronqi niAMEo)r.iEHav-rEiBruacv.
+ -t\,,,--=\-/---+1
--=--\--'-:--\----+---i 1
25. IiAMHoxsEIr: a; \tl, \2\i l1t 2]l.
26. nis;Hoxlrrra: o; { 1}; {o}; {1}; { 1; 0}; {-1; 1}; {0; 1}; { 1; 0; 1}.
27, I]paBrnbEe rBepAr{eHsn 3),60 a cdrblrnii e,leMeEr ABox MHo){ixE i neperI-I
soM aatrlrx MHo*iIrH e MHo)icI{Ha, slla Micrur]' qefi crirLrlllfi eneMesr'
28. 1) {2; 8}; 2) 14; 7i 0ll.
29. MEor*(&si A ^
B Ha,reFiar6 'rr'tcra: 11; 31
30. Hexan.4 = {1; 2; 3; 5; 6; 15; 30} - Mflor*{IrEa AinLEr$iB 'rrcna 30, a B = {1; 3; 5;
9t 15; 45] - MEo)IllrIIa AinbH[KiB qficna 45, roAi A ^
B = {1; 3; 5; 15}.
2)A^B=A;4rA^B=12;3,5,7]].
yqEi, rqo caxorlnlolorbcs Oyr6onoM e niAMHonrrHoro yqEi3 Knacy.
16. npoMiEb; liApisoR.
17. CerMeHr: ceKrop. pa,qiyc. xopra.
14. 1) MEor{vtra 6ynB croBa 4kopar € rinMso}iinHoro MHorrrHs.4.3) Msonusa 6y&B croBe <Rapr{Ha' € niAMHo}I$rHoro MHo)ro{Er.4.5) MHotrixsa 6yKB cro € niAMnoxrlllrolo MEoxnIIn A.6) MHon{r.rHa 6yKB cnoBa (rrrpErD e riAMHomllsoro MHorKrHr ,{.7) Msofiir.rHa 6yriB croBa (rrn' e ri.qMEo)rcrHoro MIIo)&nHr,4.11) Mlro}rislla 6yxB cnoBa <Aapr € niAMHor.trHoro Mnon{r.rHr.r -4.
19. 1) Talr, 60 qrropu qncna 98 € eneMesraMs nnoxngn A = {1; 9t 5; 8};2) lIi, 60 ql{Opa 0 qrcna 9510 Ee € ereMenroM MHox(}rHv A;3) raK, 60 qrropr .rz cna 519 e ereMeEraME M]]oxv au -4;4) raK, 60 MHoxcrEa IIrQp.rrcra 5858 Aopir*o€ MEo,IurIIi {5;8}, sria d niaMnoJ*rrr,HoIo MHox'{Hx,4;5) rax,60 Mnomrura qlr&p qlrcna 195 888 € MHoxrI{a {1;9; 5; 81, rxa € niaMHo,xnHoro vuo)+(fifix A;6) ni, 60 qtopa 2 .rncna 91 258 He e eneMeHroM MHo)krIIr.4..
20. Hanpxx,lai: AcAra A.-A.
21.Ilpaen,rrne raepA,*ieHHs - 2),60 MHo)IrgHa {dl Micr6rb € 'reMeHr
a, nK fr€ sMEo-xnni {a; b}, iHEri rBepAx{eHH.s He € trpaBlrnEEr-rMr-r.
31-1)A^B=A)3) 1 /l B = {19; 3A; 57, 76t 95h
B) rpoMiE6.
2) (--; 3) - (1; 4) = (1; 3);4) N
^ ( 3; 41= 11,, 2; 3i 4\.,
6) (-1; 1l ^ t1; +-) = {1};8) R. (-2; 3) = ( 2; 3).
2)(--i1)^N={1}j4) (--; 7) n fi = ( *; 7).
22, A c B qe osHaqae, u{o eneMeHT[ Mnorr(ruI{,4 e eneMell-TAMI MIIO']iI{HI B.B cC -
qe o3Ea.ra€, q B e eneMeHra-Mn MHornrHr.r C, ro6ro eneMeHrr MHoJr{n!I!. A € eneMeHraMrMHonir.rHn C. GincHo, snqo , ereMe:rr MHo?nnHa 14, ros yMoB{ -4 c B BrnnrBa€! rrto, € B. gRrr{o r e B i E - C,ro r G C, 10610,4 c C.)
23,lrCcAcDcB; 2)B.DcE.AcC.24. r) /,-;-\ ', ,/;--\
a9@232 ll:l: A'I|EEPA Mep3nrK A. r. ra iH. A(a,qeMi.rHnr pieenr il:ilil:jlljli;i;ii
AD""''' ̂ r"K " u<1, "' 7\r.2,,< .l \ ,---=i1\, ^- \" ^141,
i:.?.i:l. .
:,:i::ii{*
.:.ti:.itit
.:n::::illt
I
n'At,\'xx'"Yl(^L+)" ,1Y.
33. Ileperr.rHoM aBox rpoMesiB, rqo nentarL lra oAHiii npsMii, Mo)<yrl' 6vrr:6) Bj.qpi3orii
34. 1) [-4; 6) ^ (-2; 7) = ( 2; 6);
3)( -;2)/r(3;8)=u;5)( 2;2)^z={ ItO;lli7\ ( | 11. (ti +-) = a:
35. 1) ( -i 2) ^
rr' = {1}j3) t 1; 1).j z = {-1i 0};
36. flpasnrEne rBepatrcenEs - 1), 60 o6'eAHarns ABox MEoJ*{xs e MHotrctiHa, sxa Mic-
TI,ITT, E'EMEHTI sAAAIIfi
37, 1) MEo)$nEa qrsp .rqcna 2? 288 € MHorxwta A= \2; 7; 2; a) a:l = \2: 7; 8)' a MHo-
r{r(Ila qnsp qrcna 56 383 e MEo)rusa B = {5; 6; 3; 8; 3} = {5; 6; 3; 8}.
'fop,i A \J B - \2;3; 5; 6; 7; 8).2) MEorrclrrla qrop q!rc,!a 55 555 € MEoniEra -4 = {5i, a MEo,rcnHa rlq(Dp qrcna
777 777 e MP'ol'\ujda. B = {7}. ToAi,a Lr B = {5; 7}.
38. l) A L A MHor<tua piBHo6Fapesxx rpyrl ffiYXiB2) A u A = N\{1}, ocftirL}$r Bci q'c,!a Earepar6Horo psav, oftpiM 1, € a6o trpocrl-MrI, a6o cftraAeHqMlt.3) -4 u B = B \.) {2}, oc&i"rbRl, Bci npocri 'r]rcna, oitpiM 2' e EerapIrI'rMI'r'
i::iai{i::;::;iiit: AITEEPA Mep3reK A. r. ra iH. AKaAeMi'{Hni piBeHb:::::i 233
{r)" t'L" o'
t;r;Iifrj
iti.rl:i
i::li:li,::l
ffi
39. 1) 06'€aHasHsM M,BCi AAC, e qorfipwiyr-
'I'rE ABCD.
l>"t,/\t,/ I
ol \o
2) 06'€anasHEM AA-BCi A-4CD e MBD.
,r\/A"/,-'" \
.4
-B
3) 06'eAnaHnsM 4,4-BC
i ADE-K € nlecrffiyr-Erk ABaDEK.
l6a+320. l6x:-3.44. l) I I
Li-4r<?; lar<0;BianosiAb: @. +*1.
". lar.+19:51 1. Jrr 20,'
110x < 3x + 2l L7r < 21:
Bid,ld6trbi porB'r3riiB HeMae.
r>20-x<3i
06'€AsariHnM rprrcyrr]IldB He Mor{e 6yrlr BiApisoli, 60 06'€aEaHIItM}l{nHa, sKa Micrur6 €reMeHrIr noniHoi 3 AaE'
40. O6'€AHaHr'nM ABox ipoveEiB, ulo nen ar! a o.qHiii rp.aMin, e rptMa, npoMiEB
41. 1\ ( 2. 5l'r (2i 7l = ( 2. 7lt 2) ( -i 3) L, (-3; 3l = ( -; 3l;3)( -i8)u[ 2j+-)=( -;.]--); 4)R\J( 7i2l=Rt5)OL,N=Q; 6)RL,N=-4.
42. 1)( -; 1lu[1;+-)=( -; +-); 2)( -;5)u(3i 5]=( -; 5l;3)RL, Q=-4; 4) (5; +-) .JR-R.
BnpaBn anq noBroPeHHc
r 4! a -4' rrx 4l ly=0,43 lr _ - _ : " .''-0: ''' 0:x-4 r | !-1 ! 4 x 4.
o {;',-J-u=
o' Po3B's':*{eMo piBHsIrHs 12 +' 6 = o;
SEanaeMo posB'.r3r.r.r HepiBHocri.!'+ jr 6<0; xe l-3.21.
x= 3a6o t=2.+. +
zt -i 5 -'8., rr'r,3)-ilr 3r-18 o;. 3 ir-3 r I (r-3XJ iJ)
r'+3J. 5ir+15-18(r 3Xr + 3)
=0;
x'-zt s
-=(r:
(x 3)(r + 3)
BiAno6iAb: L
x' 2x-3=o.(j.-AXr.+3)r0; l;,';,="
d o r 4 _I o,'',, ,r' t-i i r u',r-tr rt rrtrxr I r4{l 'r l2rir..-lr.t.r lr' o. 4-4x-2, 2 x'z 2x l-o.
trr')(l jr) {i-lrll rr[t' = t,
t-4r,5 x -4r 5 'lr 4i' 5=0 1' t',''',,i-', =o',' ,'',,-i'=o'1,'-J,, ',,0, li,, ,. " 5
l*"r,BiAnoqiAb:'5.
12 2 3 l2+2tr 5t 3rir ll ^4)-U:r.r 5rtr r l) r'l , 5 (.r 5X' ri)
12 2jr-10 3r 3 o. tl- O, t'l- 0,
{r 5l,r - lr {x 5jl,r l) (ir 5){.' , l)t+1=0: lx=-l:l" s . o. ]t, = s. r-h.rev? H.cjvi.Ha.
l"*r*0, l"*-t.Btdno\iob: piBH^ Hq HF Mdc porB q'{is.
234 r::.:::: AtIrEEPA Mep3ncK A. f. ra iH. AKaaeMi,{Hr4i piBeHb i:l:i:':;:!;i':':li:i:::
,!> 0 i 4 > 0, ro6ro r.'z + 4 I 0.B'dnBib:\ *i--\.
4) L.n1- 4x+x 2 5r-2')c2rr2:.(x-2\
Ileii Brpas Mae 3Micr, sRr{o r(r - 2) + 0, ro6roJ. * 0 a6o n + 2.BiAnoqiAb: t*t 0) ,J (0; 2) u (2; +-).
sf 1f- 2". IIefi Bupa3 Ma€ sMicr, .alirqo 6 7r > 0; 7ir > 6;
(6Bidnaqidb: -rl7
,a97
r'. : +Pors r,l{pMo cxcrcMv: I - 3 2" lr '0:o<r<2.BianosiAb: Q; 21.
1rr-r-12>0.4t l110 3r r' > 0.
l. Po3B'-{}I{eMo HepiEHicrB r.'z t 12 > 0.ItopeFsMx rpx.rreHa re - r. - 12 e qtrcra 3 i 4;,€( *; 3lu[4;+-).2. PGB'flr€eMo HepiBlricrb r'z- 3r + 10 > 0;r'j + 3r - 10 < 0. ICop€HsMu rprqneHa.r r3x i0c q,,,nd 5i2ix-t 5;2).
[' :.BpaxoBy'o'rH yMoBu (l) r (2). va, vo: r - 4:
5 tr- 2-
MaeMo:r€ ( 5; -31.BiAnoBiAb: ( 5; 31.
3
5
45. 1) Brpa3 j- *u"
".i"', rlr]]lo r + 5 + O, ro6ro.r + 5.
Ja+i)BiAnMi}b: ( -; -5) u ( 5; +*).
r+4 x+42)Bupa3 +=. : Mae 3Micr, siirro (r 2r(r + 2\ + O, totuo x t !2.' x' 4 k 2)G+21Biano1i1b: ( -; 2) 'J ( 2t 2) u (2r +*).
3, Blipar ', - va. rvi'1 llp .r - R.60 x - ,l 0, ta.)vd roa.Hgi0x-+4
:i::iaii:::::::iii: AnrEEPA MepsneKA. f. ra iH. AKa,qeMi,{Hhn piBeHb i::i 235
ll i
3t,;::i
:ll:.i
,i:.:
:i
.!!ii!:,1:::::fil:ii.:
./3' + 6
BiAno6iAb: G2t +*).
7) J5-*,-+. qen supac mar rMirl. !.!-u3Jr
,r ' roi ;t. . a----'-iBiAnosfib: loi 51. u b
g J7 x - 42 - ' U.u u"0," r,ra. rMicr, sxuror' Rr
[r: e:
][- - o. - ,e lo: a)urar +*t.[x*sr
[6; 8)u(8;+-).
s) l|'' + 3' + a. 4en Br.rpa3 Ma€ 3Micr,sKqo r'2+ 3r+4>0; x' 3x - 4s0|' r e l-1; 41.BiAnosiAb: L I; 41.
lo. -:::L. ucii supaJ,ra. JMicr,Jt' + 4x 12
sHqo ir'z + 4, 12 > Oi x e ( -; 6) u (2; +-).Bi0no6iA6: ( -; 6) !, (2; +-).
f(i.) = -\ -Ar' + 2x = l;-$t2+2x+ 1= 0; 3t'- 2,. 1= 0;
D 4-4 3 {l) 4*12=ltj: x, '--n=r,, t:o -} = -',oo
f(r) = 56; 3f +2r.= 56:3x' 2x+56=OtD=4-4 3 56-4-672= 668<0 PisHslrHs Ee Ma€ AiiicErx KopeHiB.
3)l(-1)=-s ( t)'+2 (-1)= 3 2 = -5. Pisgicrs l( r) = 5 - EenpaBIrnEEa'
f(2\ = -3 2,+2.2= 3 4+4= t2+4=-8. PiBHicr6 f(2) = 8 - rpaBI'nEEa.
1a
rr i1+y=r\=rs, i(o)=oq= o; lor=f|=f =:;
y1-"1= 1L=19=-3,33 -6
2) rJ-st \=s; 3==t r-3=2;r=51
ir,l=0.s, 4= ];' - B = 36;,= 3e;
l(r)= ro:
-1L=-10; a=-s;'-t= 3' '=z-rlt
48. 1) @yH$ailo Ba{ario omcoM.
J5 x>0. Jx<5.lr'o: [x'o;
]zx +z>0. lzt>az.lx' a,r * o: lxtx 8) + 0;
' = r1 t' = r.zr.
nt J7 * s' tt ;1*. u"n ""0* "a€ sMicr, f*qo
{'' ' s* - tr - o '. ,-, -7) .l2t 7)t \zt .*).
J{r 7l(r + 7) + 0:
BiAnosiAb: ( *t 7, \J l2t 7) u (7; +-).
tzl , '*2 * =-. U"oBnparMa, JMicr,J35 + 2.r r' J8 - 4ir
35+2' x'z '0. [*' z' :s.0.la-+"'0, la*' s,
Itr + 5xr 7r < 0.1 xE(21 7).
BianosiAb: / 5; 2\.
92. noBTopEHHc I po3ul1,|pEHHc BtAoMocrEf npo ovHKqtlo
1. OyH(qit ra riocHoBHi BracrrBocri
46. f(r) - -l,'z + 2,.1) l(1)= 3 1'z+2 1- 3+2=-1;l(0)=-3 0+2 0=0;
rl 11.-r.l 'i-r.'-=".!.?=!,2-t n2t B.t2rt2 t2tlr/ 13/ 3 9 3 3 3
= 3.4+(-4)=-12-4=-16;
l----.,-'- --:-:7::r:::11-62-
2) E(l) = {0; 1: 2:3i.
--- + --\ ,.--=--\ ,--- +---,+""""":7 i)-i""r'
3)
2 23 1,7 5 -1,84g 2 5 0,5 0,4
y = uE * z = "8 = z: 5 = \G + 2, 25 = ! + 2, ' = 231
s=,1 r.ts' 2=u62r o.s; o.q=G*- 0.16 x,2,.r=-1.84.
51, @irypa r{e Mor{ie cnyryBarl-r rpa{DiKoM OyAlcilii, 6o sEa.reHlrsu t > 0 BiAroBiAae
aBa ssaqesris y.
52. 1) l( 3,5) = -0,5; f( 2,5) = 2: l(-1) = 0; l(2) = -1.2\f(x)- 2,5, roMy ' = 5; l(r) = -2, roMv r = s,5; l(n)=2'roMvjr-0.3) E(f) t 2.5: 31.
4) l(*) = 0, .ssrqo ;r = 3, x = 1, t = 1,5.5) ftr) > 0, sxrqo ' e (-3; 1); J.e( 1;1,5); l(r)<0,sr{rxo.rL t 4: 3): x( (1.5: 51.
6) @ylrllqifl l(r') 3pocra€, sxqo jr € | 4, -zli t e [ 1; 0l; Ovlrriqin l(r) cnaaae'
slrlrrox€ [-2; 1]; re [0; 5].7) a) Ha rpoMini&y [1; 2] OyHliqin l(n) nprfiMa€ EaiA6inL e ssaqeHHs, nxe aopiBHro€ 1, ra HaiiMeEure 3lraqeHlls, nlle aopiBHre ( 1).6) [-2,5i 1]. Hali6inbure 3Ea.reHss OyHllqii l(') AopilHlo€ 2, a Eai:iMerlxe slra'{el]-Hs AopiBEIoe 1.B) [-2,5; 3,5]. Haii6inr,ne 3IIa''eHHs
'rellEn aopiBHloe ( 2).
ii::liiii:i::.::Ji:i AnTEEPA Mep3ne'( a.
-i-_\ i,/-':-\ ,.-X_ l- ii---
-57'tl
-::--i::-:-r:$+i2r
2
3OvHKlrii l(r) AopiBnro€ 2, a sanMeHne 3Ha-
f. ra iH. AKaAeMi,{slaf piBeHb ii:l 237
16 17 18 l9 20 21 22 24
0 t 2 3 0 1 2 3 0
2 1,2 16
g 5 2 2,4 -5
236 ll:i aITEEPA Mep3neK A. r. ra iH. AKaaeMi,rHnr pieeru l:i!{:i:ilii!li{:i
li1:l,tE;fi
::r
:i.]
:.:
;r
'i.:{a:'.!i:.:.:L
53. 1) l( ,{) = 0,5; ^
7) = 2; f(1) = 2i f(2,5\ = o,5l2) x) = 1, roAi t = 12; flx) = 2,'to4i x = !1,3) n(D = t 1; 3l;a) l(r) = 0, nlirro r = 3, r= 1,5,x=1,5,:t=3t5) l(r) > 0, J{Krr{o r € [ 4; 3),r€ (-1,5;1,5),n€ (3; 4];l(x) < o, .sr{qo r € (-3; 1,5), J. e (1,5; 3)i6) n(qo r e [ 2;0]ir€ [2;4], 10 rDyHl{IIia flr) 3pocraa. .'IRqo x € [ 4; 2]i x € [0; 2], ro qryriHrri' l(r.) ctraaae;7) a) [ 3; 2]. HanMeHue 3lraqeFEs (Jyrnrrii l(j') nopirHloe ( 1) Hafi6i"1b e 3Ea-qFhhr +t Hs
'11 /(ir) nop:8hrc. 0.
6) t-3; 11. HanMelrtlle 3HaqeHHn dryHFrrii l(x) aopinHloe ( 1), a Eai:i6irbrre 3Ea-.reHH'r -- qncno 2.s) [ 3; 1]. HariMeHDe 3tsa\elrH.s dyEIiIIii l(ir) aopiBErc€ ( 1), a Han6inlue SraqeH
qricro 2.
54. 1) O6,racrlo Btr3Ea'ierllls $yHftIili ili = : . e Bci rilicHi 3HaqeEss J., RpiM .x = 4.
r-6'2t ftxt = : . D(f)=R.
s) /(r)= \-j'-i: Dtf\=17:+-)t 60x 7>0, rliqo:,.> 7.
lo4r /tr.r= ' ; Dl,t) { -i .1,;{ r I 0,J lr.
J-x 1
5) /(:r) = Jr' + 6:lr - ?; ,(D = ( -; 7l'Jl:rt+*), ..1.....-60 jr'+ 6jr ? > 0, sftrqo n € ( -; zl, iir r-r. i
-a1
61 /tir) = --1. SHa.reliHt OvERiIii l(r.) icHy€, nlrll{o tr 5it I 0; r.(r. 5) + o;
r.+0a6or+5.ToMyr(r=( *; 0) ! (0i 5) u (5i +-).
l56.1, l(.r)=lr 6. flxrqo x = 0, ro l(0) = 6.Toqna(0; 6) - roqlta repeausy rpa
Oirla cpyg,iqii l(r.) s Biccb oy..tlntqo l(r.) = 0, "o lr-o=0, ]-r = s; r = +2. To'r''77
Ita (42; 0) - roqna neperrsy rpaoi(a OyHrirrii f(r.) tu Bicclo Or.
2t ht.r=1?* T ".*" x 0. ro iro, 2.4. nr(uo irrr " o. . lf- 3j
o.
12+3r =O- r=-4.robro - 1 Orxe, roqI{u (0t 2,1) i (-1i 0) roqr{u reperlrliv
L2.r-5*0: Lr=2.5.rpaoi(a dryHlluii
'(J.) 3 ocsMr' RoopaxHar.
3) s(,r) - 5 - r'..ERlro x = 0, ro s(0) = 5. flI{qo s(r) = 0, ro 5 - I,= 0; :r=tJs.orxe, roqru (0; 5), (-./6; 0) i ("6; o) roql(I{ nepernFy rpaoim rDyllrtqii s(r)3 oc.aMn rioopaiEar.
a) o(.r)=rE 2. flfiqo jr = 0, ro (p(0) = 2. fll{tqo 9(,.) = 0, ,o Ji z=o: G =2,.r = 4. Orr"e, roqKr (0; -2) i (4; 0) roqftr neperrny .paotua Oyxl{llii I (.r) 3 ocfl-MrI Koopartsar,
57. 1) l(r, = 5f + x - 4. gnqoJ. = 0, ro l(0) = -4. flliqo l(.jr) = 0, ro 5r.r + r - 4 = 0i
D I 4 5 l-41 8l:.. ''0,8; , I OrxP. roqHr(0: l).r0 lot0,8; 0) i ( 1; 0) ro.rKr repeusy ryaoi(a oyHllqii l(r) 3 ocsMl't (ooparHar'
": .r" ly 3r 0,2)
^rt ' '"-. fl*uro )- = 0. n /(0) 0. flKUro /r.rr 0. o 1'' --"r a l' 8,0:
lrrx 3t o, lx 0, -I roq*" (0:0) i( 3i 0) roqKv n"oel ,H\ rpa0"{a tlryHKqriLx-8i l'= 3.
3 ocrMrr rioopArHar.
58. 1) l(r) = o,ai' 8; 0,4.r 8 = 0; o,4r = 8: x = 2O;
2)s(xr=2a+3:. ," -r2 +3x+ 28=0; rr 3r-28=0;D s 4 t r.28r 121: r. 3-I1=7.
"" 3 ll
4i223),r(r)=v[+4; .it+a=0r r+4=0; r= 4;
r'z+r 304) $lr) = ---;
5) flr.) = r.3 9r; ;rr 9.r = 0; n(irr 9) = 0; r = 0; r. = 13i6\ eQ) = a' + 4; tc') + 4 = 0, r e Q.
59. l) /(/) rr 1.r; rs-1"=0, ' 4;. o.xe. /(xr=u. nx.uo t 45.'332, flr\ = 5r' + 4x 1;sx'z+ 4.r - 1=0jD-2 i., rr-4.5-9: '.
2*3 l, ".'3-l I.4555
O,Hp.
^jr) 0. flKULo r 0.2 i x L
a) l(r)=rf,'-s; uft=o; r'z e=0; .r = 13. or'Ite, ^')
= 0, sxqo ' = i3.
7) /(x) = \,6 + .f1 ;. sHaqeHss OyHKIrii l(Jr) icnye, srrtrro
ro6ro 0 < a < 1. ToMy r{l) = [0; 1].
x a.0.
1 r>0;
r>0,
J'- o,
[:r < t;
8r /ri) . 3 "'FHIs +]hKuii /r"r rrHv.. qKuo 12 4r x' OiJl2 4x x
| 4x-12<O; 2<r < 6. ToMyD(/)=( 2;6)
,) l(') = *+ sEa.ienH'I oyHnrrii /(r) icsy€, 'iHqo
To6ro r - 1 > 0, r:' 1. ToMy r(l) = (1i +*).
ro) l(:r) = \G J r. sHa.{eErrs Ov"xqii f(,) icllye, rl{rlo
To6ro r = 0. Touv ,(l = {0}.
55.r,/(r) '1.otn (-:2) t2i -)6('x,2.' t+2I
2t ltxt , "6.Dtlt R.6o-t rI 0norr R-
3) /rir) 3j 2 . g.ro r 5r - 4 , 0, ro rlaqpHHt /(r., j.q)..' r' 5r+4'roMv ,(f) = (-*; 1) u (4; +-) (6onpr.r= 1i:,.=4srpasr: 5, +4=0).
qrfrr, u6rz \r 5.D,/) ts,r-r.oo ]i l, l i," t
238 r::::i AnfEEPA Mep3nqK A. f, ra iH. AKaAeMiqHnf pieers j:l:;:i:;:;:i:;:;i:il:ii
Orri{e. flr) - 0, sKrro r = 25.
:;:i:::i:::::::!::::::i: AITEEPA Mep3reK A. r. ra iH. AKaAeMiqH{r piBeHb :iii: 239
Jr-t>0,LJ. 1+ 0.
4\f(r)= 4trea.5r frrr=5-02'r ! -0.?{ = or
a-2 x 2
5 0,2J. = 0,
x 2+Oix=25,
0) l(:) =.r'? + ti t2 + r = O; r(r + 1) = 0; r = 0 a6o t = -1. Orxte, i(t) = 0, rlcqor=0,r=-1.
60.l) g = 7t 3. npoMixHr.r rHakocra-flocri:
y > 0, snDro -7t + S>O; 7x> -S; x<!;7
y<0,filtnto ?x+3<0; 7x< A; x>?;2) V - x' at + 16. flpoMbtrrrlr 3EaKocranocri:
A>0,f 8r+16>0',(x 4\'>O,t+4:xe ( -;4) u (4; +-);y<O,tea.3l , 6 floori**" rgarrocranorri:' 4-a
v 0; =Lr0;4 x 0:x 4itc \@i4)i"4t
u.0; " 0i 4 r 0;x 4; x-(4t -).4t ! x' L npoMiAkl.r 3Haxocranocrj:
A>O| *+ 1> 0; (1 ,X1 +t)>0;y > 0, sroqo r. € (-1; 1);y < 0, nKqo t € ( -; -1) u (1; +-).5) u = Zx'z 7x - 4. IlpomrNnr 3Hakocra,locri:y > O;3t2 7t+4>Oi3x'-7x+4=O,D=7''4 3 4=49-4a=Ii
7+1 4 1 7-l ,r.=-=-=I : r^=-=l:'633'6u<0.Uc2-7r+4<O;
62. 1) Hexan t, > t| Ma€Mo 10t, 3 10t1 + 3 = 10(t, - ,r) > 0 roAi 10r, 3 > 10t1 3,ro6ro OyHRqis y = lot - 3 e 3pocralo.{orc.2)g= 3r+ 7. Hexaii ',
> ,t, roai g(',)= 3',+ 7iy(r',)=-8tt+T SEaiaeMo:y, y,=-3r,+7 +3\ 7= 3(J', a,)<0 @vHriqia v(t) e cna'qnolo.3) Hexan jr, > r,, ro,qi y(t,) = I 2'; a@) = 9 - 2t,, SEanaeMo
v, h=9 2a,-9+2\=2(t' x") < 0. ovnxqis v = I - 2jr € craAlrorc.4) v = t, Hex ft x,> \ roaj. vk,, = r,t V@) = xrSHaiAeMo: y, yt= t,-(-rt)= 1\ -.t, < 0. oyEftIlis y(t)€ craAHolo.
ttll5r y ;x. Hexan.r, r- rori !(x,\ uG.\ -r.- .r, =;{t, .Y,)>u.
oyHRuie y(.r) c apocraloqoo.6) V 2 0.6x. Hexaii x? .r,. roAi
vk) - s(r..) = (2 - o,6x") - (2 - 0,6rf) = 0,6is1 0,6', = 0,6(x, - r,) < 0.(DyHKqii y(r) e ctra,qHoro.
63. 1)y= 2r+5
, . (--' ?-)'
"(?'.-)
y > o,.nxrqo r e t -, tr " (t|, **),
y<0,'xrqo ".{.'''*J.6) V = Zr" + 8Jc - 1. IlpoMi*{rin at u*o".-o"ti,
.+-11,
---+-\--- -\],'-r ,r'a
----\,.'-i-\/--------; --i-.j
a) ,(t) = 0, sriqo -2r + 5 = 0;t = 2,5i6) y > 0, "sRrro -2x + 5>0,)c<2,5,ro6ror€(-;2,5);A < O, t> 2,5, ro6ro Jl: e (2,5; +-)iB) OyHI(qis y(t) € cra,qHolo.
3) g=2
l]>0,re (-*;0);y<0,t€ (0; +-);OyEriqi.r y(r) € cnaAEoro.
6
a)6)B)
a>U 2f+ 3t- 1>0iy<0; -2x'z + 3t + 1 < O: -zx'z + 3x + 1 = O,
D=s-4 (-2\.( 1)=9-8=1;
" =-91= r.,^ = -3n1 = 1=e.s.
'-42Orxie, y > 0, s&qo jr € (0,5; 1)iy < 0,€lcrro r € (-*; 0,5) u (1; +-).
61. 1) y = 0,6t + 12. IlpoMiri(u sHarcocranocril0,6x + 12 > 0; O,6x> -12i r > 20. Orxe, y > 0,6Rtqo t € (-20; +-);0,6r+12 <Ot0,6r < -12i I < 20. Orr{ie, y < 0, s&qo jl: € (--; -20).h U =,18 ' 3, tlpoMinxu rflakocra-ro.ri:y>0; G+3>0; r20. Ornie, y>0, sRqox€ [0; +-);g<OtreA.3t g = 9x - x'. flpoMi)rrKr 3Hel{ocra-'Iocri:
---\ _/-T=\,.-
y > Oi 9t - t2 > O; r(9 -.r) > 0. Or!(e., > 0. ------1,-- i-----tl(qo r c (0: 9) i3, 0. txqo r.. ( *i or J (9i +-l4l g 4x' 3x - 1. flpoMiJ{rHx 3saKocra"loc'i:
u > O, axnto 4x'- 3x - 1> 0; D=3'- 4 4 ( 1)-25i._ 3-5=r,, _3-r _o.zl. -->j--_}4^' s -' i' s -o,25grinro r € (-*; 0,25)u(1; +*),rog> 0..Exqor€ ( 0,25;1), roy<0.
24o fli: AITEEPA Mep3rrKA. r. ra iH. AKaseMi,{srai piBet" {i;::li$tilrli
4)
a)y(a)=O,reO;6)u=2>O,xeRB) y(r) - crara OyHrcqis, rpoMir{RiB3pocralll{fi i clla,qaEHs EeMa€.
6)y>0,a1cflrot€(-;0);y < 0, nREIo t € (0; +-);B) dysK4ra v(t) spocrae,sllqote ( €; 0)ixe (0;+-).
;:iiiiiiil:iillii uresPA Mep3nrK A. r. ra iH. A(aaeMi.rHran piBeHb ii::: 241
a\g(x)=O,xeA'
t"iftiEt!El:
,ji
:.
i:l
:l
t.:.:.!!ii!l
I.r:.ii!:.i:.:
ti!l!!!i!i
5\s=x'+2, 3 6) a=2r x' 65.'t) s = l(x)/(r)=0,flnrqof= 3i,.=4;
66.y=l(rc),x€[-6;5].l(:,.) = 0, slinlo r. = --6,
67.y=f(r),ae | 5; al.1).trl{qox€[5;1],3pocrae; sRrlojr e [1;
2) !=e(J)e(:r) = 0, anrqo :t = 2, x = 0, :. = 3.
2) 'Iriqo.,
e [-5; -1] i [2; 41, Oyrr(qis cnaAa€. OyHriqis 3pocrae, n{rqox e I t;21.
a) y(r)=0; r.i+2.' 3=0i.r= 3a6or=1;6) .r' "r' 21 3 > 0, s(rqor - ( -r 3) (l: --r: ir' 2.ir 3 0.srtrqore ( 3;1);s) OyHXITiE y(r) cnaAae, slcqor ( -: Il.
'trvHK rq /,1x) 3Poc.a..
E(iqot€ [ l;+-).
I64. l) q=3 r
4
a) y=o,snrro r=12:6) r> 0, flrirro xe ('*1 12\; a <slrqo , e (12; +-);B) cpyEl{qiJ{ cEaaa€, sllnlo r. E -q.
3\v= a"+ 4x 3
0,
a) r=0,sl{qor=1ix=3;6)y>o,ir€(1;3);a <0,x. ( -i 1)u(3; +-);B) dlyHr.iqin y(jr) spocrae,sriu.ro i. € ( -; 21, Oylrnqir y(.') cra{a€,snqo r € [2; +-).
242 ,;t* A'.IEEPA Mep3neKA, F. ra iH'
a) y(,.) = 0, sErqo 2r r'= 0;r.(2 - rl:) = 0, ro6ro r = 0 a6o r = 2;
6) u > 0, s.asto 2x - x'z> 0; .ir(2 t)>0;r € (0; 2)iy < 0, nlirqo , e (--i 0) !, (2i +-);B) OyH:iqi' ,(J.) 3pocrae, nxrqor € ( €; 11, OyIIIlqifl r(r) cna,qae,
sklroxe [1;+-)
al U=o, xe ai6) y> 0, jr€ (0; +-); y<0, ir€ ( -i 0);B) rDyHnqis cnaaae, .snqo t € ( -; 0)i.T€(0;+-).
a) 9=0, r=13;6) y>0,'nnloJ'E ( 3;3)iy<o,sHqojr € (-*; 3) u (3; +-);B) OvE(qifl 3pocrae, .sl(qo ,. E ( -; 01,
OyHriqiE cflaAae, ERllo jr € [0; +-)
AKaIleMl9H14t'l plBeHb,ii!i:.ii:.iiii: ;
6a.-r=/(r),re -R.(DynRqis 3pocrae,sl{uro ir € ( -; 2l i [0; 3].(DyHkrrir craAae,Eri!{or€ [ 2;0]i[3j +*).
dlyExrrifl l(x)41, drylrl{qis
r l" tro. lt,t.69. l) /(r, J,; I 1 Dllt l0; lJ (l; -);r I L.r-U: '-U:112) flx)=-+-i x'! 1 + O, x + :tl; r' + 3x + 2 + 0i x + li:t+ 2;a' I a'+3r+Z
,(/)=( -; 2)L.J( 2; 1)U( 1; 1)L,(1;+-);
3) ft"t= '!:' 2.1t -r-2
4t It4 2"*1=\15-7r- 2x l-3=o'' r-3 lttttx zt o: 2a'1 7x-15<o:
: !x=o:
4) s=9 r'z
::iai;:::!iii;!lii: AIrEEPA Mep3nck A. r. ra iH. AKaAeMi.rHht piBeHh i:i::: 243
-1
J,-0,lo r>oIx.o.
[.r x>0:
liliE:t;
:l
ii
ii i:ri:.i!i!!:
]' " - o,tre.r. - I1.5:3r J13:51.
2x' 7x 15=O; D= 49 + l2O=169i1+lA 7-15 3 --.rr=-=5:
st ft'l=uE,4 *,1; s,. * 7:
xz4.l2r 8>0.I llx<1.lr' 8r+720: l-_,
tL^ _
1--ar' 8x+7=0:1" "
i,=1.Ofliie,r€ [7i +-).
fr>0.6) /rr) Jl,r -ir; lrl - r '0: I ^ a6o
lx .r " u
Orn|e,r€ ( -; o)Uf0i+-)=( -; +-)=R.
l.r . o,
["<o
70.rr /rrr J*-r. 3 1r'l'0 1' '' o.*., !' I ti4) )t4: +-)a Lr 4,0: l.rFa.
2t [tr\ '- '-, 1' ' ", ., {f ,];x'-5x-4 lx +5x A' ..x, tt
lr, 5.x 4=oiD. 25 16 .9: r.. - trt3 -,, ". - ';t -ot.
O\xe, D(f) - I-2: -1)u( 1; +-).
4) i(jr) = l'l 3. o6,racrE 3Fa.reHb
OysRqiI t(jr) = I 3; +*).
5t lt = J-x : Etr)= \oj.6) l(,) - !t-1 +!5-; t(i.]) = {o}.7) f(r) = x, + 4x + 8t f(r') = (r + 2t, + 4.KoopArEarr BepurEq t" = -2, g. = 4, iBirrcr' rapa6orr cnpsMoDaHi Bropy, roMyE(a) = l4t +*\.8) /(t) = -r': - 2r + 5. ItoopArEarx Beprxtrnu napa6onqi
l a= (-1)'-2 r'l).5 lr2 5 6." 2.1nBir(sr napa6ons cnp.nMoBaEi BHr.r3, roMy t(jr) = t -; 6l-
72. 7) f(x) = 4 Jrc; t(') = (--; al. 2) f(t) = t, - 6r; fG.) = A:t 6).
,"= 9=s,v.=-g,r(t=t s; +*).
3r [-x : 0'3) f{jr) =./_-t ffi, ]+ ,,,0;rc E ( 2t 01. orxie, ,(D = ( 2; 01.
ir<0,(2 r)(2 + r) > 0;
l'< o'
) z.'.2;
2 16 x-o' t/6'
d) /r.r, = \6 , , ,.' u-, l:"]r;";., ;,;1.,- r, ]l; :l;
r. € { -i 0) u (0i 6). or}I€, D(D = ( *; 0) !r (0; 6).
71.1) f(i=G+2.Oyr.Errii I](,) = [2;
O6nac1.L snaqeIIb
73. U DrlJ=R, Hpivr.=-2, r=3. HanprrKna,a: /t*t ,--..l-- -.(,r + z)(,r 3)
2) D(fl = ( q 31. Hanprliraa: l@) = Js - x.
3t DUt=l-4:5r t5: --1. Hanp KnBn: Ittl J'*.4 .
4) DO = I ll.Harpunnaa: n, = V' -, - "-j-,
- r. "
74. t) D(f) ( *: IJ J ( 11 0) (0; 1,. Hanpr.aKna,q: /(x, (x + 1Xx 1)r
4 D(n = ( -;7). HaEprnnaa: ftrt = -!.J-,.?3t DUt=l2i5r J (5: tjr L {tjr '-). Hanpnx,ran: /(.y) l:
' -.{x c)tx b)
:iilil::ti;i::.:i::J A'TEEPA Mep3fle( A. r. ra irl. AKaAeMi,{Hnn piaenr lilj 245
3) l(,) = 6; t(,) = { 6}.
2) flx) = 7 x'|; E(r, = ( *i 71.
244 tii:: AJIIEEPA Mep3nrK A. f. ra iH. AKaaeMi.rHlan piBeHb ::i:::i::::::::i:::i::::j
2) TaK. 3) raR.75. 1) Hi.
lx+I.ekuox< 1.76. ftx) ', ^lr' l. sxuro .r : 1.
l) f( 2\= 2+1=-1,60( 2) sa,qoBonbsse vMoBv ir < 1;
l( 1)=( 1F-1=1 1=o,60( 1) ra.qoBonbEs€ yMo
3yn> 1;
/(0) = 0e 1= 1, 60 0 3aaoBonbnse yMoBy r > -1;f(2t = 2' 1=a 1 = 3, 6o 2 :a,qopoasn.a€ yMoBy x > -1.2) f(x\ = o, .a(qo ' = 1;
l(r) > 0, nKu{o, € (1; +*); l(r) < 0,sKqote( *; 1)L.,( 1;1).OvExrris i(jr) spocrae lra npoMirriKax ( *; 1), [0; +-).oylrr{qis l(r) cra,qa€ Ha npoMixrxy [-1; 0].
[r+6.rnuor< z,
77. tt ltx\ = 1r r x. sxuro - 2 1 "r < 2.
[2 -.r. FKU{o .{ > 2.
IpaoixoM OyEllqii Yr =, + 6 e rpsMa.
(Birllnr crpEMoBaHi eropy, 60 d = 1, 1 > 0, rpaoiIi repernHa€ Bicb Or y ro.tEax( 1; 0) i (2; 0), a Bic! Oy - y ro.rqi (0; -2).fpaoixoM Oy:rRrlii y3 = 2 r e npsLtd.l(r.) = 0, sltqo r = -6, t = -1, x = 2;/(r)>0,.sRrrrore ( 6; 1); flr) < 0, anrqo r' € ( -; 6)u( 1;2)u(2; +-).iDyHxuir rpo.lac r--: -2r i (l: 2|.
l,Dyr.{uir coarac Ha ,povi1lr"ax I 2: ;li (2t *).
[r:+2r.gxruo:<0.2') IGJ = I
lr.' - 2r.. eKuro r. > 0.
fpaon{oM OyH}iqiii y, = t2 + 2rc i g2 = )c2 2t e na-pa6onn, (Birllr' nxrx crpsMosaHi Bropy, 60 a > 0,a nepfinrnaua e iovxr (-1; -1) i (1; -1) siaroBiaEo.l{r) = 0, sKu{o r = -2, r = o, z = 2.l(;r) > 0, suro .r e (-*; -2) u (2; +-).l(r) < 0, flflrqo r € (-2; 0) u (0; 2).oyn(qis craaa€ l]a npoMirn(ax ( -; 11, (0; 11..Dysl(qis opocrae H npoMix$ax [ 1; 0], 11; +-).
l8I .rnax< 2.
78. ftxt = l2x' - a- qKlo- 2 s x =
2.
ls ^I .sr{4n>z.RR
f pdoirov OyHRrrifi u, -- i !r, - .rilpptx
6oJrrr, a rpAOi{oM OyH:1'\i\ y,= 2tr 4 e na-pa6ona s BepIIIrHoro ! ro.rqi (0i -4).
f(x) = o.,tr"DJo' = -2, k = 2.
i(r) > 0, n}lqo r € (-*; -2) u (2i +-).l(r) < 0, sllqo r e (-2i 2)...OyIIKrris l(r) spocrae Ha rpoMidiEax (--i -2)i [0: 2]. OyHXuin /(i.) .naqac Ha npoMi]{Kax[ 2; o] i (2; +-).
ro 1079, l) u=-:-:-,.r L [2:5|. O)HKuifl 1/:t'Bosa 3pocrae, roMy Ean6irbnre
qe y(2) = 5.
to 102) a = -, )c e lz; ol. oyurqra g = I lrenepepBlra, Ha npoMilR&y [2; 5] craaae,x.xaoMv sQ) =.5 qe Ean6irbrre BI{aqeIrHs, a y(5) = 2 qe IIaiMeIIllIe 3Ea.renHs.
AO-g= t'+61 7
1) r E [1; 2]. (DyHI(qis ! = r'+ 61 7 - EerepepBEa, Ha trpoMiri{fty [1; 2] spocra€,rpaoiKoM e rapa6ona B BepmrEoro B ro.rqi (3; 2), iBirnrr cnpsMoBaEi Bslrs, 60a=-1,-1 < 0. ToMy Hafi6inr,ure BEaqeHHn \e v(2\= 4+12 7=1,asafiuesme
qe y(1) = -1 + 6- 7 = -2,6(r.' = 3 He Hane,'irrb rpoMi,riEy [1;2].2), € t1; 41. IIboMy rpoMix{(y Eane}I{'arb il: = 3, roMy y(3) = 2 € Ilaii6inblnuM 3Ha-.{eEHnM OyHxrrii. IopiBHneMo 3HaqeHHn aG) = -2 i a@\ = 1. HanMeEtlle 3rra.reHHs
v\t) 2.
:::::il:iiltti::lt: A'TEEPA Mep3nsK A. f. ra iH. aKaaeMi,{Hnr piE,eF.b iitlti:. 247
n.
5) Hi, 60 roai a,'ls 6yar,-sno.o sHaqeHEs, icHy€ ABa pisssx sriaqel]Hs y, lro He
BiArroBiAa€ BnsFaqeHslo oyEnqii.ir ;:,iil:.i:.:.:{lr:.!alt:.1.1n1.:-':.i!]1i:.:{
l'ilt i.!i:.i-i:.ti:ii-l:.i!-ai:.:lt*:.i:llll
FenepepBEa, Ea rpoMfun&y [2; 5]
\e aG\ = -2, a HafiMel xe 3HaqeII-
IpaoirioM OyHKtIii U,= t" t - 2 € tapa5ona,11 r\ -r 1
r sepuuHoo B'ro.,u.i A\rt 24) (t" 2=1./tl'z t 1 I 1
= -l 1= - -2=-2-\-", \21 2 4 2 4
246 lii: AIrESPA.Mep3ncK A. r. ra iH. AkaaeMi,{Hrfi piEeHb ,iii:':,i;i:iitlil!
4) Tan.
3) n e [4; 5]. Ha qboruy npoMiJ(I(y senep€pBEa Oyrliqis cra.qa€, roMy y(4) = I € Han-6inr,mrM 3IIaceHHsM, a y(5) = 2 e safiMeslllr 60 x = 3 He EanealrrrLnpoMi'{llly [1; 4].
81-y=)t'+2, 81) , € [ 5; 2]. Ha rrBoMy rpoMixrRy oyrHrris EenepepBrra i cna.qae, a6cq{ca B€pIIIuIrH
Mpa6orq x, ; -l He Hajexnrb raHoMy npoMrlr{K). rov} Ul s, 25 l0 8=-7e Ean6inbme 3HaqeEHn, avC2\= 4- 4 8= 8 e llanMeEnle sEa.reHlrs.
2, xe [-5i 1]. A6cqrca Bepr x r napa6oJrlI n = 1llane]iillrb qr,oMy rpoMinc&y,{sirKu, trapa6onn crpsMoBaHi Bropy, loMy y( 1)= 1 2 - 8 = -g e HaiiMeHriesnaqeElrs OyErsrris. flopiB$seMo 3Ee.reHHs v( 5\ = 7 i y( 2) = 8. Han6inb e 3Ha-qelrHs
- 4e y(-5) = 7.3) r. 6 [0; 31. Ha qboMy rpoMir{rcy HenepepBEa ibyHnrriF spocrae, rs = 1 He Hane-
rnr{rL rrEoMy rpoMi:riliy, roMy y(0) = -8 e HaftMeErrnM sHaqesEsM, a y(3) = 7 € Han-6inErrr.rM sIta.reIIEsM.
A2.l) g = x, - ta - 21, + 25if t to 28t2b Oi
D - la - 2\' - 4 . 1 ..25 = a' - 4a + 4 - IOO = a.'z 4a 96.Ans roro, rqo6 Aaxa Orflrlliis Mana ABa Eyni, rpe6a, qo6 o? 40 96 > 0. Po3B'g}I{eMoqro EepiBnicr!: a' 4a 96 = 0:D=4-96=roo: o.=2--i!=n o^ 2 to
8.4'1 1
Or}r{e,.El{rqo a < -8 a6oa > 12, aalla ibynxqis y = t'+ (a 2'), + 25 Mae A3aEyni.
2, a = 2x' + 2(a - 6)x + a - 2i %c' 2(a 6\!+ a 2=o; (1)
2=g-Ay 2@ 2).o, tza t 36 2at4 ar t4aa 40.4
Dfllrqo:> 0, To piBHrEHr (1) Ma€ ABa Kop€Ei, a Cryrfl{qis y = zt'z 2(a 6\r+a 2-ABa Eyri. Po3B'ndieMo HepiBHic?b o? l4a + 40 > O) a' 14a + 40 = O;
9-qs oo 9, o, 7-3 tot a, 7-? -4. =\-,--:>6-'4'1 '
tlpr o € ( -; 4) u (10; +-) AaEa Oynnqiot ru" auu rrv,"i. 10 t
A3. 1, a = r' + (a - 1rr. + 1 - a - a'! (*li
''z+(a 1)r+1-a-a'=O (1).IIe piBssnHr Mae ne 6inblne oAIIoro llopeEfl, nKqo, < 0, a AaHe piBffrflra (*) Ma€
He 6in6tne oAnoro Hy,rs.D=(a t\' 4.1.(1 a - a'\ = a' - 2a + 1 - 4 + 4a + 4a'z = 6az + 2a 3.PocB'&rceMo rlepiBtricr:. \at + 2a 3 < 0.
50 | 2a 3 0; - l-5 (-3J=l-15=16;4
", =-]4=!=o.s. " =-l:!= r.-1
flpr a € [-1; 0,6] aalle &ys&qis (*) Ma€ se 6irL e oaHoro Hynr.
2) u -1 x" -sax -9a -8a (*J:'4
- 1 x' + sax - 9a' - 8a = 0 (1).4
Ue piBEssEs Ma€ ne 6irErre oalroro ftopeHs,.aftrqo, s 0, a aaHe piBEsHEs (*) Mae
HF 6irbure oruol.o Ryna.
248 til: AIrEEPA Mep3rqKA. r. ra iH. AKaaeMiqHrf piaenr i;ii:liiii:i:ilijl:l
/ 1\
D 25a' 4 l +l I go' -aa)=25a -ga -8a =16a'1-8a;\ 4'D < 0; L6a'z - ia < O;84(2o - 1) < 0i + , +nDn a € [0; 0,5] naHa Oyll&qi.s (*) Ma€ He 6inbl]re
-3----;:------;a4. a = L, h> o, x € (--; o) u (o; +-).
Hexafi r, € (--; 0) i r, E (-*; 0), x, > r, (lr,l < :c1), roai:
!. !. o'*.:...^' >0.60k 0. rt-x2 tr.a xr2 o {lr.
Heiaii jrt € (0; +€) i r, € (0i +-), ,, > r| roAi:h -t =h(t" \)>o,6('h>0,)r2 x2>oixf2>o (2).
xtt"
3 yMoBr (1) ," > r", ^rt L, L.rt xt
B y,l,oBtt (2) a" > r", un" L , L .
orrrre, Ans t, > ,r MaeMo V, < y1, ro6ro C = L op, * > 0 cnsqa€ Ha npoMix{Kax(,-; 0) i (o; +-).
,=!. u. o.r.c r-@:o)u{o:-a)
HexaEt,€ ( 6; 0)it,€(-;0),r,,r,(t,<n,),roAi k -k =k(" '')<O,
60k<O,x, ,r>Oir1r,>0. MaeMo: x, < xz i r(r,) < y{x,). ro6ro ,=L, U.OBpocra€ lra rpoMi'Iiriy ( -; 0).
Hexan ', € (0; +-) i ', e (0; +-), x, > ,"""^, +-+=u':,;''t <0,60*<0,haz rt> O i rJ,> O. Ma€Mo: rr < r.? i 9(.tr) < y(x,), ro6ro y =:, k.0 spocra€
Ha rpoMinRy (0; +-).
85. y = i(r) - ctra,qEa Oylrxqis.1) a = sflr). IJexan \i x2ha.re:!l,aat D(g) i x2> tr ron\1f(r,) - gf(t)= 8(flt,)-
^x,D
<o,60 f(12) < f(t), ockuttLn f(t) cnaAsa abyEnqis. Or*e, y = 8l(x) - cransa OyEx-qi.n (3/(r,) < }f(x)
'rp*r x,> xr x,e D(vli.\e D(a)r.
12t y=;ftrl. AEanori.{Ei Mipr{yBaIIH.n ao3Bonsrorb 3po6rrrr BucI{oBoI{, rqo
1
u .tt(n .Eansa OyHqqin, ocki,rERr ra yMoBoo I . n"r) - cnaaHa OyHKqifl.
3) y = -l(jr). Hexert tr i ,, HaneBarb D(A) i t,> xrrIopiBHs€Mo y(1,) i y(r,\t a@ ) - ek ) = - f(r,\ - (- f@ )) = - flr,) + f(r ) =, ) flr,) > o.Eo y = l(r) - cnaAHa, An" tr< tc2, f@,')> f@"'), s(n\o \e D(A), r,e D(y)r,orrKe, y(x,) > y(x,) rp h> xr'roMy u=-f(r) - spocralo.ra Oyl{Itlri.r.
da. y = 11/1 3pocraroqa OyIIKqis.1
l) y ,ftrr. Hexaiir.. D\gl.x,- DIUILx,.xr3a yMoBoro y = i(r) Bpocraroira ibyEnqin, ro6ro /(r,) > l(r,). (1)
:i{::!i:a.:1i::.iti{a AITEEPA Mep3reK A. r. ra iH. AKaAeMiqHrat piBeHb l:;..i 249
0,6
lllPo3r,rsHeMo el'3iilrn ;ltxtt - rlt r,t ztftxtt-ltx rr' 0,603yMoBu (1)
fl',) > fG).IIe ossa.ra€, qo y(',) < y(',\ lplj r, < t,t_lotrfo g 2llrt - rpo.rarcqa Qytlr(urs.
2ty zltxt.Hpxanrt- DtAt, x2c DIC)r r. x.3a yMoBoro, = l(') - 3pocraroqa (DyEEqi.', ro6ro fl',) > f(Jrr) (1).Ilopiesr€Mo ptusxqrc aQ.,, ve) s EyneM nns OyElclrii y = -21(t).MaeMo: e(',) a@,\ = 2f(r) ( 2f(,,tt = 2^!j) + zflx,\ = 2(f(':,) f(x1)) > o.
or,fte, y(,,) > aG) i xt < x,,'t e D(!), n' € D(y)' m6ro v = -21(') e ctraaEoro
OyEliqi€Io.
87.s=Inr+ 6-20rt s = x(zm 20) + 6 (*).,4n.a roro, qo6 dpyHnqi.a (') 6yna spocraloqon, noBIrHIra BtKoEyBarlrcn BIrMora
7n 20>O.tn>zO: n>29. HaiiMesne qine 3lia'reslt.': n'3. IIpan=37
OyHllqi.n, = Imt + 6 - 20, € spocraloqorc'
88.!=h' 2k + 3 + 6') A = x(h + 6, - 2k + 3 (*).
Ann roro, qo6 {byHriai! (*) 6yna cna{Horo, roBuEHa Birl{oHyBar'ics BlrMora k + 6 < 0;* < 6. Or;ne, npl':&€ (--; 6)OylrKqifly=kt 2&+ 3 +6recnaaHolo
= *= Z oy',.qin y = 3,'z b' + 1
trapa6o.Ilr EarpnMneEi Bropy.
se" r; n';1={:35=o j[l*rt= . 12x + 48 12tx + 4\ 122) Ilx)=-=-=-,.ir' + 4.x jr(r + 4)
.f,ltrqo r r 4i.r.*0;D(' = ( -; 4) \.r ( 4; o) u (0; +*)-Ipa&iftoM € rinep6ona, (sir&Er srioi1re Micrfr6 roqiiy ( 4; 3).I
t' 3t-+4l llrl=r+1
(.{+1Xx-4)r +1
r+ 1.D(f)=( -; 1)\,( 1;+-).rpaoikoM € npsMa y = r. 4, nlta FeMicrnrE ro.rl(r' ( r; 5).
5) u (5; +*).
.-r'*-r--.111i:.:':i1:j-{l:!ii:-:ii$i
iln:::::.fl|
l:::::::].:ft|e rp.t
v5)
89.V=3x' bt+t,x e [3; +*). SHanAeMo t.3pocrae ra rpoMiniliy [t"; +-), 60 (BirKn
ro*u 4<a. asra.'6Or]{(e, rpr D e ( -; 181OynKIIis y = 3ir' D, + 1 rpocrs€ sa npoMitnlly [3; +-).
bb
IpaoixoM OyHKqii o==Ma, sl{a reperr.rEa€ Bicb Or(-5; 0), a Bicb Oy y ro.rqi (0inpoxon y ro.rqi (5; 10).
3) l(x) = ::- = 1,
flr'nJox+4,r*-4.fpaoilioM dpysnqil € npsMa, nlia na-panenbHa oci Or i He Micrr]rb roqoll( 4; 1) i (4; 1).D(f) = ( -i 4) \r ( 4i 4) u (4t +*).
90.a=tu-4x', a€[ 1; +-). SEaiAeMo ' 2 (-4\ 8(DyExrris y = b]. 4x'zctra,qa€ Ea rpoMit*ry [t"; +-), 60 lBirr$rr napa6onE sarp.sM-
neHi uEE3. ToMv l. -r. a = g."8
Or*{p, trpr b € (-*; 8l OyHRqin y = rir 4jr'?cna,qae Ha npoMi}Itftv [-1; +*).
91.y=-0.6r lSir c (*).Brxoaqqr s roro, rqo a = 0,6 < 0, ro <Birnltt rapa6orlr HarptMneEi Blrus i Hai-
6in6-e ruaqeHan O) Hxuin r+) aocrrd. npu .r. 3 - . + - ^'" ,r.2a 2 ( 0,6\ 0,6
3a yMoDoro BHaqeEns OyIIXqii (*) B rrin roqlii AopiBErc€ 2, roMy 2 = 0,6r' + 18ir + c'a6o 2 = -0,6 . 225 + 18 15+c;c= 133.
92.s=2r' 12r'+c(*).IpaOiRoM Oyn(qii (*) e napa6o,la, iBirnl{' sKoi EatrpsMnelri Bropv, roMv EaiiMeH-
-12nre rHaqe{Ht ut O) HHujfl np{iva. B ro,rui ," 2 2
- "
3a yMoBoro EanMernne sEaqeEEn OyElrqil (*) aopiBEroe ( 3),roMy-3=2.9 12 3+c;c= 3 18+36=15.
25o l* ATTEEPA MeFTKa. r. ra iH, AKaaeMi.{H}ri piBeHb Lil;iili:i:;::::i
2x'1+5x+2 a'z+4xbl ll.r) = -_--=-
-
=
2(x + 2')(x + O,5l _ x(r + 4\x+2
fiErr{or*0,r* 2;2x, + 5x + 2 = Oi D = 25 - 16 = 9:
,="3-2.,=!a3=6.5,'4',4D(f, = ( *t 2) u ( 2; 0) u (0; +*).fpaoiftoM Aarioi Oystr4ii € ripsMa y = r 3,flria Ee MicrlrrB ro.rok ( 2; 5) i (0; 3).
D(f) = ( *;
D(f) = ( -i 4)\r( 4i
::al:i:i:::::{::::* ATTEEPA Mep3rcKA. r. ra iH. AKaaeMi,{Hr4n piBeHb ::::i: 251
'l
6) l{r)=-
D(l) = ( -; 2) u (2; +*).IpaoixoM .aaHoi OyExqii e rapa6ona y = .t: + 2r. + :1,
sepuuHa snoi 3HaxoAr.rrbcrr B roqqi (-l; 3), a (Bir-(r' rranpsM,'reni Bropy. Ilapa6o,la r{e Micrrrrb ro.rlln(2; t2).
95- 1r f(jrr =,;. i € t-2r +ar.
Hexa; r, i x, Eanexarb rpoMix{fty (-2; +-),,!.. > r..t\x) It,.) 4 4 A:L:]-jyL 2t 4t)t 2-x 2t-
.t .2 x..Z |x, . 2\x._2t lxt_2|)r A -4(x. r.t
rr, 2rr 2it0 60'r -r', 0 r'' 2 0 r'-2 0'
or,lte, l(.rr) > fo) p4 i ', Hanex(ar! npoMixKy ( 2; --), ro6roIl,*r= ,,, c .rr3nHorc qbvjrKui.'o rra asHoMy npoMi,+(Ky.
2) fG)=-r. 8'+ 10, i€ (--; al. Hexan _rr -.r,, h,l , k,i r.,, € (_@; .11.r - I --:
41. Ilxtt fix t. -ni S.r ' t0 - { x- 6,r, tO, -- .,', ,.8r.,
+.r0+.ri + 8Jr- - ro= 'i:xi * e1"" *,y = 1',. -,,1(r, + r, + 8) > 0,rooro /tr,) ltr,t.Orxe, /(r) = r, - 8r + 10 - craAHa OyH&qir, F&u{o r € (_-; 4).
gz. f(x)=G. ,(D = t0; +-)- Hexan xt e Dlf\, r" e DU) i r: , x,, roaitG,) - fl') = .,!\ - !'t < 0. MaeMo /(.r,) < /(r,).Orxe, l(;r) = yG Bpocrae, snuro, € [0; +-).
98. r)9=f(r), r€ R.3a yMo3oro y = l(r) - 3pocrarcqa OyHI{qis, f(r) > O Epu r e re. BBiacv npu ,, > ,,Ma€Mo l(r,) > l{r,), ae r, € R i .x, € .q. gEanaeMo l,(r,) f(;r") i noptnraevo": uy-neM..f{ir,} - llr,) = rfl}tr - ft.xz[tf(rt + fljr")) < 0, roaro f(r,)-< /:(,,), rovyy = f.(!) - 3pocrRe Ha MHolRxHi R.-t,, , = lrrr,
.r c R. OcKirlxx fixl .O. A |txl Jpocrao,ra SyHKuir.\o f(x,) > f(r), sxu{o rj € .R, 12e R, ,-2> rct.IIopiBHr€Mo 3 HyneM pi3xHqro:
I 1 I\x,)-l\x.) ^ , 1
tr,,t i,,t=-i',tr'. <u roolo v /(t "n*u'HaMHoxHHiRt) s=.rti@, r€ R. ocIltnLRE f(t) > oi s = l(.r) - spocraroqa OyHkqin, aot(:(tl > Ilxtl npn .r, - r| Ae rr e R, r, e R. IlopirnseMo e ry.nelr pta"s,r-,,,!lr'.r .,ln'"t. o. 1o6.to u - ,,f;Gr .po"'u, Ha MHoxrrHj n.
99. 1) Oclcinllcu V = f(x) Ha MHoxnEi rR € rpocraroqorc ii npr qLoMy/(:r) < 0. ro npr ). r, Lrj € R) flr,l < l(jrr). AaEo rbyHxrrirc, = f(,).-BHaiiAeMo:l'txtt f'lx,J = (fG t\ ftx,l\ftr\t + l(',)) > 0, ro6ro /:(rr) > f(rr,) trpn ,r < ,,.01)t(e. y = /itrt ue cnalHa OyHnuir.
I2l g = lD ).
,r € R. BiAoMo, rqo /rnl < 0, OysRr{ifl V = l(.r) 3pocraloqa {DyHx-qis Ha Mllo,rlulri R, ro6ro anr ,rr € R i jr, > .!, BlrioHy€rLcs piBHicrb /(x,) > l(-r,).nopiBHrr\o J lrynFM pi.rn"u,o, -r .. I llt') 1",' -o-,no,n J ,-1Ir.\ Iktl /{jr,l/tx.r - ltx.t l\.t,t
lx 2\r! + 2x + 4t' .-=r-+zx+4.t-2
s4-tr,r,r= r +4n+4_I1 !=r +2 r - l
_ (jr +-2)i (' - 1X' + 1)
t+2 ir 1
x+2-(x+ 1)=n+2 r. 1=1,
D( =( *; 2)u( 2j 1) u (1; +-).fpaoixoM aaHoi $yEklrii e npaMa y = 1,gl{a He Micrnr}, ro.rox (-2j 1) i (1; 1).
2r: - rt r:tz - rt2t I(I)=-==!2-')=2r- r',
D(n = ( *t 0) v (0; +-).fpaibiEoM aaEoi rDyHXrrii e napa6onaV = x2 + he, BeprxuHoro rrcoi e ,ro'rKa
(1; 1), a *airxq" HanptM-,lesi BH 3,60a = -l < 0. lpaoili se Micrtrr! To.rKr(0;0).
6ir 18 6lx - 31 63l u=
-=
= r+U." x'3r x(x 3) x
' * 3.
'(' = (-*; 0) u (0; 3) u (3; +*).
lpaoinoM Aanoi iby'rKqii e .inep6o-,ra, {uirirr' flRoi He Micr.srb ro.rKu(3.2\.
.. -r' + 4r: 5 -(irl 1)(,r': r 5).*' 4'= "rr
= t* 1x*+t, =
=12+5,r.*-1,x+I.D(a) = \ *: -1) u (-1; l) u (1i +*).fpaoil.oM AaHoi dlyExqii € napa6ona,B€prxxHoro sKoi € roqKa (0; 5), iBirK,"tranpsMneEi Bropy, 60 a = 1 > 0. rpaoiKlre Micrurb ro'roK (-1; 6) i (1; 6).
l
I
or*e, anr x. < jr. Ma€rro I r I-.*' " fijr,t lr,)100.y = l(r.) + s(:tl, r e M.
OcRirEKu Oyrl(qii l(r) i c(,.) - apocra,o.' ua MEox,rHi ,,u, ro an, 6ya6-flrnx ,. E M3a yMoB! x" > r,, BrxoHyerbcs lnMora ir.r > lxj ), g{jr-) gtj,l. nopiBHgeMo 3 HyreM
;:;::-:*i::.::t:::i:;: A,lTEEPA Mep3lek A. f. .ra iH. AKaAeMieHri piBeHb ::i::t 253
1roMy y=- - qe cnaA{a OyuftrriE.
252 :::::: AIrEEPA Mep3rsK A. f. ra iH, AxaAeMi,{Hnn pigerr i:i::.:li:$iii:i:i:::i
pi3Exqlo: a(j.,) s(x,) = /(',) r c(r',) flr,j,) - c(j.,) = (flr'') ('x)) + (s('r) c(jr:)<0',ou,olr,,r ttjr r. or)v".ir " 'rr't v''r i t' x' tt i U ovv'l'v 'ui', /rr) atr) ,rjo' rr, '' Yro rn tZ
II c ttocitti"
",*.'.'. d,vsxqi; /(n) i e(x) 3poc"'nr. F' MHoxnHi M flKUro t' > i''' ro
ftr | > ftx t i El:r^t ' llx.) AoAaloTti ro'rnelrHo ocratrHi tsepiBrrocri' oaepxvcMo
ii':i r J,'1, ii',r rt' , or*{e' cvMa rbv''lqin l(.t) i s(r') e 3pocraloqoto ovrx'ui, ro rra 'rloxlrri V
1Ol. Hj. Hanprr{,14r. atsuro 'i'}rrK t\ st't 2! I!t -! -p''': "'" l" ]ll'' '
[0; +-), ro-ri vfiuris v(j.) = ft') - e(ir) = r] 2jrr = r'tcniaHoroQvH1{ur€rolrirMFo
x'rtsi [0; +-).
1o2.Hexan.i.r € M i r., e NI, x,> x\, roai l{r') -: l(jr,)' c('') < s(:'r)' 5() d'jvHkuii' -
g ili"i i y = ct,l ciaa}Ii na;Ilo,1!trrli 'vr' ea vMoaoio 1ir; -' o' eG) < 0 no8eac
i'., ''.,. ,f,u""uj" y = /(') s(') e spocraroqoF Ha MEo)litrHi M' Po3r']IflEcl1o pr3E'
,,- ,r, r'l ,r""r= tr.,) c(r,) l(j.,) s(.t,) .:0, ro6ro v(x,) '' l/('r) or'{e' r, > r,
:r-,;; ,,i r.'."vri r''' s{'' rpo" rrovoumter{u 'oH'Ho\r'Hr '1I
103. Hanpntraa: OvHRqin ir(jr) = xtr(r' 2) lle € 3poc
Ilcxari /(r) = '': i s(r) = x 2 spocraloqi OvE1rqii
'{aMH(,itrHi[0; r*), a-re q]vHRiris,(:n) =
j"\! 2)-rt 2tHP. 3pocrdn,orrl ", Mho)H/ii l0: -l'
Ill.nDU{ir{{tsvI0; - 14J""' iai'(rlc nad' aH1 lDo-_3
Mirl{k\,Iai]F)3pocta€
lO4. cyv" nBox qr'.c r aopiBF o' 8.HF\bnrcpurei rn-oo / rD)rc ". '
1) Poamsserro rlvrlnqirc v= a(8 a), s=80 a rprtbiRoM ' nar'rbor'r' ?Rr1r"-8
'koi HanDq{,lPHr ^ ' l ()610 ' ' 32 16 ' 16 uP H'nb rr'' c
r a,reH.rfl,IyHtsuii !/ at9 dt tf{I 'o n'pde "/'1o '1 ii lpvrP 'H'no l ro noojror
qlrx qrcen € Han6inEurM, r\e 'rtrcro I6-
2) Po3r,lflEeMo drvlrrirrilo v = a: + (8 - a)i, v = a'+64 76a+a'1=2A' 16.,+64- fpa16
tlilioM qi€i 4 vtsllqi; e napa6ora, (!ir(u"l{oi EarpEMjlesi Bropv' a x' = : = 4'
y,=2 16-16 4+64= 32+64=32' qlrc'{o32 e HaiiMeH Irlt 3HaqeHIt'M cvMl'
riBaApariB 3aaallnx qIrcer.
1O5. P --. 200 \' Bztci ABt 20o AD AB 100. h'x"t AD :(' rcn
,r,a = IOO ,. 'S,,,",,='(10o .I)=100:r a! Po3tnflEeMoOvH-
nqiro ri = 100r Il rpaoi(oM e rapa6o'1a' (Bir(s' Enoi Ea
100npFv rF dH/J. * '1" ro u 50nu 2500 2i00 A
BnpaBu.qng noBropeHHg
107. 1)(7):.7s =7t.7'=7.= h.21
36-'6 6-6'0,,c ti. 36:
", ur:.:;,"
=(25')' 5' "1 " i " r " 5 r25;
2) 0: (-3,7)3;5)( r7f= 176;
3)(-12)'<( 6)a;6) (-34)r :- ( -39f.
qt'c'Io 2500 € naii6i'1!ue 3IIaqerIIr€ OvH(qii v = 100ir - ir:' roMv Eaii6i'1!Il]a ltroultr
Aiffrllrlr aopiBEllr€ 2500 M'.
106. AaHo f(x) = 1:, r. e R.
Hexan r., € (--; 01, x, e t0: +-)' roai r,:-'rc' ftqo ,x'l ': r" rogi ""'i
O)'
sErqo lr.;l > tr,l, ro,ri :ri < 'i (2) vMobf (1r i {2r^arctt -:lllal:T Jro6rr L!''
' oBoK. Llu /i') r H' ' H Jpo'aao 'oro i " 'JHo'' Ir''
254 i:i:: AIfEEPA Mep3flcK A. f. ra iH. AKaaeMi'{H n pieenu :i:i:i:iijl::ii:i:::::i
41 0. 125 32i rro.srJl 12 r 0.; 2'o 0.5 .2 l .: 0.b.0,5 0,5 ' 0,5 2
1o8. 1) 18a3 = tt I l' = 18 + =;;t,t"
2) r18a):= 18 : =( 3)r=9i\ \ ail3) 16 + bf= 16 + ( 2f= 76+ 4=20; 4) (16 + b)l=(16 2)'=141 =196.
109.3ayMoBoFa > 0, b> 0, ro/Ii ai + b3 (a'b + ub') = u3 a'b+ b3 -a.b'.== a!(a b\ + b\b - a)= a,(a _ b) - b,(a, b\=(a- bxa, - br== (a b)la b)la t b) = (a b)'(a t b).Bnpa3 (o ,)r(o+t) >0, ocd,'r!l{na'0, b > 0,,tor{y ar + b'>a'b+ ab' npas'r6!a epiBrriclr,.
l10. 1) ( 5,8)': -- 0i4) -8$ < (-8)3;
2. napHi i HenapHi OyHKqii
1 1 1. 1) y = l(ir) e rapHoro OyHriui€rc, ro6ro fl- jl:) = i(r).fll{qo f(7) = 16, ro i l( 7) = 16.2) , = l(r) e EenapHoro OyHlirii€ro, ro6ro lC x) = -l(r).flnrqo /(7) = -16, ro fl-I) = 16.
112. y = l(r') € rapEoir, ro6ro /( r)=flr),ronii1) f(2') - f(-2\ = f(2\ l(2) = 0, roMy piBFicrB f(2) f( 2) = 1 Henpar nbHa.2) piBHicrr, l(5) l( 5) = 2 llerpaBr.,rblIa, 3tsa.Iel{Fn l(5) = l(-5), 6i) rDyHX4nnapHr. ro!) ro6l-ox ' 'rrri " a"arr e.
a | /l l) /' ' ' ,. ,,*, ,:,-:"." /r | | 0 !. no.'-r. 6Ha./r Ir /(l) l\ t)
I 13. y = l(Jr) € naplloro dryH'{[iep, ro6ro l( x) = l('I). PiBFicr! j]ll = 1 u,,*o,,y.'*o,/( 1)
5()/( 1)=t(1),rllqo t€Dl i1er(f)il( 1) * 0 i /(r) I 0. Anc, rnrqo 1e,(/)r I s ,U). ro rhs r* " ' p'""'""' /rl) I F Rr{oHy.rq, r.t( 1)
114. y = /(.') € senapEolo (DyER4i€ro, rosro l( r) = fir).1) l(1) r l(-1) = l(1) l(1) = 0, roMy piBHicrB l(1) 1 /( 1) = 1 EenpaBxnBEa.
z, I'.-:' !:' r. ','uro ^
2) . 0 i /(2, , 0,ovy p'BH'*" /1 ]) o HF,.pht(2) /c) t(2)
I 15. 1) J. E [ 9; S]. Mnor{rEa cr}ierptr'{Ha BiAHocno llynr, roAi rbyHlrrtis y = r': e rapsoro, 60 a,tE Ro}]txoro r, icnye npormre)I{lre rioMy ( r,) i (x,): = ( r )1, robro flx) = fl jr).
2) .r G ( -; 3) L, (3; +-). A,r'r xor{Horo € ( -i 3) BaBJ{qr Mo}r{
Ea Bsanrfi liAnoBiAHe nporxrrexHe qr'rcro ( jr,). MHor{xEi (3i ]-),i (r,)'!= ( r.,)':, ao6ao
^r) = fl r), roMy, =j.'j- rapHa {byH(rris.
i:::::::::i::itiii:: AnTEEPA MepsncK A. r. ra iH. AKaaeMi..rHun piBeHb ii:;t 255
3)x€[6; 6). 'DvHKrris, = "
He Mo'{ce 6vrT napEoro' 6c annr= -6 IIe Mo'i{Ha
BEaiirr{ nporlrne)+rHe qrcrro 6, an}ile 6 4 [-6; 6).
a) :r e 1 -; 41. ovHKqifl v = a'?Ire Mo]l{e 6vru flapHoro' 6(] Ar's .I < -4 se Molt{Ea
snafiru rporlrner+{Iri 3Ea'reEHs. MHo}trUIIa ( -; 4l ae € crMerps.I}ioo
116. 1) f(f,) = 171. fpaon{oM QvHriqii € rpsMa' sHa rapanenlEa oci or i-rpo](oa'rrL
'"f"" i"""v t,; lfil, 'o'v lt ,l = tzr. orxte' l(:,:) = fl-')' roMv l(x) = 171 rap
il it,l= s,^,te R:f( x\= 5 ( ')1 = 5'{- l(r) or,re, l('J=-5'1 e napHol(,
OyHlrrrielo Ha crMerpnqnil; MHoniEHi (-*; +-) eiaHocEo roqnr O'
i -L l-r.l l /:_l r' I3r /rrr ''--i. ,,',= i ,i -; : =rrjr) or'j{e /(r) r'-a 'ndpts.ro
rlyerqierc'ira ctruerps.rHii MI'oxsIIi ( *i -21o (-2i 2) u (2; +-)'
q f@\= \E- + Ja+ x, o6racr6 BIr3Ha'reHHs Ovrrrrlrii [ 4; 4]'
i a= rZ;. uZ- = 'it'- ' *,tri = ttrl orxe' itrt = 'f+-i+''[+ r
" "tp"". OV""oi". "a crMerpxqsili MnoninEi [-4; 4] BiasocHo roq(lt 0'
it /rrr" --L- , o6nacrb BxJrro'{PHHs O!HKui-,: I l: ll:Jl-.r .,/x+1
t-Jt/{ ',r ,i,;-F=-r,r.* ,r*l) "[*-'r'*Or*{e, cpyllxrria f\)d = -: t:=- e naprolo Ea c'MerpnqEiii Msoxxrli [-1i t I
'l-t \x' I
uiaEocEo roqr$r 0.
6r nrr . rx , 2tx 4 lr 2,l' t 4, o6narrb Brs"aqeHHs Ovlt(uii: { -: -):7-,, ,-t zr-, 4 -l x-2) r 4! -lr 2t) -4 t tx 2tx a - ftx\'
tehoto.,qo a = d. roM) x-4t x 4"! 4tx'4tdrxe, l(r) e napriolo iDvllKlrito sa clrMerp{'rHifi MHo'lrclxi ( -; +-) BiasocHo roc'
xr 0.
117. 1) l(:r) = r", n € N, n - napse, jr € R.
fl-ir) = (-r)" jr' - l('), l(') e naptlolo OvEnqi€Io sa cl'Merpsqsifi Mllo]*inHi (-*i +*)BiAEocHo rorKr,l 0.
2tflx)= 3x"+ ir 1,r€R
^x).4lxf - x-r 3r.? 'r-l'lrl'
b;;'., ;" 4 = i ,- o'*", i(.r) e napsorc ibvgllqieto Ea c'IMetpn'rgiii M:roaaqi
(--i +-) BiaEocEo rovtiu 0.
el ifrt =.,,f,' 3"+5*G'*s"*5' xe R(x' 3r+ 5 > 0 i r2 + 3' + 5 > 0 npJ'
jr € R).
fCtl' =,F*l\ z, t n. v[,)' * s(') * 5 = !t' . 3t. 5 + uE - z' + s = fO'Oi*", ftrl - Eapna OvHnqis Ha crMerp"q{iii Muo'{lisi (-*; +*) BianocEo roq
Irfl 0.
a) l(') = \6 - '' r n-,,;1 = uG 1-'Y = 1G:? = 1,;.or,iie, l(jr) - napHa Syt{Ktlis rla c"MerprqEin MHoJ'iI'Ei (-*; - '6)"
(.'6; * *)'
5a-2+l;x+2l5r /ur -:' ;= 1
j. x I -1. x t Ll
. 5r xr-2'r15 Ixr-2- si 2 F-5jr-2r =5':]:j! l. h,ln-xl - i),.1 - x,_1 r r
Or,{e, l(') rapHa ibysliqis Ha c MerpE IHin Mso]*iEsi (--; -1) !) (1; +-)
256 i:i:i: runrgspa Mep3ncK A. f. ra iH' AKaaeMi'{H}ri piBeHb ::::::: :::::::: :::: :::::::
or tur --L-- - l - I .=- 1
{3r ll' t3"r-lt l-3.r Ir ( 3r' Ir' .(3.r-t) -(3x lj-
= 1- * --L- = r,,,.(3x + 1)' (3x 1)'
Orxe, flr) - napHa Oyrnqis sa Mso,(r{Hi
clMerpuvHiri BiAHocno roqKr.r 0.
118. 1) l(r) = 4r:i, o6nacrE BrssaqesEs: xe Rif(-rc\-4.( r\1 = 4x1 = -f(:().Or,{e, l(r) € Henapsolir QyHI{qi€Io Ea Mso'{aHi (-€; +@), crMerpuqHiri BiaHocHo
2) fla)=2x 3r3,re Rif( r)=2.(-r)-3 ( r)E = 2r.+3f = (2t - 3x5)= -f(xj.Orxe, flr) e nelapHorc ibysliqi€Io Ha Mnonirlri ( *; +-), crMerpurrHiri liAHocr]oro,llrr 0.3J fe) = xx), r. € nj l( r) = (-')l-'l = rr.l = l(ir).Orr{e, flr) e HalrapBolo Oyllnrri€Io l1a MHor{rlri ( @; +€), cEMerprr{Hiii BlAHocHo
4l f(') = (5 r.)5 (5 +')' = (5 - ('))" (5 + (,))' = (5 + r)5 - (5 - x)5 == ((5 r)' (5 + r)'?) = -l(r).Or,rc, l(t) € HenapHoro OyH(rdeb Ha MHor{trEi ( @; +@), cxMerprqlliii BirirocEo
5) sQO = \E a ,tT-n,ct-i=J, e,) J,+t xt=rZ;-rZ:; =,( ,E*r*"E-)= it,l.Orr{e, g(}) € EenapHoro OyEEaiero Ha MHolrrsi [ 2; 2], ctlMerpn.rfliri siAfiocEo
- 3x+2 31 2bl g(r)=-+-.x' x+1 x'+r+13.x t2 3, 2 3"r-2 3x12/( r',' x'ztttl t "r'l .r'-x t-l l'?x 1
( z* z 3r+2 \= lrL+1+,-.4r]=-/rjr)g(J.) a seflapsoro OyFriqiero Ha MHonirHi ( -; +-), crMerprqEin RiAriocHo ro.rnr 0.
re. rr /(-Yr ' 1.t,,,
' j= ,..1-t n',Ou{e, l(ir) c retrapEoro OyFnqi€rc lra MHorirHi ( -; 0) u (0; +-).2) ftx)=(r"+ x)(x' r,),xe R; f(-'\=l( r.f +( i'D(( j'), ( r.f) == ( :.3 xt(x1 jr') = ('. + rxrl - r') = -l(r.).Or}rra, flr) e l]enapEoe) OyFruri€rc Ha cnMerpuqHjn Mnollxsi ( *; +F) BiaHoc'ro
3) e(j')=r",r€ N, n llerapHe,.ir € -R; c( r)=( r)" = x.= f(r\.orxe, s(r) € HenapHoro oyHrirriero Ha cr.rMerpqqFi; MHo,nrHi (--; +-) Bi{rocflo
t,-"4) 8(r.)='" , .r , 0; g{ jr) ' , g('t.
Or,Ile, €i(r) € HenapEoro OyH(rri€ro Ha crMerpFHin MHo,{rEi (--; 0) u (0; +-).
;) c(i) r' .r - (-3: 3r;,/3 r J3+r
r rl4( ,l sljl.
i3 J 13 r (J3 r \3 \l Ji r ./3'x
:r;::iiliiiiiiir: AITEEPA Mep3reKA. f. ra iH. AKaAeMiqHr4i piBeHh ii::: 257
[--,-;)"1 l,l..,l;,.r,
: r.. i.-.--.-..-..::til].ai:L.:.!:
:i.: !!:.iill:'i:+i:ii'lii
Orx{e, g(r) e EeflapHoro ibyH&rliem IIa crMerpuqtiii MEo)r IHi ( 3; 3) BiAEocEo
. l-4,x t.-4..,.t ax r ax-rl _ lqr t.qx t .ptxt.sqx)= -. :-(,r, -r r I r' I
OrrKe, g(t) € Hetraplrorc Oylrnqi€Io Ea cv MerprqHii MHot{rlrni( €; -1) \r (-1; 1) u (1; +*).
120,1) f(r\ = !. O6nacr6 Blr3Ea'rellns OvHRirii: (-*; 0) u (0; +-) IIn MHo'{rEa c!r-
MerprqEa BiAHocHo lryn.s. sEaiaeMo f ( 4 =
==:=
f @)- orxe, SvEt{qis l(')
x-l -2l f@ =
=.
o6racrb BnstsaqenHn OvEltlrii: (--i 1) u (1; +-). Us Ml{oxrlrEa se
ruowe oyru cr:oaerpllqnorc BiArlocllo roqxlr 0, roMv OvII&qis l(t) se Motr'e 6vru sEi
llapHorc, arli IIerlaplrolo.
3r frxr = *. o6nacrL BruHa.r€IIEs: (-*; 1) u (-1; 1) u (1; +-). LIn M$or{r'EaI t-rrr I r' 1
cvMerprq'a BiAEocEo roq*r o. 3'aiiaeMo tr-"r = arffi =,,
r- = flrr' or,'ie,
OylIlcrris l(t) trapsa.
4) fG)=Jr"-1. o6nacrb BrclracelrHs OvHKqii: ( -;-1)u(1j+*) IIg ruHo:nnsa
c'Merpuqga Birrlocllo ro.rxlr 0. sraiiaeMo rcn = 'l.,r" L = 'lV= = l(') orxe,
l(r) - rapEa OyH(IIis.
5) l(r) = .rt L .,6 + 1. O6nacrE B[sHaqeHHe OvHRaii: [1; +-r' ris vuoxrua se
€ cnMerpr.rqHolo BiAHocIro ro-rKr 0, roMv Aasa OyH&qis He Mo*ce 6yrl'r alli trapEoro'
aHi HcoapHoro.
6) /(x) ^ , :. Oe,ra"rr Bu3HaqeHHt Sytsxuii:
x3-rro,ro6ro( -;-1)!( 1;0)u(0; 1)u(1i +-).. x -x tx'-t") x -x
3.ranaeMo /( x)=- , = lx- - t)(Dyl{}{rtin /(ir) Ee € asi napHoro, asi HerapHom.
121.1\ f(', - x'+ 2r - 4, x E Ri f(:t) = (-r','+ 2 (-r')qir /(x) He c aBi napHoto. aui HcnapHoro Ha crvarplsHifi
2t ttxt 9, ., orn t--; 3)\ t-ar a). {3: -):' I, -96 l-rl'3 613
f( x\=-:- 1=-=-Ilx).( x)'-s .r" s
lt ll .'- =--L-=-/(r,. O\,HKqia l(r) c HenapHooI x'J" - 2 l-x) -x" - 2x x" 2.'
Ha crMerpuqEiii Mrioxc""r (--; - "E)
, (-"8; 'E)
, (.8; + *) BiaEocFo Eynn.
st ft', = !l!7. o6nacrb BusHa,{esHs OyHr{qii x + -{r, ro6ro MEo,rinHa (-*; -r') u'' 2t+12lJ ( 6; +-) He € cnMerprrrHom BiAEocHo synn, 60 qi,Icno 6 He Ma€ rporlrne)rGoro( 6). roMy naxa OyHKrr'fl HF. aHi napHoto, aHr BenaD-oro.
of(t)-1x - 1l -2lrl +lr+1, jr€ Rtf( t)= x 1 2l'+ r+1==lr'+1 2l.!i + r-tl=flx). Bieor.ro, urol r 1=):+1, '+1=r 11.
oyrllcrri.a l(r) € napEoro Ha crMerpn.rHin MHoi{ir.'Hi ( *; +-) BinHocllo Hyrrs.
122, a) IapHa OyHXqis; 6) EerapEa OyH(Iti.s;l;: .:,a:{.i$:li:ii-l:di:i:li ':ji::-::.:::Uvitlii'.ii:iilli:l)::::*l:J
i :;;:::::::::i::i!
OyHKqis l(r) e HenapEorc Ha crMerpFrEiii Mllo]IctrHi (--i 3) \.r (-3;
B) DapEa OyHKqin;
:ai;:ilitllllil anrE6PA Mep3rrK A.
9+
r) Eeraplra ibylrxqis.
123.1) A = f@) napEa Oyllxrris, r € [-5; 5].
4=x'-2x-4.Oyrrlc-Mno,ntrEi ( -; +*) Bia-
3) u (3; +-)
I I /r-.r) l- I =lttt.3r /rxr=l r- -.
xrl,xz I l-r. r-.r@yH$qis l(r) e rapHoro na MEo,riIrHi, € ( -; 1) u ( 1; 1) u (1; +-)'
q I\xt- ,I ^-. o,fl (*: JzJu(''lz, Jzl -,(Jz, --),v'-2x
258 ll{: AITEEPA Mep3reK A. r. ra iH. aKaaeMiqHrar pisenr liiiiiilll::ii:.i
y = f(x) senapEa Oynxrrir,
f. ra iH. AKaAeMi,rHran piBeHb li.1 259
124, I'J 2)
125.f(r\="-4awvr>o.1) l(') - rapEa;
127. /(r) - Eerapsa OyEnqiF, 0 € l(f), rouv l(0) = 0.
12A. ft!) Heuapua S! Hxuis. BoHa nae 4 Hyti.AoBeaeMo, nro 0 e D(r. flpmrycrxMo, ro 0 e D(n, roAi l(0) = 0' ro6ro OvHXqinBnie Ma€ 5 HyniB, s aa yMoBoro - 4. MaeMo npornpiqqs. Ort*e' 0-€ ,(r.
129. I\x) - HenapHa oyHKtrifl i Ma€ 7 Hy'rie.,(f) € crMerpnqEa Msox{LIHa BiAsoctro ro'rKIt 0, lra sxiii Br3sa'resa OvHKqin l(t)'l(0) = 0.
13O. flx) - napEa.byHKqin i Mae 7 sy"ris, to,ci f(0) = 0, 60 D(D € crMerp"qna MIIo-
,rinEa BiAHocHo oci Oy, Aa Eftii Blr3Hs.resa abyHRqis l(t).
131. 3a yMoBor M orMerplrqHa MAo*{ssa Bi,qEoeHo toqarKv RoopAl-rlrar (o6nacrb
BEBHe.rel{Hs OyF&qii r, e@) = f(x\ + r), roAi g( ir) = l(-r) + l(r) = s(x), ro6ro
EG) rapEa OyHHuifl,3a ylaosoo M - cnuerprqlra MHou{ItEs BiAEocno Iloqar&y l(oopAr'Illar (ofulacrb Br3-rla'reEEs Oygxrrii n, h@) = fixl - f(-t\, roai ,(-x) = l(-;r) tQ, = -( t) f(-x\\'ro6ro t( ') = -t(t). oril(e, n(r) - HenapEa lbysKqin
132.3awoBoo I ig trapHi lbyEnqis lla MHoE{I'IEi M, ro6ro l(-t) = f(') is(-t)= g(a).
florpi6Ho aocniarrr tra napHi.rb SyHHqiIo:l\ v = f@) + s(t\, aC t) = l(') + €(-t) = l(ir) + s(n, = 9(r). ovnKl{in I = f tx I + e(x, -[apHa.2\ s=f(x)- sXt),v( r)- -x)-c, t)= x) -s(t)=y(a). (D]'El{qiss= x)-s\x\-rIapEa.
260 iJi AnTEEPA Mep3reK A, r. ra iH. axaAeMiqHnr piaexu ill{liiNi'i:li;I
:t\ s = f(x\ . s(x.\, a(r) = f( ,\ . c( t, = tG.\ . e!c) = y(t). @yllllqis U = /(r) s({) -
r33. AaHo /(r) i €(r), BllsEa.reHi Ea Mlro'r(trEi M, f(itJ - napEa, ro6ro l(') - l( '),a g(r) - neDapEa, ro6ro g(-r) = g(r). Iorpi6Ho AocniAr.rr IIa napHicrb ibynKrrilo:t) a=f@)+ e@), a|x,= f(-z) + s( x\= f(xl - s('). @Frrcqis y = l(') €(r) ree aHi trapHoro, aIIi serapEoro.2J a=f@) e@\,v(,)-fl a) s(-:t\= fG) +s(r). @yE&qisJ=l(,r+ s(r') se, asi EapBolo, aHi Henapsolo.3)a=^x) cG\, ae,\ = f( ', e(t)= r\. ( s('D=-^r).s(r)- y(,). oyHKr{isr, = l(r). g(r) € HetrapHoro.
134.@tErcaiifigB 3saqeEi Ea MHonirHi n4, /ig - ueDapEi OyHrqii, rc6ro l(-r) = -/(r)ig(-r) = g(jr). Iorpi6Ho aocriarrn sa napEicrb OyEftrrilo:1) a=f@)+ s\t\, vtr., = f(-,) + e( r)=-flx)- c@) = (l(r) +s(,))= y(r).@ysriqis y = l(r) + g(r)
- lretraptra.2) a=f@) s(rr, y(-x.\ = fl-x) c( Jd)=-l(r)+s(')= (flju) €(r)) = -y(r). @yE-Kais a = flx\ €(r) - EerapEa.3t s = f(x). s(x\, vttcl = fFr',.c( it)=-flr). (-e@D=f(r). s(r) = y(r)..DyHXrru,=l(r).s(r)-napEa.
135. / ig - seDapui, ro6ro /(-,rt ftxl, gFxt = g{xt i npr aboMy OyHnurt
hIt'l - -- 3safrAeMo ft(-.r).elxt
fl-tl fttt ttrtht x) . = -- = . lr-r). oyHKtris ir(.r) e napHoro.gt xt gr.r r g{,r)
136. I i g lbt EKqiI, oAEa B srclrx napna, a Apyra seflapua. <lyrrrrris h(i = 19)
flErqo / r'apHa, ro l( a\ = f(xl, a s - rieraprra, ro g(-x) = s(r), roMvfGt\ ftrt ftrthFxl. . .et-xl sltl strt
flKqo l- s€trapEa, ro fl-r') = f(r), ag- napEa, ros( r) = €i(J.), roMy.. ft xl ftrt 'ftxth( lJ .- =
- ' ,(r.). OyHxuir lt-rt HenapHa.
c( .r.) c(.r) eG'J
137. @yEX4is / BnBHaqeEa Ha MEonirEi fi.1) Hanpuftirag: y = a3 - Henapsa Oyl{ftqiF fi Ea MHoxcrHi rg 3pocra€, ocdnr,xr An!t"2> x) (tt e Rl, aG,, - a@) = '3, t > o, rc6rc v@,) > uQ).2\ Hanpve'nlat y = '4x HenapHa OyunEis fi Ha MAorrrBHi R cna{a6.3) flpulrnaa seBecrr.r He Monitla, 60.anqo ibyHriqis rapEa, ro ii rpaoix c[Merpr.q-ssii BiariocEo oci OV, roMy Ha oAsifi riAMHor{rrHi QyHprqin spocra€, a Ha iHrrii cra-Aa€, i IIaBnaKn (sa yMoBs, qo o6nacrr, Br3naqe[Hs cxMerpr-rqHa MnoxuHa siAHocEosy.ns).
138. I rapEa OyE&rris, .sna spocra€ sa npoMix{i{y [0; +-), roAi na npoMir{(y ( -; 0]roHa e ctranHoro, 60 rpaoiK O).Hriqii cuMerpr.rEnii BiAEo$ro oci Oy.HaDpuRnani lJ = t2: y = x).
139.1- HetrapEa OyHlrrtis, BlrsHaceHa na MHoxr{Fi R, spocra€ Ha trpoMt(Ry [0; +-).Ipaoix EetrapHoi Oys&qii crMerpraqHrfi Bi{Hocno noqarlly KoopAt Ear, roMy ii Ea xpo,Miliiliy ( -; 0l qs dyEl{qis spocra€.
Hanpxknaq: o=L, o'oro t".
i:ii:;liilliil:it: AnTEEPA MepsnrK a. r. ra iH. AKaaeMi,{Hrr pieexr :ii!: 261
126, a = f@)= o,sf , r e LOt 2li\ aQ\ rapEa;
flx)=-:, !>2.2) g(js) - EerapHa.
2l f@) I{enapHq.
14o.J napHa.byE'iqis. Tlli{.v) 2. TqI /l'rl 5. oc,(iiLHx/- napsa OvHHui',
ii rpaoiK cl,verpfiqHri EiasocEo oci 9. rovy ,minrllx) 2. rnsx /(r) = 5.
141. Oyr&qi'I I e senapnoro i nti'll(xl = 1' maxfla) = 3. Oc(inbKr'r f(x) - He-
rapEa Oynriqin, ro ii ryaoin clrMerpr'qHri BiAHocHo roqarKv rioopAl{nar! roMy
min l(') = -3, maxl(r)= 1.I-i: 2) l-3: -2)
BnPaE'l Anc noaropeHHt
u 7x 3, l{ 3*?-" (l),142.1t l" l"-':' " ll 6xs. y s, I.r - 6113 I 7xt-tB 1xt'z=9 tzt.
PoaB'rJ*{eMo piBEnl{Hn (2):x2+l8r+4212 g 42x- 4g!'=9; -6t2 24a- 18=0; t'+4t+3=0;''= 3
a6o x = -1.
143.3d )voBoo /, /r sa I ror. 6 xB. I -6^ l.l .oa.:60
s 66 66 66 66 ll 6 6 I - ^'=t=t' t=;-' u, ,-', l0i u ,, t0{r) ra lp{ roarHh Bonh opo
lxaru 66 HM, ro6ro 3D1 + 3u, = 66; \+D,=22(2')i t> 0, I,j >0, u,> 0.
\=22-D,,661
= r:l)-22 D, u, 10
= 0; 60u, - 1320 + 60u" - 22v" + o: = Oi
o +98a -1320=0; .D -qg' .lSzo 24ottl32o 3721, J3721 6tl4
D, = -49 + 61= 12.
r,, = -49 6l= 14O-
BpaxoBymqr yMoBy ,, > 0, MaeMo u2= 12, ro4l Dt= 22 12 = 10.BidnoqiAb: 10 F"Lr/roa.; 12 r.M/!oA.
3. no6yAoEa rpaoiKiE OyflKqit 3a AonoMororo reoMerpreHnx
fo 'o 22,t' 'I'o3B rlKeMo rxcreMy piBHflkb: i6 6_ l.
[u, r-', ro 'PGB'.'xeMo piBEnnEs (3):60tl, 60(?2 p,) p,(22 1,,\
D,(22 - D,)u" + O, L),+ 22.
'.4:i a-.:.t:.:'tt
:i:t:.:.:.:i.I.
flxrqo jr = -3, ro 3/ = 3 - 21 = 18.ffxqo jr= 1,roy=3 7=-4.Bidnosidb: t B: _18)i I t: -4).
l*_q=ro.
,, Jt - u, 2r! too. atx vl - roo. ] ' , ir ar
'' ly,, s, u-. Bt l['-r' '0.Bi.)no.)idb: (gi-t): { li 9t.
'fr t Y = 6;
lfz* = re. l[* = g.
]lzs = -2. ly = -r,
JP'= ,' l['= ''lL2, = 18: [1!/ = e.
"r[,tv',0= 15. [x-u-rv 15.H"*u,;, tu=a.rc b.
x'zu + xu - 54t ltvk ' u\ = -54'
l, r b = -15. ]d -15. b. rlr
It'" 54: lrr l5 bt = -54 (2r.
PorB exeMo piBEflHHt l2r:15b - b, = 54i b' + L'b 54=Ot D = 225 - 4.1. (-541= 223 + 216 = 44li
A -ls{ 2l -6 r, a =_15-2I=_!9 t8."t22-"'z22g$rqobr=3,roa,= 15-3= 18; sRrco b,= 18, roa,= 15+18=3.
1r ]x ' = -ls lx -I8 e (3r po3s sxeMo piBHnsss r4r:
lxs 3: L( 18 y)y = 3 (a).
,18v y,=3,a,+18y+3=0; 2=sr-s=zg, y,=-o-.fia; y"= -g+rte,
roai '' =-18 (-o-.fa)= s+.,,Fs; ,,=-rs-( s*"8 )= g .,88.
orxe, [-o + .,Fa; ,-.,fis), (g '[s;-s*'q8).2t x + a = 3' [x 3 - s' {51 poc"
'*.'o pi""',r' (o),l'y = -rA: l{3 ,)y = 18 {6).
3 t s t23u-y"= \8; y" 3y 18=0;r=9 4 {-18)=9+72=81t u.=;=;=61," t-n=j 3. rori .r, 3 6=-3..r, 3 {-3) 3 3=6"22Orxe, (-3; 9), (6; 3).
Biono iob: (-3i 6), (6; 3); (-e+,fi8;-o-'fte), (-o -.,fia; o*.4a).
262 ::::::: AnrEEPA Mep3nek A. f. ra iH. aKaaeMiqHnr pieeHb :ii:::iii:i:::.ii:i::i
145. BiAnosiAb: 4) y = (t 4\2.
146. BiAnoqiAb: 1) a = f + S.
147, BiAnMiAb: 3\ Ea 8 oanHr.rrlb rpaBopyq.
nepeTBopeHb
144"AarJoV=t'.1)a=x'+5;4Ju=(x+6\';
149. a = fl;r).
1\y=f(xr-2;2\a-f@r+4;3)y=f(r-3ri4\a=fk+1\;5) a = -fl'');6)a=3 f(r).
2)v=Q a)'i5)y=(.Y-g):-2i
3)a=z' 10t6)r=(r+1)'z+1.
148, BiAnoqfib: 4) Ha 3 o4HElrEi niBopr,.
:ittiitliillii: AITEEPA Mep3rrx A. r. ra iH. aKaaeMi,{Hnr pieexu i{li 263
Pxc.61)a=fQ) 2;2)a=f(r)+4i3ry=f(r 3\.4)v=f(t+t);5\ a = -f(r\:6)r/=3-l(')
:.-:if il:]:I i ::t.:.!:i.
151.
154. ArropnrM ro6yaoBr .paoilla OyErirrii:rl a=nE-+:a) 6yay€Mo rpagill dryHllrrii y = G;6) ryaOiK Oygrllrii v = G ""p"""""*o "upajr€nr,Eo IIa 4 oAnHrlqi lHra.2\ lJ=n64:a) 6y.qyeMo rps$iK OyHKrrii y = Ja;6) rapanenbHo nepeseceMo qefi rpaoiRIla 4 oArlrnqi npaBopyq.
3) y=G;+3.Cflo.rarKy 6yny€Mo rpaoin OyHnqii y = G. noriM noro nepeEocrMo napanerBFo
Ha 1 oanfl}rqlo rpaBopy.r. OaeprKrMo rpaoiK OyHKriii , = \fr i. noriM qefi rpaoiEnepeHocr.rMo napanenl,Ho Ha 3 o4aHllrri Bropy.
155, 1) y = ?;
2) Y=1 1:
lt = l-;
4r u= - +6.
flHqo ryadliH Oynllrri.i2
napanenbHo
ncpprrcrTfl sa I o.trxH qro BHrrJ. ro onnpy.'{Mo rpa$ik 6ttvt" y ? 1 '2r.
flr<u{o fpaoi( OysKr{ir y = a rspanenbHo repeHecrr Ha I oArHrrlro ,'riBopyq, aoxcoAeDxlvo rpaoir oyHl. (ii 9 r-tl3).glrqo rpaoir{ OyHEqii , = ? tup-"rr""o ,r"Oesecrl sa 3 oAuHuqi npaBopl r, a troriM
Ha 6 oaxHru6 vroD\, 1o orepvHvo rpaoiK O)HKuii, ='--.--6 {4r.
iiiliiiilittiii AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hnr piBeHb ::::::: 265264 i:::l A'|EEPA Mep3nrK A. r. ra iE. AKaAeMi,{Br'tr pieext il::iliiiiiiill:i
t
E
156.l\ !/ = x'1 4x + 6;g=A' 4r+4)+2la=(r 2)"+2i
2)a= r'z+6x 6;y= (j.' 6n+9)+3;y= (r' 3)'?+ s;
Io6yaoBa rpaQilla OyEtcqii2g= 2-' ..
2a) 6yayeuo y= ;
26) 6yAyeMo r= j;
2B) 6yAy€Mo v= ,_t:
2r) 6yAyeMo != 2 , I.
, ,l:!: jl.:3)A=2a'!-4r+5ia =2(:t' 2t+t)+3,a-2(, 1)2+3:
4) u = O,2x' 2x 1;y = 0,2(r'? 10r + 25) 9lv = 0,2(r 5)r - 9.
3r+8 8157.1) y=-=3', ,
,, ,, 2r-'14 2t! Jt I 2, .8'tc ' 3 x'3 - r 3'
xt 2t 2t\ lt ,. ,._,-''rIrLI
266 l::i A'fEEPA Mep3rst< a, f. ra iH' AKaaeMi'{Hxi piEeHb :::::i::::::1t:::::::: i'.:*ii:1:il:lil:ii: UfeSPA Mep3neK A. f. ra iH. AKaAeMi.{Hrt piBeHb i::* 267
1s8. 1r ,, 4' 14 4{ir l) -lO = 4, l0
.
rtl rrl .r,l'- 7 jl: (x 7)
- x2 12(t 2)s - 5
): 2 r-2
159.
161.1) s = 0,5aF; D lt = -z"E:Z.
,l a =o,b J;
164. 1)
169"
Bianoaiah:2. BiAna6iAb:4.
167. 1)
BiAnt)6iAb:2. BnpaB14 Ar9 noBropeHHe
171-Hexan r rpE. qiHa roBapy. fliABrqeHa qiEa roBapy - qet + 0,25x = 1,25r ryn. Ma€Mo: 1,25r rpE. 100 %; r !pE. ! "/";
100 a l0 0OOu 80: l0O l, -80 A =2lak.- 1.2tu 125HoBy qiHy roBapy rpe6a 3I{]IsIlrr Ha 20 % .
Bidnoatdb: Ba 20 rl .
172, I]icnn BrraposyBaHns 3anrnrr,rocs 200 40 = 160 (r) po3qrHy. y 200 r pos.LrHy Micrnrbcs 8 % coni, ro6ro 200:100 8= 16(r). y 160 r po3.rrHy MicrrrEcs
t6.too%I fi r .oni To6rn
-=toi,
160BiAnoRiA,: 10 a
.
fiitiil{li::.::.::J AITEEPA Mep3rqK A. f. ra iH. AKaaeMieHrt piBeHh !ii: 269
BiAno6iAb: \ 4.
268 l::l: AITEEPA Mep3fleK A. f. ra iH. Ar<aAeMieHnn piBeHb ::::i:;:::::ii::::::iil:i:
t173. Hexan v roqar$oBoMv crl,'laBi t lir qrlrxy, 3al'anbHa Maca rlEoro crlraBy -
(12 + r) Kr. -Biacor&oBLIE BMicr Irllrrny B roqarxoBoMy crra;i crag.t"tt ', 100 %
." 12+ xSararEra Maaa HoBoro cEna3y cl(,'lana€ (12 + tc + 2, = (14 + jr) I(r. BiacorKoBr'di
(2 r.r) 100 ooBMlcr qIrHIly B EoBoMy cntaBr cl{naAa€
-.
iJa yMoBoIo BrAcorHoBtt
2. lpaon{ y = lflr)l 6vAy€rBcs raR: ra r{acrrEa rpa&iKa OyHKrrii y = flJ.), sria,'lexcrrEBnqe oci Or (i lla caMin oci), saimrra€rr,c.s 6e3 3MiE, a sRa rer$,ii6Hrxr.re oci Oir, BiAo6paxa€rLcF crMerp*iqso BiAHocHo rli€f oci.
176. Anrop rM ro6yAoBr'.1) y = lG);2) v = f(b) vacruaa rpagiRa OyllKriii l(ir), s&a,!e){Crr6 trpaBopl r BiA oci y (i Ha caMin oci), 3anr.ruacl6cr 6er rMiH r BiAo6palHacrbcfl .IrMFrpr.r.rso BiA-HocHo oci Oy;3) qacrrHa rpaoilta OyEKrrii u = f@l), axa, rcxe]lTsBrqe oci Ot (i Ha caMifi oci),3an[ aerbcs 6e3 sMi1i,a ra rracrrEa, Hrli.re oci Or, BiAo6pa-}Hacrb.s cIrMFrpxqHo BiAHocHo uiri o.i.
177 -
sMicr lr'Rv B HoBoMv "o,uui
ou al " = 4 ","33
12 r x) 100 r. 100 25Mat Mo PIBH'HH': J4 x 12 - x a
:
6iftmsii, rrr{ y Doqarr{o3oMy.
(2+!\'474+ x 12+r 3'
ir't Ei:.i:.:
i,:i#:i::..iit:i1l::l:::
3(8+ 4rX12+r) 3 4jr(14+')-(14+')(12+') _ 0.3(14+r)(12+r)
124' 12xltl2-xl-12xtl4t xt 1168 | l4x I l2x x'l n.3\14-x')l12tx)
288 + 24x: + 144t + 12; l6At - 12r' - 16A = 14r. l2r I=0j3(14+'X12+r)
x'-26x-tzl ^ [x -26x-]20=0,= (,: l
3tl4 rr.)(12'.r) (14 x){l2.ir), 0.
Po3B s,l{eMo piBHflHHr I x' - 26x 120 o, D t69-120=289,4
\= 13+17=4.x,=-13-L7= 30,t=4 BianoBiaa€ yMoBi 3ana'd.BiAnosiAb: y rrosa'rxoBoMy cflnaBi 6yno 4 &r q!,rrrcy.
ForyeMocr Ao BllBqeHHg HoBolreMx
3A=r+7it:=3! 7:174.1) "3ro 10 10 I02\'=- t tt: " tt : t-2=-t t t2lx/,li" t 2 ' x-2 .Y 6 u 6r:--= t-
fry u*--'=tr g-t=!-'": Stgtll Lx+2:'5"525(y +1\'=r.+2. x=25(u + 1)' 2(r> 2,y> 1r;
I I 1 1 I 1 I a-. 1 c-o I o. a.4l --=-: --=- - -i b=- O'a h c b t a b K b ac c a(a+O,b+0,c -O,a+c).
Konu 3po6neHo ypoKl,t
'175. 1. rpaoiK y = l(t) 6yay€r6cs raR: ra.racrlrHa rpaoiKa Ot'EKqii y = l(r), sfta ne-)Icr-rrL rpaBopy.r Bia oci oy (i Ha caMifi oci), sa-'lsllla€rbcs 6e3 3MiII i Biao6p&r€€rr,cn cnMerp[.rHo BiAnocno oci Oy.
fia.\ a=lx' 1)
-4 z-, r.?
u
zt a=)G-zl
n, "=l "" l'-t
27o it;:t::. ,.IIIEEPA Mep3neK A. r, ra iH. A(aAeMi.rHrr pleenr :iii:i:i:iii:i:i:i:i:ii :it::iitili::ilitl ATTEEPA MepsnrKA. r. ra iH. AKaaeMi'{Hrr piBeHb li::it 271
f
loAiropl-rrM no6y4oBlr rpaoina OlBlrrii y =': I :
XL2
1) a= :
2\ a== 1 (Dapanenhflo nepeEe.eMo BHt{3 Ha oalrnxuo)i
3) A =la -1 t.{acrrrEa rpasira OyEXuii. sl{a ne}rnrr, Bnlqe oci Ox a6o Ha oci O.r,
sanrma€rbcs 6e3 3Mif, a ra qacrrtsa, i Ot, BiAo6par{a€rr'cscriMerpnqno BiAHocHo oci Ot).
179.1ra=@ t)'i
rso. 1) y=r/r+21;
3, v=,tE-rl+2.fpaOiJr Oygns,ii lt = ,1, tl , 2 clrMprpvqHxfiBi.qIIocEonp€Moit=1.
14) u = --=_.'- ix+11 3.1l Dadrk rhvHknl'" " .r+1 3
crMerpr.rHz ii BiAsocHo npnMoi t = -1.
Itijh:Uf::i
)i::c+!!:.1i,:i; .llt:
4, O6epfleHa OyHKqit
181, a), B) - roMy u]o r MolrcHa oaEosnaqHo Bnpasr{rs qepe3 y sa o6nacri sIIaqeIIl,3anhsoi oyEKqii.
lA2, a), 6), B) roMy rrlo r MoniEa oAEossaqEo Bspa3nrl-r qepes y Ea o6nacri sEaqeEbqa,qaHoi oyr$cqii.
1A3. D A = l, , , e n, y € [0; +-). OcFiinErc.r r Ee Mo]Krra oAHo3Eeqso Blrpasltr]r qepes
v Ea o6nacri 3EaqeEr, sa,qanoi abysxqii, ro Aana OyEnr\is fle e o6oporEo1o (Hanpu-
&''.aA,V=2,ax=-2it=2).I
2) u=+, xe (-*;0) u (0; 1-1, g e (0; +-). OcKinr,RrI, Ee Mo*clra oAIioBEaqHo
Bnpa3rrrr qepe3 y sa o6nacri sHa.reHb sa,qasoi O}.Ir&Irii, ro Aalra Oylrriqis Ee € 060-
PorHolo (1lallprRra.q, Y = 1, a t = i:1).
3\ a = 5, r e R, v e l5l, Octiinbr r t He MolrcHa oasosrraqtro Bllpa3rrlr qepes yHa o6nacri snaqellr, Ba,qasoi OyHftrrii, ro Oys(qis y = 5 Ee e o6oporlroF (I{anpuKnan,
I s. a .r = 0. 11 ra iHroi).
184.1)!=3x: 1,xe R,3x=V +1; t=g-!, ge RlDlxl=r(y,t. nosHaqlaMo
B oAepniaEiii OopMy,rd apryMeEr qepes t, a ibyHKqiro .rep$ y. MaeMo OyHXqirc11
s==x -, sl{a. o6epHeHoro ao OyHHrii, = 3i l.
12t u = 1, x e (--; 0J u (0; +-.). OcnirE(Ir Ha Bcii o6nacri Br3HarreHss AaHa abya'ttKtrifl o6oporHa. 10 Bl4paxa€Mo.r qepe yr ( @i 0lu(Ui i-1.
i:iii:,1!{iilliii LnrEsPA Mep3rrl< A. r. ra iH. AKaaeMirHrr piBeHb .allj 273
zt v =',Ei;
2Jy=(lx-2-1)"
272 ',:* NllEEPAMep3ncK A, r. ra iH. AKaaeMi,{Hrr pieenr' lll:ill{ili:iii:i
f
SMiHroroqrr no3Ha.reHHs Ha rpaArqirlHi, oAepniyeMo
1l ,l )..at u= it. 2x-r.0.'=;.'.1, -.;) l;, *J. Hasci;o6.1a.rioy
Kqir o6oporna, ocllinr,Kr s lirnrrrrro y = ! MoxHa oAso3HaqHo Bupa3xrx .r
.rep$ g (y + 0 Ha o6nacri 3naq€Ilb 3a.qaEoi OyHRqiI).
orxe,2r-1=1, z,=!.'t, zr=!'u, r=t e,,,,o.9C92!'
nosua,r Mo rpa,qaLlifin., o t !' ,ur rDyHK(ir. o6ppHeHoo !o OyHKuir
t"'" z'-l
tlAt U ;x t 4. r r R. I{a sciii o6nscri OytsRuir o6oporHa. 60 3 piBHrHHfl y r'i 4
Mor{Ea oAHGrravHo Br.rpa3urrI r qepe3 y: v= g-4:.x=3c- 12. Iloosaqrr,{o rpa-
,qxuiiiHo:|] =3x .12.t\e SyHKrir. o6epHeHorc ao.byirxuii n j- +.
z,c I. x 0.ro,ais o.spiBHo.ri s ] "".*., ri$=r, vr L../r-JraItpaxoByroqx. qora yuoBo,o y O.Ma.Mo r=]. n."**"". tpa.qlqiiino: u I
rr ' U. y l,t. Ur OyHRuis o6epH"r" r. Orr#.
3, a = 'lr"-.3a yMoBoror(y) = [2j +*), roai y 2 0. 3 piBEocri s = lFJ MaeMo.
s'=i 4i t2= y!-t 4; r=!,f}i, ane.!€ [2; r-1, 'o-y '=.,[t*a. nou"u-.ra€Mo rpaAxqiiiHo: U=.lF+4 Q>O,:(>21. qs dlytlRrris o6€pHeHa Ao Aauoi.
1 IIs OyH(qis o6epHer$
186. Il u=-L. r+oc&in6xE B piBH.sHHs
l, r e (--; 1) u (l; +-). Ha Bcii o6nacri Oyrxqis o6oporHa,
I = ---:-: MoxHa oaHosHar{Eo Brpa3rrr jr qepe3 g. !(r - 1) = .r.
188. 1) (DyHKait yt(r) o6epHeEa Ao OyEtl-qii V(r). rpaoiKn OyHnqir; cxMerpr.r.rHiBiAEocHo 6icenrprr$r l.
3) g = 1_ (DyHkuir ,,(rJ o6FpHeHalzx, t < u.
ao OynKrrii y(r), ixHi rpaoiKn cniBtranarorb,FRUro.f,:0: a flKuo.r' 0. BoHu CrMeTphqHiBiAsoc[o 6iceErprcr l.
149. 1), = 3t - 1. @yHXIti.s yr(t) o6ep-neEa Ao QyERqii y = 3r - I, ixsi rpa,Oixu cuMerprqsi riAHocEo 6icexrplrcqI i III r.oopansarr[x KvriB.
2) @yHKrrie !,(r) o6epBeEa ao OyHR-qii y(t). fpaoi"t OyHXqifi cuMerplqEiBiAHocHo 6icexrprcr l.
2\ v = r' - t. oyHxaifl y,(r) o6epHeHa
Ao OyHKqii U = )c' - 4. IxHi rpaoit{Irc[MerprrrHi BiAsocro 6icerirp cr{ I i IIIKoopAuHarssx nyriB.
gx c x, yr r = U. xtg 1t = g. , ! .. g, l. norHaquMo rpa{ruiiHo:vt.., r l. olpuvatMo oyHK(r'o. ooepseHy,4o aaHor.
. r [r ,2ta J2x 1,2! lzO, x,:, Dtcl l;t r-1. Ha rriii o6nacri.r MolxHa oaHo.2z3HaqEo Bnpa3xrn qepe3 y. Bpaxoryrcqr, rqo y > 0, Ma€Moi y2 = 2a 1;2t = g' + 7i
r=?. no3Ha,r,rMo rpanuuifiHo: u=-- - ur ibyHxrIfl o6ep:rera 4o rblr.
I{uii y J2jr l.
3)C=2Jx t, r > 0, r e [0j +-), y € [ 1;0) (r oaHo3Ha'{ao Mo}rcna Brrpasr.rrr.r qcpej
y).3AaHoi piBsocri Maer'ro: y+l=2./r, Bpaxosyror .r yMoBy, + I >0,ro6roy:-1.1-I
onepxrfMor (y I ll: - 4r. x-'llJtlf. nosHaquMo rpanhqiiHo: g= Otx
rlf.o,qeplttvMo Oy,rKrilo. o6epHeHy Ao AaHor.
qu=r!,D(yr=( -;01, roAiy > 0.3 piBEocri g/ =r? rpn y > 0 orepxyeuo r = tJg.BpaxoByroqr, qo 3a yMoBoo r € ( *; ol, Ma€M. r = -u[. n*"rr**o rpaa'qiiiEo:y = -G. U" Qysxqis o6epHena ao aarioi, srca 3a,qaga rirbnr Ans, € ( *; Ol.
ft7., y=!12, r€ ( *; 0) ..-l (O; +-). Octinlnr r oaHGHaqHo Moxlga B'pasrlrn
qFpF3y.roirr x 2, ux x -2.xtu ll=2. x=:t,g-1.
Ilo3EaqaeMo rpaArqifiro ii orprrru"*o: y = _f .
Lls iDyElcqifl o6epse!.a ao aanoi.
274 ii:i AIrEEPA Mep3nsK A. f. ra iH. AKaAeMi,{H}ri piBeHb ::i,;i::i:li:!:i;:i!::: i::::illiiiit::ii: AITEEPA Mep3rsKA. r. ra iH- AKaAeMiqHy.y. pi*e{h r* 27i
["G. " : o.ar y=lr
lt.r. .r < 0.
Ipa@ixu o6epaerrx OyHriqifi v(r) i yr(r) ctr,Merprr.rHi Bi,qEocHo 6icekrprcr I i III KoopAn-
195. Hexan 1 - po6ora, roni rep a rpy6a 3a g roAlrH HatroBlrne ] oo euy oacenna,rrI
.Jr 3 ro,{r{sl-r loHa nanoBHro€ : 3 =: o6'€My 6aceiiHa. Apyriii rpy6i 3arlrllrnrloca93ranonsur{ f - i = i 06 eMy. BiaoMo, rqo apyra rpy6a EanoBnlo€ 6aceiiH sa 12 ro-
nHH, roAi 3a 1;oo,;v ".r" ","""",rr I ooc'y,, I o6'cuy eona 'anoa,r,rtr
.,^ 1,+- I rz s 1"oo,u1.su"",loovie'"a,,o",,""o"lt*t=11 (,oaxnr'
B;dno6idb: ra IL roA!,t}l.
196. Hexafi Apyra 6pBraAa Mo]rte sopar,r rone (S rlroqa) sa J' roArE, roni rep-
rrJa - 3a (, + 12) roar.rE. 3a 1 ro,qnHy.qpyra 6pErara MoJ*ie Boparlr !, u ,r"p*"st
r l2'ToAi pa'oM Ba l roar'y BoH' Mo,{yrr, 3oparr, 9 * "r - = "t1
* '.1]) = "\'. 12! ,' x r'12 ir(x. 12) "r(r+12)
vce none pasoM BoH' Molriyrb sopa'r 3a s , s(i* *,ll) "oaoo,
ro6ro sa 8 roalrH.x(x + 12\
MacMo DiB,,EHr': s , 2sl' *-9.1
-- e, r(r I 12) I' x(x - t2) 2(r 6)
'2 +2r=16' + 96; r* 1; x'z+2r-L6x-96=O: r' 41 96=O,orxe,
! 12 a6o x 8. 3a 7 roArH vot+re soparlr nonc Apyra 6pHr eaa- e neprJas.\ 12 + 12 = 24 (toAt E).Bidnosidb: 12 roa H i 24 roaHHr.
197. Hexan trorpi6Ho IlaroBllrrs 6acenn (1 - norc o6'€M) i nep a rpy6a Mor{e Ha-
noBHrrrr-r ioro 3a .t ronrH, npallloloqlI cauocriitro, a apyra s (:. + 24\ toELr'J
1l3a 1 roAttHy neprra IlanoBHroe i, a aovra _ 3a 8 roam po6orn Apy-x24
ra rpy6a ,rafloBxro€ j^,. ".
1 fo,qrrEy, npaqrolo.ru pa3oM, rpy6r HatroBrrolorl''" x+24I I ^^(r I ),t ,tro. roai 3a 20 ro.ar-rH 20 lrtrrZq).
Tarir-rM.rrIIoM, 3a 8 roalrs po6orr.r apyroi rpy6r{ ii 20 roallH cyMicroi po6orll repllloit
ir apvloi rp\6 B,rxoHaHo : po6orH. Ma.Mo pisHfl'rHs:
s /1 r ) 2 14 10 r__2tt.t - __f _I :r-24 \: t,24) 3 r-24 ir 3
42. + 9Ot + 72O= t'+ 24r, t+O, x+ -24| x'- 48 x 72O=O;
4,=24r.17296 r,, = 24 t 36; ' = 60 a6o it = -12.YMoBy sanoBoJtEEs€ qlIcno 60.3a 60 roarn MoJ{e HatroBHtrlr 6aceiis nepua rpy6a, a Apyra - sa 60 + 24 =
BiAnoqiAb: Ba 60 rcllrl{ i 84 roAnEr.
5. PiBHoclrnbHi piBHgHHq. PiaHeHHg-HacriAoK. PiBHoclrnbHi HepiBHocri
194. 1) Ta&, 60 Ha MHor*{rlri (-€; +-) t{rcno 8 e xopeue*r i repEoro, i Apyroro piB
2) TaK.
i:iiii:.ffi;fliii:jiuresPA Mep3ncK A. r. ra iH, aKaAeMiqHnn pieeF.s l;l:l zzz
191, IpaOiKI, o6epEeHrx rbyHr{qin y(r) i y,(r)crMerprr.rEi BiAEocEo 6iceB rpr.tcr., L.
192. y = kx - b, k + O. O6,racrs e[rnaqeHin -4. OcKin6RU r oaHo3BaqHo
Blrpasrrsqepe3 v,roh'=v b,,=+, "=it-i leni',nHa3aHicrb, sa yMoBoro fr + 0. TaKrM qrrHoM, o6epseHa d}].'HKqis a,= ia ; Nnqii v = kr + b reri € niEifiHoro.
193.3a yMoBoro y = l(r) - HenapEA Oyllnqis. Hexarl Ol.llltqis y,(r) o6epHena Ao Aa-Hoi. fpaoil{r.r qI-Ix OylIxqifr cr.rMerpr.rsi BiAHocEo 6icellrpncs I i III &oopaslrarsr:(RyriB. IpaOiK Aanoi Ot'EI{qii cnMerpr.rHri BiAHocEo ro'rRn O (0; 0), roMy ii rpa$iKO]'EKr{ii yr(r) re'rc cr.rMerpr.r.rErii BiasocEo qiei rocKs, ro6ro y,(-r) = -yr(r). OrrRe,yr(x) c EenapEolo SynKai.rc.
BnpaBx Arn noBTopeHHq
'194. Hexan.4 [4 > 0) - ycs po6ora, sriy rp€6a BrrcoEarr. flepnllIii po6irE{x Brrco-
Eye Bcro po6ory sa 20 roarn, ro6ro sa I roaagy BiH ""..""" +. Aplr{n po6ir-2V
nrrc BnrcoEye Bcro po6oay Bs 30 roAn$, ro6ro sa 1 roAr.rHy BiH BrRoEy€ jl. PasouAA50A5A--'"30
3a I roAr.rsy BoHr.r Br.r(oHyror6 20
1 30 60 6 . v.rc pobory pa3oM BoHH Bu-
5A_6,46A:6 roAxH. lobro - =;=l.z r-oAxBu.
BiAnMiAb: 3a 1.2 ror]j]l r.
276 llliAIrEEPA Mep3ncK A. f. ra iH. AKaaeMiqHr4i piBeHb
12) TaR, 60 na Mso}I{I,IHi ( *; 1) \-r (1; +-) trepDe ii apyre pi
5) Hi.6) TaIi.?) TaK.8) Tal{.9) TaK.
2OO.7) 2x - 3 4, x ts R. -r 3.5. fioMy piBHocn,"6He pisHsHHs -r 3.5 = 0:2) lxl = 1, r. R, r r-1. iovy piBHo.xnbse piBHa\He r I 0:3),r+6=,r-2,re R.0 I 8 xopeHiBEeMa,. ioMy piBso.xnbHeEsr:+1=0;ql L I
O, r F { -; l).r (l; r€), KopeniB Fe va€.rliolay pinnoca,r*re piBHnHB' ;- ; o.
-I-I czoci6. Apyre piBlrnHHs 4r - t = 8 + 3 MoJr.I{a oA€p{arl{ 3 nepllloro 4t 8 = t +nl(rrlo Eepen€crrr AoAaHRr s oAniei cacrEEE piBHsHns B iHtrry .racrr.Hy 3
nc)rHrvr 3Ha,{aMl,l. ToMy piBErHur pjBnocHn6Hi 3a reoppMoro.
e KopeEnMtr nepuroro piBE.sEHs IIa rii caMiri MEor.c1-IIIi.
a) 3'r-5 'r I {treourc DiBHnHHrr:9r Ib jr 6i gr '21, r=11 .10r..26 18
HrrrHr Lr ls ,r = 6 re]:{ Mac KopiHb r. ;. Orx.. Ha MHosHHi I -rqi piEEsEEs piBllocrn6Ei.(A60 Apyre piBE4sEs Mostsa oAept{arlr, sKrr{o o6tABi qacrtEr nep oroHa 6. 3a reopeMoo 4i piBll.sHss piBnocrnbHi.)
4) PiBIrsnHs (2r + lr(r' + 1\ = 3(" + 1) t 2t + 1 = 3 piBEocr.'nbsi, 60 apyrcMoxHa oAepr{arr.r s nepllloro, sRnlo o6BABi q6crrs6 nepuroro piBErHEfl noAinnrrHar'z+1+0(reopeMa).
2O2.1r Ia'/".2) Hi; 3) Ei; 4) tri; 5) raE; 6) Iri; 7) lri, 60 ftopeEeM piBHnHEs 2r + 1 = 5e.ircno 2. ,firiqo o6taABi rracrsEi riboro piBHFIlEn troMEornr.rr IIa (r + l), ro oAep*crMo: (2r + 1Xr + 1)= 5(a + 1'), 2r' + tu + 1 = 5x + 5, 2x' 2x - 4 = 0, r' x 2 = 0,'to6ro t = 2 a6o )e = 1. Or)rce, &OpeEi apyroro piBHnHHn ne € xopeHsMn nepnoro.
203, 1)r+ 3 > 6; r> 3, re (3; +-); 4r< 12i x > 3, r€ (3; +-). Ili sepiBEocri€ piBEocrnbEzMrr.2) (x + 2)'z(r+ 1) < O ir+ 1< 0 ae e pianocr-r.rlEurrur-r, 60 MEoxcnEom posB's36iBnep oi irepilsocri € r € ( *; 2) u (-2; -1), a Apyroi - xe( *; 1).3) (r + 2)?(jr + 1) < o, poBB'ssKoM € MEo,r{r{Ea ( -; 11, a posB'ssnoM sepiBHocrir I ' 0 ( MpostsHa ( *: -11. Orxe. qi RepiBHo.ri 6 piBHocr{nLts vs.
4) Po3B'sBKoM HepiBEo"ti 1.1, 1 a.0 e MEo!@ira(--;O)u(li +-). P$B's3rcoM
HepiBEocri r > 1 € MHolcrHa (1; +-). MHorrorEu IIe cniBfla,qaorB, roMy qi lIepiB-Hocri He e piBHocrnbExMr.5) Po3B'.a3rcoM HepiBHocri, x'> x, x2 r>0,i.(a 1)>0€Msonrl-rlla(--;0lu[1;+-);posB'.sBKoM EepiBEocri r > 1 € MHo{r Ha [1; +*). MHoninlrn He ctriBtra,qarorr,, roMyqi HepiBHocri Ee € piBrrocrri6srMr.6)(r+4)'<0, re 6:lz 2l< 0, r€ Z. HepiBsocri € piBEocrnbHr.rMrr.
2O4.1, (x 3t'(r + 4) < 0t r + 4 < 0 t x 3 = 0j r < -4 i ' = 3. MEo,IlnEoro posB's3rdBe MIIoJxrHa ( -j 41 u {3}. PosB'ns$oM EepiBnocri.r + 4 <0, r<-4€ MnorrcrHa( -; 41. HepiBEocri He € piBsoc*rnr,EnMlr.2) @ 9l'(x + 4) < 0; r < -4. MHo}I{rHa (--; 4) e po3B'ssnoM qiei EepiBHocri.,4r.8 EepiBFocti t + 4 < 0 po3B's3KoM e MHoxcnHa (--; 4). Or)$e, qi sepiBnocri
31 {--? ' g. pooB fl3tsoM c r'r'o)nrHa (-*; 2l (4: --).x4 --. -\,.-- -Y-- ,
41 1E < 0, posr'saxoM e .rxcno 0. ra < 0, poBB's3KoM € qrcno 0. IIi HepiBsocripiBHocrrnLHi.
205" 1) PiBEsHEs x'= r e EacniAKoM piBr.sIIIIs r = 1, 60 lropirlE 116010 piBEsHEs e Ko-peEeM piBHsHs.fi r'= r, a"re se xoxes xopinr piBHeEHr ,v'z= x € kopeHeM piBEsHHs
2) PiBnsEEs 0 r= 0 e EacniaKoM piu""""" {=f.
3) PiBFnEHn I'9= I € HacniAnoM piBHsHHs x3 = 1.4) PiBEnEEn ,r = 1 e EacniAKoM piBnssrs.r3 = 1.
5) PisunrlHs r'?= 36 € nac,rirxou pinsgssg {1=
6) PiBrr.sgrr.a t'= 4 e qacniarcoM piBHngns .'--!= = l-J=.t+2 x+2
7) PiBHslrHs:t'- 1=0 e saciri,qxoM pin""""" t'=-0.
lri:l:iiiilti{lti: AITEEPA Mep3reK A. r. ra iH- AxaAeMiqHan piBeHb tii: 229
Ans nepiBHocri, 2> O, r > 2 posB's3KoM(2: -). Ui HepiBHocri Hc c piBHo-
3) Hi,60 Ha Msor{nHi (-*; +*) repue piBEtHHs Ma€ oArH liopillb, s&ai AopiBnm€5, a apyr. piBseHHr - ABa xope$i: 0 j 5, roMy RopeHi npyroi'o pisnnFBq nF. Ro-
peEsM! rep oro.4) TaIt.5) Ta&, 60 aHi lep e, aEi apyre piBEnEHn Ee Maror6 riopeHiB.6) Tan, 60 trolcrre s piBnsHb Ma€ 6e3niq nopesiB fi o6tABa piBEsHEs6yAr,-nfti BEa.reliss t.7) Hi, 60 &opeHeM rep orc piBEsIrEs Ha MEorrinEi ( *j +-) e qucno 1, a ApyreEqEEn Mac pra KopeHi: I i l.8) TaK.9) Hi.10) Tax.11) Tax.
nopiEb .r - l. roMy BoHU pisHocMi6lri.13) TaR.
199. 1) TaI{, 60 KopeHeM xoEclroro s l{t{x € qrcno 4.2) Hi, 60 Depne piBHsHEs Ma€ aBa rcop€Ei: 0 i 1, a Apyre piBHsEEn oAxn HopiEbx=1.3) TaI..4, TaK,60 r{oAlte r piBHeHb ne Ma. HopeHiB.
2) PiBHssEE piBsocrnbni Ha MHor{nHi (-*; +-), 60 (opesi repllloro piBEnHHn2 i -2) € KopeEsMn apyroro piBri.flEn.n, i EaBnaKrr: &opeEi apyroro piBlI.sHH.s (2 i -
36
r-6
278 i::IiAIrEEPA Mep3rrKA. r. ra iH. AKaaeMi,{H]4t piBeHL
206. 1) PisssEgs.!'=.r s sacrirxotr{ pisHalrlr.E 5 = 1.
2) PiBssHHs r(r - 1) € sacriAkoM pilHsHss.,.'? + 1 = 1.
a) piBH'HHe ,r, = 64 c Hacni!{ord pt""'"'" _i.8 =;],
4) PiBHeHHn r:=9c Hac,linffoM piBHflBHn r^- J ^ s, 1-.a+3 ,+3
207. 1) PiBHsHs.s 3r - 5 = 1 piBEoc',rElre piBHssEIo t = 2.2) PiBssHss (:r - 3)(t + 2) = 0 piBEocrnEEe pisHgHsrc i:'- rc 6 = 0.3) PiBnsrIIIs 0 . r = 0 i 3r - 5 = 3t 5 piBlIoclrnblli.4rPiBHqhHr0 jr- I i 0 .r=3 - piBHocr,rbsi.
208. 1) (' + 3)fl') = 2ltl + 6, (jr + 3)(flJ.) - 2) = 0. IIe pi:gssgg naae KopeEi '=13
213.1tx,+t-6=0, x,+x-6-(r+3)(x-2);
x,+2x-35= ( t2-2x+ 35)= (r+?Xr-5);
3t2x'z t gx 18 0:D=81 -4 2 ( 18) 81 | 154=225t,r, = -9-15
'4
,"= j#=+= 6; zx, + er . 18 = 2(x - |)r:u + o) = rzr-axr+o);
4) r' 16x+3=OiD=16' 4.5 3 = 256 - 60 = 116; ,, = 19# =
'f, = +;
,, = tu;tn
= r. sx" - rc, + z = s(t |)r,,r = ru" - rx" - rr.
6. MeroA iHTepBaniB
214.1) (i + 1Xr - 2Xr + 5) > 0;r € ( 5; 1) \-/ (2j +*);
2, x.(r 3)(t + 2) < oir€( -; 2)u(0i 3);
3)(r+7xjr+5Xr-9)<0;J' € (--; -71 u [-5 91
4) (.t + 3)(, 8Xr - 10) > 0;r€[ 3; 8] u [1; +*);
5) (2, + 3X3, 1Xr + 4) > 0;/r )x€( 4 1.5)!, ::+-:\3 )..
6) (2r - 1X3 jr)(ir + 1) < 0;r€( 1;0,5)u(3;+*)i7) (r 6)(7x + 1X2 - 9r) > 0;
( 1)x € :; _
= l\_r [4,5; 6];
8) (r 3X2r + 1)(1 5a)(:r + 4) > 0;f r\ fr \rF 4i -Lrr -:il\,2)\5)
215. 1) (r + 3)(x - 1)(.! + 4) < 0;t € (--i -4) u (-3' 1)'
2) (t - ?r(t + 8)(r - 12) 2 0;r € [-8; 7] u [12; +-);
3) (3r + 2)(, - 5)(4r 1) > 0;/ 2 r\
.r el- 3: aJU
rbi + @);
+.r, = -1. fr= a.
'x,= 6: Lx=2i2r-35=0;
lx,
2135-2x-r'=0;
)r, + x1= -2. lx =xr 'x, = -35: I r. =
32'
/lii:l:.:{.!:.i:,!!it:l:i'i-:a.a:.i::::i::
i Rop€Ei piBEsEns f(t) = 2. ToMy, sftqo qe pitlrssHJ' 3aMin'rr FIa piBHsEEn l(.t) =ro Mriox{{Ha xopeHiB BBysurLcs.
zt,gn.qo pluoono" I(') o raMiHr.,ru Ha piBusHss f(.r.) u. ro MHor{,rnat'+1
3) PiBETIIHS (r + 1)l(r) = r. + 1, n&e Mo)KEa sarrcarta rall: (.]r + l)(f(r) 1) = 0,rrMe 6irBrrle nopeEiB, Hi,{ piBEsHEs t(r) = 1 (qe r = -1 i (opeHi piBEn'isn flr) = 1)'ToMy MHor$rrHa xopeHiB sBy3rrr.cs.
q f(4. c(x!. Uc piBHauH' Ma€ kopeHi. nxuro x F -1. PiBh'HHt /lx) = s{.rr'i+1 r+1
6i,rblll xopeHiB. Hi]l. raHe. 1o\ry MHo)}{HHa nopeHiB po3llrtrpltrLcs.
209. 1) HepiBHicrb r < -4 € EacniaKoM rrepiBEocri x < 1.
2) HepiBHicrL r > 5 e HacniAEoM IlepiBlrocri, > 5.3) HepiBgicrb r' < 0 e IracniAKoM EepiBnocri r < 0.
foryeMoca Ao BnsqgHHg HoBoiTeMx
211,1)(r-5)'z>0,r€( -; 5) u (5; +*);2) (t - 5)'> 0, , € ( -; +-);3r(x.-5t'<O,)c€A:4r(x-5)'<0,x=5;
s; I :-l | > o. r.. ( -: -5,,, r-5: 5r r. (5i -t:
o; lll >0. ie ( -i s)L,r-5:--r:.r+5 t r.'5 2{r r5l - x-5-2r-10 ^tt>-'-<u.<u.'xtb 2 zlx -51 2tx+5)
r €( -; 5) ! (-5; +-);
8t +>O. jr€ ( -r O)u(0: +-l;
sr *:0. r=n.x'+ l
212. 1) Ocxi"nrxu .r e (2; +-), ro sEa.{elltls Bvpa}y , - 2 € AoaarrilrM;2) oclcirbrir r € (-3; -2), ro sHa.reH1is Btrpasy x _ 2 € BiA'€ME!iM;3) ocEinbrir r e (--; -A), ro 3lra.reEns Brpasy x - 2 € Bi,q'€MIrnM;4) oc&irErcr r e (5; 9), ro ssa.resHs BrIpa3y .t - 2 € AoAarH{M.
28o llJ: AITEEPA Mep3reKA. r. ra iH. AKaaeMlrxrr piBexu lililillli::,'.:i;X
-GG€5 1
- -\,,-=\7':\/--+j--ffi-:
- -)/-_. -Y--- -Y-a -
-7-50:t----Y--i/-=)/-+ ,
3 a 10 x-
- \,--F\/-:-\/'-- ti---t-i-23
---T-\,.-- \-,--f\-z---1
--;\/' \,,--T\,,---+-------- +-1 4,56x.7
0,5
.x 5 .r+5
-<u.
2(x + 5) 2(jr + 5)-4!!3
215E4
--\./-iv. \,,-+---1i----i--1'- r---Y-lr-=Y-
-a712-----l\ 7_i\ /-='\ /7------{.--------fF - l<
:iillliilliliii A'IEEPA Mep3rrK A. r. ra iH. AKaaeMi,rHrt piBeHb tl! 281
4) (1 3'Xjr + 2)(3 - t) < 0;
/r )r€( -: -2)ula:3]i5) jr(s rX6 - r) < 0;n€(-; 0l u [5;6];6, r(sir 3n2 ,ll1x 3l(.( 5) 0:
rEr-: 5r L I , ?, ol ,19, ,1.\ 5 ,r \4 ,/
216, 11-<0, r€ ( 7;8)r
z; 11] ' o, ' € (-*; e) L, (11; +-);
3, ' -2'4 o, ir ( --; 2,4 | (3.7: -):
ar
-10.
r€ [ s.2i 1.,1):
5) -:
0. r € [5: 6]r
6t 6r I 3 6 o, ir - ( -; 0,6l (0,5: -):2,5 - 5'
-. {r + 15Xr. - 2) - ^r-15
I _<U. r.€{x + 5l{r. I6)
rir + 5.4nr + 4.2) ^9t 2U.(12 - rxx 4)
r e l-5,4, 4,21r 14;12).
\ /--+--\?-- -\/- -
ti3a
+\' -\..-"-\,,- \ 1i€53032)c
54
-=-\ .,-'-,.I 11
r----y'---.\:1,'= -
2,4
-,i -:-{+
=-\J'1-fl-0.6 0,5
- )/-tr)/--)t- .1s 2 15 '
:.zfr.- -)t-+ -5 3,8 16'
)r+-Y--v?Y-,-5,4 1,2 4 12 r
+ -\..-- \€-3 1ic
l--\-,-- --\,,'- +
--j -; -
)cG41 ,4
--Y-li--\ra;-r,2 1,4 1,6
-AAr-1,3 1,9 2,3
'' 13' ^2r4--ll .0.
" .f r, il t,,0,,(x + 3Xr 1) I 3,/
sr latlq llso.(8 + xX10 r.)
r € ( *; -8) u [-1 ?] L, (r0; +-);
u, (x+1)tB rt ,n(3x 2)(4 3,Y)
/n r,xer-: 1lul1;:] uta: +*r.
-\7zl\/- \,'-i\/-3214
3
-\ /-?\ ,--\ z-+\ Z-t+r--ra17t}x
-1 243
';:l !ii::!i
i ii:':i.:.!!:.:
'::l-!]i!it:.
2'tz.tt * 1 ,0, '. r -;.3, (t; -):i-1
21 L. g, xel2:o)i
3, :] 1>0, r€( -i0)![,t:+-]r
{x 2l(x+1) <0. r€{ -i 1tu{2:4)ia4(r+1,2Xr-1,6)<o.
;n 1,4( -r 1,2] L/ (1,4; 1,61;
->ll
(1,I rX, - 1,3)(-*; 1,3) !r (1,9i 2,31;
2) (jr'? 6rx.r' + 5n - 6) < 0;r(r 6xir + 6Xr 1) < 0;rE(6;0)!r(1;6)iJr {x 4.r 3)(jr' 31 2) 0i =\ - -l(r 3)(r lxx+1Xr+2)>0; -ffijr€ ( -; 2lu[ 1i 1]u[3; +-);4) 4r1 - 25r 0: x(4x 25, 0; \/'---'\/'--\/'|x(2.r-5x2'.r-5)<o; + a--;--"r. € (--; -2,5) u (0j 2,5):
- x-4 - lt 2x 2t -5) 0. .0. r-v.-\,/-l\,,--\Zi.' I (r 3)(r 3) --i.
!-lre(-; 3)u( 2; 2)u(3j+-); -3 2 2 3 a
r' 3r rrr 3r6) - r0- : -' 0- --:\,.-- \ /--\ 7---\,.-_J. ar ; (r i,(r l) ----.-1- t-irE t0; r)ut3;7); 0 1 3 7
7) '=-:'- ' :0, l) 2x 5x 2 o, D 25 16 - I,r' ,1r 45+3 5 3 l, - - 2. 0.i:2lrr 3"r-1=0,'4'42
lx I 3. fr a. 2,r.-2xjr o.b, ^ }A'QA€-lr r 4t ! l: rir 4r{x lr v l I 2 4 tr € ( -; l) u lo,5;21 u (4j +*); 2
- x 16r - xtx' 76t8). ..0. -::: - 0. -\./-.\./---\",'\/'--\,,-jr r 30 tr 6X\ r5,,rr 4lrr+4i 5 -4 0 4 6 x
219. 1) (:,r': 6axr, 10x + 9) > 0,(r 8Xr. + 8)(.r lxn - 9) > 0,r€ ( -; 8lu[1; 8]ut9; +-);
2) l" + l;\@'z 7i. + 6) < 0,ir(x + 7Xr 1)(r 6) < 0,ir€ ( 7;0) u (1; 6);
x! t 12 rr+3lf,-41lJt _ <0- <{l-x' 36 (r. - 6X.Y + 6rr€( 6; 3lu[4;6);
7
_T)AOG46016
-)f-f-.)/-)/-r,--i\,,- \,?-\./=\./- +
l-V-)/T-y-Y-,-6346
[ 15i 2] u (15; +-);
( -; 5) u [3,8; 16);
-84)
5)
6)
--Y-1rl-G€
218. lll\ 2l{n' lr '0: (x 2)(-r I)(r l) 0: -V----\.-'---\,,x € (-2; -1) u (l; +-);
= --i-i -
242 iiii: arregpl tvtepsneKa. r. ra iH. AKaseMiqnr4i pieexr iii::::i:;l:iiffii;: i::!:ii:!ii:iiiiij: AnTEEPA Mep3rrK A. r. ya iH. AKa,qeMi,{Hrai piBeHb iai::t 293
T
11-\ /-:\ /-\ /l\ ,.-l
I a{ J--.....a',1----
5) (.' - 3)'(x' + x-2,<o,(r-8)'2(r+2Xr-1)<0,x e (-1; 2r;6) (a 3),(r, + t 2, < o,rx 3f{r 1)tr 21 10,rE[ 2; 1]ui3];7)(:c-')'(t')+x 2)>o,(r.-3)'(r-1)(r+2)>0,r € ( -; 2,) u (1; 3) r-, (3; +-);8)(,r-3)'z(r'2+'-2)>0,(r-g)?(r-1Xr+2)>0,r e (--; 2l u [1; +-).
223. 1) (r 1Xr + 3)'z(r 2) < 0,x e (1t 2ri
D, 41(x + 1X' 3)>0,jr € ( -; 1) u (3;4) u (4; +*);
3\(2r+ I\'(r'z 4, + 3) > 0, 1) x, - 4r+ 3 - 0,
fx,+',-a. lx =1.
1,, *, =a, l'=a,(2!+1),(t-1Xr-g)>0,, € (-*; -0,5) u (-0,5; 1) u (3; +-);q Qx + t)'b 1)Qe 2) > o,r e ( -; -0,51 !, [ 0,5; 1] u [2; +*),ro6ror€(-;1l!J[2;+d);5) (r - 5X, + 4)(r.'+ 6r + 9) > 0,(r 5)(iu + 4X, + 3)'> 0,, € ( -; 4l u [5; +-) u {-3}.
224- 1\ t'(t + lxr - 4) > 0,r € (--; -1) u (4; +-);
2) (a - 3)(r + 2):(r - 5) > 0,r € (--; 3l.u [5; +-).
zzs. t1 '',t l- 2l , o. {' al(1i.1 ' u,x'-6-r+9 t,r 3)'
re( -; 5)!,(4; +-);t'+t-20 lr-41(r+51zl -. >0.
->0.
' .r'-6.r+9 (x-3)'x € (--; -51 u [4' +-)'
(r+ 3)(r + 6Xt + 5)> 0, x e [-6; -5]u [ 3; +-).t' 4r+5 =0.D=16 20=-4 <0, a iBir-kr.rr rapa6onE HanpaMnelri Bropy, roMy Blrpagr' - 4, + 5 llplti.tM e AoAarHi sEa.reHHfi.
222.1) @ q'z@'- ?r+10)<0,(r - 4)':(r 5Xr: 2) < 0,t e (2; 1l w (4t 5);2) (r - 4)'(x' 7r + 10) s 0,(tc - 4\'(t 5\(E - 2J s o,x e 12, 4l v L4t 5l - l2i 5l;
---;\ /--:-\ ?---\ 7----:{-
I21Bx
-T\,/'-\r-?\,Z-
_-;\/_:\.2=\/--r i r----.r+
2tB'
--F\/-T\,,'-:\------t---ra-- i r---Tv--i\-.--r\,,- +----1i-i.-i-
1-t---Y--/-r\r-T,
112,.2
-F)/-'-)/----vTl-4-3Ex
2
, r, / 1 \3)(3x 5.r - 2r2x'z x l) 0:3[.r' 6Jtr 2t(2x'-x-1\' 0' .rcl-E:2Ji1,2r'+ r+ 1= 0,, = 1 8 --? < 0, a aBirnr' trapa6onr saEpsMneEi Bropv,roMy trpr .I € -A MsoroqneE 2x' + :c + l rplrllMae AoAarEi 3Ea.reHnfi.
2. 3x' - 5x - 2 = O, D = 25 + 24 = 49,5 7 1 5+7 -. r^=-=2,'63'6
1-5a)(4 r)(3r + 1)(r* + r'z+ 1) < 0. OcRinEKIrJ.'+ 12 +l>O, r€ -R, roaaHaEe-
221.t\rxa+1)r5 6ir)rx 2'.0: x.[ -,i) -,r,-*,.Bapa3,ra I op'fliMa€ ao.q€rHi rBaqeHHr npx - -\?---V. -r € fi, roMy AaHa Hepisqicrr pislocumna Hepin-
-i--
-{-,Hocrr (.( sxr 6X.r - 5) > 0. 62\ G + a\k + 6Xr + 5X" - 4r + 5) > 0. 4n HepiBEicr6 piBllocr'I'6lra EepiBnocri
\,/'+-\/.'\//---1t--=- a'---!-i\z-- -\?'-:-\_t_t_ _i_____
- i\ ,,-=\ /-- \,2-+--'3---a--r -
3)x'z+x-2O - lx 4Ix+5) -
-<u.
+<U-.r" 6.r + 9 11 3)'(-5; 3) u (3; 4);
x'z+t-2o4t -. <0.r'-6r+Sr e l-5; 3) u (3; 4l;
--l-\,,--=-\,,---_---113-2
1x'z+2x-1 -4l
-zu,a) 3x' + 2r -1 = 0, D = 4+ tZ = rc, t, = ]# =
q Axt - x - 4 = 0, D . 1 + 48 = 4e. '- 1:!=t.
8
>0,
, e r--; -rru( i, il"o, --,.
22O.1\ (2r + 1)(x - 3xr'9 + 4) < 0;
2) 12 - rXSr 5Xr' - ir - I) 0i .r E\ 3 '/'
'x' - t + 1 = O. D = 1 - 4 = -3 < 0, a (BirIiIt' ra-pa6onu EarpsM,'reHi Bropy, roMy piBsa1lH-t Ee Mae
l(opeHis. MBoroqneH.r'z-r - I DpHiMaFroAarHiBna.reHss np}l t € R.
3l @ a)'@' 7x + !O\ > O, t e (--; 2) !, (5; +-);4r(x- 4)'(t'- 7a+10)>0,re (--; 2l u t5; +€) u {4};
2 1 2-4= -1:63',6
1-7 6 3
'aR4
-4
".( ;,r'
---+-\,/- -\,/-=\_/-+-----1i--1--a -r)/-),G4
-T-v-:)z=)/T.534r
284 iia; AnTEEPA Mep3ncKA. r. ra iH. AKaaeMieHxr piBer" ii::ilfiili!:l:ii:i ::iril!Jil1.;iit AITEEPA Mep3reKA. r. ra iH. AKaaeMi,{nrai piBeHb ltt 285
=-.,,-- \,-' \,/--.-.-!+412
E-a€14 1t--aA€
412'
)/-+-Y---!-r;745_
t:+2t 2 - l-2r+2 ^,(j' - 1) ,(' 1)
Mroroqner J.j 2r+ 2 nptiiMae aoaarHi 3Ea'relrE.a trpl{t € -R,6oD=4 8 = 4'oi iBirIiI0 napa6ontr y =f 2x + 2 fianpflM'leHi Bropv; xE (0;1)'
286 ::::::: A]nfEEPA Mep3neK A. f. ra iH. AKaAeMi'rHral pieenu :i:i:::i:i;iiiii:ii::i:i:i:i
224.1') (2x + 3)(1 - ar.)a(, - 2)3(r + 6) < 0,x e (--; -6) u (-1,5; 0,25) u (0,25; 2);
2) (1 3r)3(r + 2)?(r + 4)r(,. 3) > 0./r \r.€{--:-4)Lr r3l.\il /
3) (rc': + 2r' 15xr.':- 4r -f 3Xx - 1) < 0, (x + sxr 3Xr(.r r. sxr 3)'2(r. 1)i < 0.
2. v=-5,1. r'|t 2r- 15=0: I lJ: r 3i
r, r 4, x 3,..1. x'? 4x+3=0: I
1,, ,. 3, I' r:
rc(-;5l',/{1;3};a) (1 2xxr 3)3(2r + 7)6(jr + 4X, 2)'z> 0,
/r lr. €1--: - 4)!I t| 2] u (2i 3).
229. 1) (3 r)3(r + 2)r{x 1)(2x 5).- 0,jr € (1; 2,5) Lr (3; +-);2) (r: a)(ri + r 2) < 0,(x 2')(x + 2\(x + 2)(r r) < 0,
- x 2-t I lr lr lx l') 0.br , '2, 8 (r 2r(i | 4r' r'' 2nr I ll
a E (--; 4) u (2i +-)i
n, I 2"+1-n- lx-ll': -0,- .r' + 2:r 8 (x 2)(r. + a)
re(-;4)u(2;-r*)',11);
-r r-,2.x+1<0. t" lt _0.'' r'|+21 8 (jr-2Xx+4),x€(.1;1),J(1;2)j
R, r ?{lr. o. lt lL.0.- x +2r I (r.-2)({+4)r. € ( 4; 1l L, 11; 2) = { a; 2).
226.t, x 2 3:t t 4 , t! Zl (3" 4)
0.f,+3 x+3 x+3
21 2 o.2tx-r'n,, 1 1,,.r_( J:tl:r+3 r+3 .j.+3
2) t'*3i: 28', f, +3jr 28-0.xb
i\. 4t(.r,;) u. r_l?;41 L;:,_lrr5rl 1. r, 1-I. o,
ir € (-*; O) u (1; +-);I 1 2x-r 3 ^ x-3o'
' -, , -r,r-ri o r;; ;, o
i. e (--; 3) u (3; +-);
r € ( -; 1) u (0; 0,5) u (1; +-).
7,2_ | .1, 2(n lr '_1,, tt.O..{ I I r(/-r,
r€(*;2)u[1;+*);]1 L22. '-2(r'+l)-0.r+l x+l.re[2;-1);.,1 5'1!.2, 7'+8 2G !\.0,
1a4xxE(-j0)u(4;+-);
x-2x-2 x 2 r+2>0. :0. <0.r+1 r+1 r+1
5r+8 8+21 7r.0_ < {l-4-r 4 t
--GA44,5-23'
227. tt I r. I (r 2) o. l--'.2 o. ' I o. '-l .o-x 2 ,,2 r,2 r.2 x-2
1111111\l
.!!!!!!:4Il
ir::::::::::::1$31
,, 2 , 1 2(x-1, ir+3) .n' j+3 .ir 1 (x+3r(x 1) ''.. e ( 3; 1) u 15; +-).
(jr - 2)(r + 2)'9(r. - 1) < 0, x € I1i 2l\J \ 2j:3) (ir3 ar)(ir'? + 21 8xjr'?+ Ijr + 10) < 0,xlx z\lx + 2)O + a\x 2)(r + 2xjr + 5) < 0,x(x 2\'(x + 2)'(r + 4X, + 5) < 0,x€( -; slL]t a; 0lLr{2}.
23o. r, 4l !11'1!l , o.(x 8XI 4t)/r \t€r 5i 0) u lt; 1l ,-r(1t8lr
2t t' 2{?!l!, o.(3 r)'(1 sr)'
I tt lt rI€l -; lul r,l:
:::::::ii::iiii*i: AnTEEPA Mep3nqK a.
2x2x} 15> 1,.
-- : tl.
(.r + 3Xr 1) (x + 3)(r t)
\?-T\/- \7' \/-+631,
ti
5+ 3Xr. + 1Xr 1) < 0;
)/G)t--.)/-r ,513n
., I 3- x-3, 3rr. 2i-0. r 3-3r 6 0, 2- 9-.0."'x'2 x 3 (r. 2)(J-3) lr 2){t 3) tr'ztt:t tt-2(j.+1,5) <0,(t+2\/'-3\
r € ( 4,5; 2) '.r
(3; +-)i
0,,_l ,_ I Z, lr-l|n! ll ,1..1ll 2irlir l) o.
xl x(' l)
r." 2x+1 '"'-r' 2r'!+2x <o, ,41: jrl!<0, 1"trJl;\.o,
:,l](x 1)
2a" + x-7 >o. 2x!'t r 1=o,r=1 +8=9,r(r 1)
,1 3 -1+3 2 1t *"= n =l=t'
- +--\7-:\,,-_\,/-+\ /-l\ /-4 ,1
2
-*--d-lt-\,1r1-2 12,5 3ir
+)/--+\/- --)/-1 -
272l.
--Y-.')/--Y-)/-r)1 ,5 2
-1 0112
2x 2-r x'+r >O,r(x -I)
0114
1123ti
+\/' \,-f\?- \z-
f. ra iH. AKaAeMi.rHLah pis'e{b tiii.. 287
n, ,'la' llg + zt =o,
st !- :ya' - 11.. o, , . [- 9, - z] - t,r, , *r,(x-3")(x+1)' L 4 l-\ /.=\ /.=\ /_;\,,---dIIa-
-1 _i_4
)AAOG30l2t
= (:; 3) !, [o; 2); 5
^ (jr 6)3(,r - 4x6 - .rtrj)
- -, >0.
,r+5tr€ (--j 6l!t 4;61.
rii,iifiiiililli.;i!ili.:i-ii z3r . rv t* - "'*^ .'-r . o.i, ltl;: .:.:i.i:.:* l.n - itl;;:,!tj::d..i!itj x. [l:21 .r[2:3)=[ri 3r:
ililf::;i"t+li 2r rx-1)'?{x+2)3 >0.,iilii-::.!1:ri!t Y , 5'i::,--::.i::::::ii.:: r._ t _t 2, . (5: _-)u{11:
3t !'lt' ll . o. 'r'?lJ' - I,(r' - U , 0.r 4 x-4.r € (-1; 0) u (0; 1) u (4; +-);
{r l)':{t 2)'t'Y 3}i < 0,4'_--
J' e (0; 1l u [1; 2] u {3} = (o; 2l u {3}.
z1 1r'-g,["" nrO. tvtu"*o 1[La'0, sliqo r € ( -; -2) u (2; +-) -3Eari Aanoi HepiBHocri sen€nirrr, BiA sEaxa Brrpasy .r2 - 1, rorry r, - 1 > 0,(x lxju + 1) > 0, sRqo r € (--; -1) u (1; +-). I]eperEEoM aBox MHo]r{Ilrr € Mrro-]]{lxrar€ ( -: 2)e(2:+*\,BiAnoqiAb: t. ( -; 2) u (2; +*).:1 1r'-rluft 7<O, posB'ssnoM e.r=12.Bdnoeidb: x . !2.4) (r'z -1)\rV 4 > o, posB'ssnoM e Muo,rcr.rEa ( -; 2l !, [2; +-).BiAno6i6b: te ( -; 2lu[2;+6)S1 1r" - Sr+qu7 lt*tO<0. Snan sapaay
.,tt:t;lo aoaar''i Ha Mso rlr*il,I -( -:2\v(5t -). royy AaHa HepiEEicrb Bn-KoHy€rbcs. rRrlo (-r? 5r. 4, 0 Ha MEoxfisiM. Orrfte. lx 4X.r I ) 0i r. e (1i 4r. SHafiaeMonepernH MHoxrrs M i M\ (lt 4). -v e (1: 2).BiAnosiAb: t€ (1;2).t7 1"" - t, + t1..,Q 7a11s,s.r€(-; 2)u(5j+-).
-65 4
\,,?\,,-T.\?'=-\/--
+\/'=\ /z \ /=\/1-3--i---t-1---
233.1) ?E:j) < 1:, 2G - 3)(' 1)-{'-6)<o,
r(x-6)('-t)
tQe 6)(r -1\t'z-2r+6
< {)_ < {)./(' 6XJ. - 1)
MnoroqneE r' - 2, + 6 npd;Mae AoAarni sHa.relrss, roMy sHa& Aalroro Apo6y sa"'re:
){rrrr, BiA sHaKa sllareEExfta, , € ( -; 0) \-] (1; 6);2a-3 1 2t2xt3t rx'/,x -t2l2i"t'+x-12 2 !'+x 12
r:+3:r+18 - -{,!"-Jr-18) -
-<u.
<u.tr + 4)(jr 3) (.r + 4X.r - 3)
x+12 <0,(r+4)(r-3)--T\,,--\,4\,/- \,r--
-4-336t1"-6lI+,0. r - ( -i 4) ( 3i B) ,(6: --).(.r + 4)("r 3)
zs4. ti @' -\JV - +. o, (* rxr + r)uG zX,+a<o.3sa,{eHHr srpary rr:4 ic}rrr.nrcuox' a-0. ,--\/'-=-\/-ro6ro Ans r e (-*; -21 u [2; +-), ane aana l{e- t--- --piBHicl! He npper6a'rac piBHrcr6 Hyiro, rovy ir
po3B'ssxr yKarlrMeMo Es MEoxIrHi ( -; 2) u (2; +-), Ae 3II"*"""o \f,L A t O,
roAi snari AaHoi HepiBHocri Bane)&arlrMe BiA BsaRa Blrpasy (t- f)(r + 1).
--- +---\---- --
---1i -i -
--+-\-,--=\-zT------i-i ---
SEan Brpasy Jl-?r.10 aoaarnri, ssrqo
Ba yMoBn (r2 - 5r + 4) > 0,
1:-:;!i+zyr-n>0,
*.,:, tt.,,fo, ll.,[], r'lL UI tU ,/
-1
AaHa HepiBHicr6 BsrcoHy€rr.cs Ha rlii MEorr(sEi(r 1X, - 4) > 0, snrqo r e (--; 1) u (4; +-).3HafiAeMo treperrH MrrorlnE:ir e (-*; 1) u (5 +-).BiAnogiAb: t e (--; 1) u (5; +-).z) (tc" -rx + +r.[x" lt+ to< 0,, € t1; 2] u {5};
e\ @" Sr++\Jr' -Zx+tO ) 0, .r e ( -; 1l u t5; +-) u {2}.
"-' x(z-6)- t 1'2z'-6x-2x+6-x'+6r
235, 1) (, - s){4 + 5r - ''z > 0,
jr e (3; ?).-x2 + 5x + 14 = O, t' - 5x 14= O,,=25+56=81,
5+9 5-9-I 7. ,t z - -2. Ha usoNntti (-2i 7) uryxaruMeMo po3B fl3xn nanoi
EepiBHocri. 3a yMoBoro MaeMo: jr 3 > 0, r > 3.BiAnoBiAb: zE (3;7r.2, (, - 3rJt4 + 5, - "" > O, o!:s. , e [-2i 71.BiAnosiAb:
': € f3; 7l r., {-2},
-- 7. X---\29z'
-----a21) )'7-7v'--.2-/A7'
t.' - sttx + srfa - x1a -'1 . o.u/i+ *rre xt 'o --\,..+t\,--_Ea MEor{rEi ( 4; 4), roAi Arf, BlIroEaEE.a AaEoi -------------- +EepiBgocri troBr.rH'a Brr.orryBar"J;;;l;;l; -4 4 x
x' 25. o.lx 5)(-! 5) 0. r. c (-5: 5). 3safi. - --:--\ |
AeMo reperr.,E Maolrcr*: r e ( 4i 4\. ----1i':"": ----BiAnosiAb:te(4;4).
iii:ilillttilii: AnTEEPA Mep3rsK A. r. ra iH. AxaaeMiqHrn piBeHb i{t 2a9
l0 Yci rnP, lou.,r.l
al (r - s).,,/ia + 5" - '' <0, sxrlo .r 3<o,r<3Ha MEoxcnEi (-2; 7), 10610.' € ( 2; 3).BiAnoqiAb: re ( 2t3\.4, (, -3r^114+5, - '" <0, srcqof,-3<0,r<JEa MEo,{rI{i [ 2t 71, ro6ro r < t-2t 3] u {'Il.Bidno4iAb: r e t 2;31 u{7}.st @" - zlJta - ,' <o,
UIo6 6yrTa BqRoHaEa yMoBa, rorpi6Ho po3B'fisarxIIepiBHicrE (, 1)(r + 1) < 0, x e (-1j 1). 3Ha;AeEaMHo'lrrria IIe rlan${Ifr6 MI{or{I[d (--; -2) u (2; +-lrovy aala scpiBHicrb Hc Mac porB'rrtsiB.BiAno6idb: E.piBl{lcrh He Ma. porB arKrs.
z8s itjl! ArrEEpA Mep3rrK A. r. ra iH. AKaaeMieHrt piBexr tlililllllilitli!
o) (r' zs).,/io - '' '0, '"pu" .,/io - '" 'oHa MHo)n si ( 4: 4). lqo6 46Ha HepiBHicrb BU-
xoqysria.F. troBfiHHa BHKoH) sartrc't HFpiBuiclb(x 5\(r + 5) > 0, ,. € ( *; 5) \., (5; +-) BEa;-AFMo nepprlrH A. AaHa sepiBHicrb He
Biano8iAb. pos3'ssftiB EeMae.
r\ @" zli|Jta - ," < 0. Aalra EepiBHicrb BnrloHy€r6cs, sKqo 16 ,' > 0 na MHo-
rc'Eil4; 41,"G'-25)<O,(x 5)(x. + 5)<0,jrc[ 5; 5].SHaiiaeMo reperrE MIIonitrE: , E [ 4; 41.
.[aHa EepiBnicrb Brriolly€rbcn, srcqo t e [-4; 4].BionosiAb:tel4t4l.
ay 1r' :r).,/ia-l <0.PocB"rsIloM AaHoi EepiBtsocri!5al4i4l.
236. -L s -L.x'-9 r" I
+4, 60 +4 € [-4j 4], a 3Ha.reHHfl
," gt t" -g'-{ .o-
--+-\ _-.',-'+.5\- ---zs x
.-\, -a--a5-445x
:-\-/-+-\7--r-\-/--ti---t- 1
BnpaBl,l Ar9 noaropeHHt
1' r:f ::':.:.:.:.1:.::
10-2x!t= 5
4 " =9
'' \e, +zs = 61-6-3rt, ,
'. ]*' e-''-e'uooz.
ln:=o'Po3B'fir{eMo c creMy:
[.' -,' .0. 19".0.r, l.r'-e .r' e lx'-el=:."' l=:'o'
r. € ( 3; 0l \.r (3; +-);
24O. 1) lv ,' =,,I2x+5s=ro:
t " ' lzx,, ]'' s "'-n=u ]t n'u,_r.
-j-. o, i-5. o:tr.'-g |,r'-sBi1nMiAb: t3.01 u (3; +-).
. lI-1 -o. [ll.o."-.1+1.,:-:u' l',,-iu r,,-, j1",',' x t
1,, ro -
*^ _ rs, 1,, _ ro. ,. lo.I r-1- .o,
Po3B's)+rFMo rr.{r'reMv r,f, ]*"u x - ( 4i Il' (4: --).llr
; 'o
o'
I r-1-- -0,P..'R excMo.r.reMv r2r' ]'' I6 x ,..
'"^ 1'o:r? - 16
Bilnosilb: (4;11 u (4; +-).
290 ai{: ATTEEPA Mep3neKA. r. ra iH. AKaaeMi'aHxi piBexr {iii:lliil:iiilti
BiAno6i0b: 2 napv. (r; U) | G,: v).
l6241- u=1 x
lr',snqor'-t.BiAnMiAb: qy'lr{\nr 3pocrae Ea npoMir{Liax( -; 1l u [0; +*); Oyslrqis cnaAae na npoMir*xy ( 1; 01.
BiAnosiAb: crrcre!\a Ee Mae
:il::iJtiilitiai ATTEEPA Mep3reK A. r. ra iH. AKaaeMi,{Hui piBeHb i::]i 291
l0*
BiAnosiAb: x=-1, a=3-
BiAno1iAb: , = 2.
s3. cTEnEHEBA OvHKqlC
1. CTeneHeBa OyHxqit 3 HayypanbHirM noKasHt(oM
242. v = i6. Toql(a B(2; 32) Eate'Iirrb rpaoiRv OvErcqii v = t5; roclca D ( 3; -243)Irane){r{rE rpaoiEy oyEnqii y = ,i.
/ r r)243, rpaoiK QyFrqii y = .r' rpoxoau rb sepe3 roqKn: A(2: I 6)r Cl - i: -8
t.J.
_12 _3244.A12i -12)t t2=a 2t. a , i;.r= ;.
3ncn a - - i rpa+iK Svsxrii v = axa opoxoanrb sepe3 roqKv,{.
'" '-st'=
a'B(-8i 3): -3 = a (-3)', a = -. =(-3) 271
nor a ' -fi rpa$ix (DyHHaii Dpoxo4 r!, 'repe3 roqRv B.
_1a 2245. C(3: 18): 18 = a 33; a
3- 3. g: = J
fipri a = -: rpaoilt SyH$qii y = ai3 trpoxoAxrh qep€ roqnv C.
64DF2;64\:64-a (-2)", a _-=-8.tlpu a = -8 rpaoiK O],slcEii y = af npoxoar'rrr, 'Iepe3 roq}tv D.
246, f(xt = x's,1) f(1,4) < l(1,s); 2) f( 7,6, > l(-8,5):3) l(-6,9) < l(6,9); 4, f(o'z)'> f(-12\'
247-ftx)=x.1) l(20) > l(1?); 2) feaa, < f(1,5\',3t f(-52\ < f( 45',.
24a.
^x, = x'zo.
1) t(s,6) < l(4,2); 2) l(-6,7) > t(-5,8); 3t f(-2,4, = f(2,4\t 4\ f(-15) >
^2\.249. l(x) = r{.
1) l(9,2) > l(8,5); 2\ f(-t,I, < 1( 1,2\i 3) (1e) = l(-1e); 4\ f(-7) < f(s).
iso. '" = 1600.1) n - trapEe LarypaiEEe qlncnoi aBa riopess;2) n - EerapHe sarypanr'Ee cltcno: oanB KopiEl,.
.82251.1) 's = 32. r = 5i 2\ t' . -;7, x = -il
3) 'i =81; t=13; 4, ,.a=-16: xe O.
252, 1) tx = -27 , r = -3; 2) t' = 0,00032' x - O,2; 3) xo = 64, t = !2t 4\ 13 = -l'reA.
253.1) 16 = 2, rarci 2) .'5 = -3, rali; 3) t? = I, Ei; 4) t6 = -10' IIi.
,s4.[ ;J', i-?]', t ll', (-fJ'
255. (-0,48){i (1,06)'i e2,12)a', ( 3,25t4.
292 iili anrEEPA Mep3reK A. r. ra iH. AKaaeMi,{Hur piaeau i:3i1*ili:iJlit
256. r\ a = f iy.=zxa; x6 = 2a4, a1(z' 2\-o,x-o,,=-"E, ,="E; a =o,a = I,y = 8; (o; o); f"E; s); (.8; s).
2l U = ra i A = -27xi xa = 27x,a = o, t = -3: a = 81i (0; 0); (-3;
257. y = x6 i y = f , ri = ts, x3(z' -a,= O, a"= 1, ys = 1; (0; 0); (1;
t(x3 + 27)=0, t(x+ 3)(r' 3, + 9) - 0,, = 0,81).
t) = 0: r3(,r - lr(r + l) =0. r =0. r = l. r = -1:1); ( 1; 1).
258.1)a=x3-1i
3) a = -t";
5)y=(x-1)ai
2\a=@+
4)v=ra 4;
er,= 1''"2
3
iiiiitlillllili AITEEPA Mep3rrl( A. r. ra iH. AKaAeMi,{Hr4t piBeHb :iiii 293
lit! ::4.'ii:.ii::
' tit;ria!!i:.!
259.1\a=t3+3i2\y-(x-3)3i3)a=rn+2i4)a=G+1)\:
t"5\ Y= x',
6\a= xn'
260, 1) l(.!) = r's, js e [0; 2]. Ha rrBoMy npoMi,r.fty {DyErirris spocra€, roMv EafiMesIIIe
slla.rellHn Bolra np[IiMae, nriu{o, = 0, ro6ro 03 = 0, a Hafi6in]'ue - qtrqo t = 2'
ro6ro 23 = 2a 2a = 16 . 16 = 256.
2) t e f 2i 11. Ha qboMy npoMix(y OyHxIriE cna.4ae, roMy san6irLrre sHa.reHIIn
Bosa nplriiMae, sKrqo t = 2, ro6ro (-2)3 = 256, a nailMeErre 3HaqeElis nKulor = 1, ro6ro 13 = 1.
3) ' e [-1; 1]. .fl{rqo jl: = 0, ro OyEtcr{in rpl,liMa€ HaiMeEde sHaqeHss' 03 = 0'sknroJ' = 11, ro &ys!{qis rpriiMa€ Haii6irLre sHaqeIIHs, ro6ro ( 1f = 1a = l' 60sa rpoMixcxy [-1j 0] Bosa cnaAae, a Ea rpoMi]cRy [0; 1l - 3pocrae.
4) (-*; 2l. Ha qboMy rpoMirri(y &yllrlllis craAae, sail6ijIblnerr rre MornHa, a HaiiMeHlrre 3HarreEEs oyllRqif rprfiMae, sntqo x ='2' ao6'to
r 2)3 - 256.
261,1)f(rr=t5,re t 3; 31. Ha qboMy npoMi}}{ny OyExuiF 3pocra€, roMy Ea;6inblne3HaqeHnn rpriMae, sxrqo t = 3, ro6ro 35 = 243, a HaiiMeErre 3t{a'{eHEn nlcqor = 3, ro6ro ( 3)i = 243.
2) [ 2; 0]. Ha qboMy rlpoMiJrtl(y OynRrlis 3pocra€, roMy Hafi6inbl$e 3Eaqet{Hs tbvH-
Kris np iiMae, nriqo t = 0, ro6ro 05= 0, a EaIiMeIr e 3HaqeEEn $11\o r'-2,10610 ( 2)'. -32.3) [1; t--). @ytsl(llis Bpocra€, EaiiMeEsie sHaqeEHn trpriiMa€, sR[Io r = 1, ro6ro1r = 1. a Hai6inB]le 3Ea.IeHEn BKa3arrr He Mor(Ea.
262.1\ t3= r + 1- aBa 2)x5=3-2x oarrE 3)/=0,5r. 2 - ]Koa-
Ilopesi; lcopiHb; Irorc $opeEn.
266'.1\ xt' = a 6.y = r" - lpaoilr qiei OynKlrii cnMerpltqErn BianocHo oci Oy, y > 0.
a = a - 6 - rpaoiRoM qiei OyEliqii e rp€Ma, Ena npoxoavrb 'repe3 ro'rKv (0; 6).flRrqo (, - 6 > 0, ro6ro a > 6, ro pisH.nHH.n Mae aBa lropesi; sr{qo d - 6 = 0, ro6roa = 6, ro piBEsHEn Ma€ oAIrIr RopiEb; .slirqo d - 6 < 0, ro6ro lr < 6, ro piBEsEHsEe Mae KopeHiB.BiAnoqiAb: 1) a > 6, aBa l(oped; 2) d = 6, oar'tH nopiE6; 3) a < 6, xtoaHoro rcopeHn.
2)'^=a,+7a-8(1),a = *4 ryaOiK qiei Oylllcqii crMerpt'rErn BiaEocHo ocl O!, ! > O.
tbrrJ\oa'+7a 8=0, roa= 8, d= 1, roAi piBEsHrIn (1)Ms€ oAtlr EopiEI';.sHrqoa2 +7a I > 0, ro6rod€ ( *; 8)u(1; +-), ro piBHnsHs (f) Ma€ aBa lloperii;sllqoo'+ 7 8 <0,ro6rod€ ( 8; 1), ro piBEsIrEn (1) He Ma€ EopeEiB.Bionosi.Ab: tt:1"n\o (r € (-8i 1), ro piB1rnlrHs IIe Ma€ KopeHiB; nKqo a € { 8; 1}, ropiBEnHHE Ma€ oAlr]i RopiHb; nErqo o € ( -; 8) u (1; +-), ro piB}].'sH.t Mae ABa
lcopeEi.
267 - ts = 9a a3 (l).rpaoni Oysr{qii y - '3
caMerb@sr; gi{lloc:do oci Oa, a > O.
fiKqosa a3=0,ro6roa(9 a'z)=0,4(3 aX9+a)=0, a=0, a= 3ia=3,1opiBE.'riIIr (1) Mae oar.rE llopitlB.
i;;iiJiltiil!!! AnreSPA Mep3rqK A. r. ra iH. AKaaeMi,{Br'ti piBeBb ::i::: 295
26s. Iv = '"'l2x-s-3=o;
a=2x-3;,{oanoro KopeEF.
Ha IlpoMirftI(y ( -; 0) OyHKrriE craaa€,a Ha rlpoM { cy [0; +-) Bpocra€.
[x'.sxuox.o.265- tQ)= \ _
./r. nxxro ir > U.
na ,'poori*rry (--i 0) OyE(-qis spocrae, a Ha npoMi*rEy[0; +*) cnanae.
,, r,,, {r" axuo r ' -r'I r 2. '*nro x: 1.
Ha npo}tiniKy (--; -1) OyH Iis spocra€,a Ira rpoMi){Ky [-1; +€) cna,qae.
I:r'.sxuor<0./(r) = I -lJr.rxqor>0.
294 l::i AITEEPA Mep3reK A. r. ra iH. AKaAeMi,{Hrar pieeHu illlii-:::::il:!ii:l
gKqo 9a - 03 > 0, ro 4(3 - a)(3 + a) > 0, ro6ro a e (--; -3) u (0i 3), roai piB-EsEIls (1) Mae ABa KopeEi.fiRrqo 9a - a3 < 0, ro a e (-3; 0) u (3; +-), roai piBHsHns (1) Ee Ma€ I{opeHiB.Bianosiqb: ttKLr\o a e (-3; 0) u (3; +*), ro piBHrHEr Ee Ma€ xoAHoro nopess; Elcqoae (--; -3) u (0; 3), ro piBEsEEs Mae aBa riopeEi; sRqo a = -3, a=0, a=3,ropiBEsIIlIs Ma€ oAnH (opiH6.
264. f@J = x^.1\ tC4') > f(-21, r, - rapHrrfi noKa3rrnK;2) f(-4) < f(2), /, - HenapErdi noKa3slrr{;3\ f(-4) < f(-2\, n - senapgr{ia ronasH*rx;4\ IAI J(2\,, - Mo)ne 6yr,.r i napH M, i HenapEuM,5) f(-4j > f(21, n - napHr.rii nol{a3Er.rli;6') f(41> f(-2\, /, - Moxce 6yur dapll rM i H€rapFrM,
.r' =( ;)' =* rpaoi* se rpoxoa'rrE.repes ro.{xvB;
(i)" = * = rt rpaabi& npoxoat rE.repes roqfty c;
. {Jr) -li-l =i. rn.oi* He npoxoruflr sepe3 rocK} D.
273. r)-a(o; 0), 0 5 - 0. Br.rpas IIe Ma€ BMicry, rpaabilr lle rpoxoalrrL qep€3 ro.rRy-4(o; 0);2) B( 1; 1), (-1)-' = -r. fpaibiK npoxoarrb qepe3 ro'Dcv B( 1; 1);
:r cf |, ezJ. lli = r' = n. rpsoilr trpoxoarrb qep* -"*y c( 1, 32 l,
ar al -s,---L1., sr' I tl'-- t\ 243) t 3' 243
fpa(bix npoxoArrh qepes roqfty D[-3: - 24A-J.
274.y=aat,
1) A(-5; 20), 20 = @ . ( 5)-s;
", t(r'l-). L = ".2'.\ 24) 24
275. y = 6t.t
o -3t l: a=-2q.a:I)A(3: -3): -3=a 3{t 3 d 3.r 8I
,, r( -",11. 1. = o . r-2\ , . , = I , I - I l' - I , r .s.' \ '2) 2 2 \ 2) 2 t6
1276. f(rt = x ", flxt = :n,.
1) fl1,6) > flz); 2) f(-5,6) < f( 6,5); 3) {-e,6) < fls,6); 4) l(0,1) > l(-10).
I277.f(xr=r". fr = ,*.1) l(18) < l(16); 2l f|a,z\ < f(2,5)t 3) l( 32) > l( 28).
t27A. fU) = x ''. flrt = --:.
1) f(1,61> f(2,21; 2) fta,6l < fl-3,6tt 3) l( 3,4) = l(3,4); 4) l(-18) < l(3).
1
275. J(xl = x 1o, flx, . xao.
1) t(6,2) < l(5,5); 2) l(-1,6) > f(-1,7\t 3) f(24\ - f( 2a); a) fl 8) < t(6).
11280. x'= 2500; " 2500r r'= r5_.
7l n trapse tsarypanbge {rcno. com} pisssHlrs x' - -l ** ouu nop"ti;
2) , - Eeilspse HarypaibEe .rrcno, roMy piB """rs
,' = ,h Ma€ oarH Kopixb.
rl{ltil::tl:ij::: AITEEPA Mep3nqKA. r. ra iH. AKaseMi'{Hr,rr piEeHb iii: 297
"(', *)'
"l.1, rtl.t3 )
"@'i)
.frtii:il:::Ja-:::i:
:t;lI'lAi-:J..'1.',
liii:ra:t::::i!:i:rj :ti;Ar'.' ' ry 'u'. 'r " =(])",
' "^=(:)"'
foryeMocs ao BrBgeHHr HoaoiTeM,
, *=(;)" a) a-
s1 n'=l; 6) -'
/ll- l;,r '
1
/ 3rL=\- z)
51 0.5,.4, = l1l-'.1= 4.1= 1.\2J446r r2.,-s ,.16r,
= I 1- !. rel '_ I t -rl '
t2 8 ) \2 )
i_rr*i
lr.t.:.{1
z\ 1a-01" =--J- q (2x-3! a = 1
lo-b)' "' (2x -3!J)'
zzo.r ar 4'-1 1=4-3= 1:3412 12
!- I 9t? !!.8367272
:r l2l', rz.sf s, 7,r r _ t75+50- 2. =?23 -a2?.\7) 2 25 50 50 50
4.)9 0,1 .9 r0 goi
=l-,11'\2)2
3
271.It a'z+d '=1-1=S+,2t nn-rn ,,i
3)r., d,)r. ,,,_f' ll t __ d.c _ t .I c d)(e d't'- .d(c d)'z (d c)td'
"., (t r') I s2+x' I 14l (x -u llx -u ) =l-+-1.-\r' u)r-c" x!2 xz-a'? x'/
2. CTeneHeBa OyHKqie 3 qi,|rM noKa3H]'KoM
272. a = xa
e [:, ,'u.1.
z . I j l' ,'u. .0"o,* npoxon,'rL qepe3 roqky A;
296 iii: AITEEPA Mep3reK A. r. ra iH. AKaAeMi.rHr,ri piBeHb ii:.:iii::iii:{i:jj
26=--L. o=-25691125
la124 R'' 3
ii$i#$ii'l{l ;A:::::::l
'iiIijfiiiriitirljft:iii
ttr'2a1.tt!=tx 't'., LJ - u=x.r'oO6nacrB BE3na.reIIHs {ryHKaii qe r(y) = (-*; 0) u (oj +-).
2) u = ttx - zt"t'., =l - !-l\tx-zt )t 2+0, r.+2,a=(k 2r')',A=G -2r4, D(a) = ( 12) u (2; +-).
282.1t r' z. l. z. ,, o.Toai ro I 11
x"2
ra', piBEEHr' r d= 2 Ma€ BiAtMErn r{opiHb, r=-i/!.
r 3 to iro2r -r' 0.3.
" = 10, ' 0. To4i x'=
S , r, i: .
Hi, piBHnHHn r. 5 = 0,3 re Mae BiA'eMHoro IropeHs.
2€.4.a x" i u=.1x. gxqo rpa,liKx d,yHXqria nepelrHdlor!'.s. ro BHKoHycrb.fl prB
nicrs: ra l'. l=1.,.o.32 1" 0. x"=32.r' 2.32 t' 32 32r'
r** **-"* fr, 11.- I 16'r
285.1)g=x'+2.D(. = ( *i 0) u (0; +*).
2)y=(r 3)'.D(fi = (. *; 3) u (3; +-).
1
' tx 3f'
1"2
,(/l = ( -; 0) u (0; +-),1
113tx-=-3,
", t -,0.ToAi -'.3i,y
TdK, pisFaHHF j ; 3 Md. Bin'cvprt kopi'rL.
/r
!arli/-
ir!B
4txs--2. )^ z,,, o.Toai x'=-.1t
qs prBl{rcrb He BI'IKoIlv€rrcs, oo JIlBa
qacruEa AoAarna, a npaBa - BiA'€Msa.
Hi, piBEsstl.s r 3 = 2 He Ma€ Bi.q'€MEoro ftopell.fl.
2ag, I a = x, ryaoinoM € trpsMa, sKa € 6ice('rpncorc I i III noopalrHarHr'x riyri!.
1y=x3.flnqox+0.ro y=-.Toq&r nepersl]y .paoilliB: (1; 1) i ( 1; 1).
1
II cnoci6: x= r 3: r==. x+0r
T=0,,,,=1,n=11.MaeMo ro.r(r: (-1; -1) i (1; 1).
1
2) i/ =,r'?. flr{u{o r + 0, ao u = 1rIu = 8, rpaQrk qr.r qryHKUll - npFva.
.filga rpoxoArr6 qepes roql{y (0; 0)./ 11
ro.rKa neperrHy rpaoiKjB: { 2r ].
.l1rII cnoci6: x. = rr , = a. .r * Ui
: j =0.:r'=s,x=2.
r*'. -*', lr, 1)" \ tl
5)y=(, 1) 3,D(R=(--; 1)u(1; +-),1
6) a = tt", D(f) = ( *;0) \, (0; +-),l
4)s='3 1.r(1,=( -i0)\,(0:+-),
' (.r - 1)"
298 iji AITEEPA Mep3rcK A. r. ra iH. AKaaeMi,{Hlln piBelh l::itl::liltlil:i iiiliitiiiiilt! AIrEEPA Mep3reKA. r. ra iH. AKaaeMi,{Hrai pieexe illi zss
2)a=415,x+Oi289. 1)
CrcreMa Mae qorrp'r rapr pGB's3rciB.
290. 1)2t l!=*
[''r'=''2s2. f(x\= 1-.r-"-1<1s
1;
l-!",x>1.
(F}'Irrqis cra,qa€ Ea rpoMilriKax:(--; -11; [0; 1]; (1; +-).OyEXais spocrae Ha npoMi}Irlly [-1; 01.
1"8
1287./t.rt=xb.RkuoxtO.'to l(xt= a. npaoiK OlBKuii cltMPrpxqHxri BinBocso oci
l' lOy. Ha trpoMi)Rlty jr 1J rlaoix Qverculi cna,qa€, roMy naii6inr,Ee 3Ea"eEns abvH-
| - 'l I' ltu ^" -'xqin Ha6yBa.. nxsro r = 2. ro0ro /[tJ = | z) . r' = on. savMeslDoro 3HaqeBs'
abyHrcqiE Ea6yBa€, ff{rqo r = 1, "0610
l(1) = 1.
Ha npoMi*c(y lt, - |l Ou'^*'" rpocrac. rox,ry sanMexne 3HaqeEH': /(-1) = li-/ rl / 1l
Es*6inhme 3HaqeHHn: f, ;) ,-;) =( 2t6 64.
Ha rpoMixir{y [1i +*) ibytrKqin cfla{a€, roMy lrafi6inblt€ sssqenHs: l(1) = 1' a safi-Mesmoro sHaqeHss OyEKqis He Ha6yBae.
288. f(x) = t3.lr 1 1
I) Ha npoMilxnv l;;zl Ovxxnin /(x)- -" cna-aac. roMv 'rafi6i,bore
3sa'renss
,(!\ "'
,r., .'u*"-" ""'""", I I
'\3/ sa ltzt= '' I2) Ha rpoMixclcy t 2; 1l Oygrrqin /ttt = I "ou*"",
roMy Hai6inlrte 3na'reEs.E
ft z\ 1._=-1. " rrn.a""-e sEaqeHsn: 11 11- f= 1.' (-2)' 8 (-1)
3) Ha npoMinrxy {--; -31 Oyrxqig l(rt = 1 cna.qae roMv Hafi6inbr',roro 3Ha'{eHEs
BoHa tse Ha6yBac. a Ha;MeHUe rtse*e'nr, t, 3) . (-1," = +.
CrcreMa Ma€ rplj napn poBB'ssRiB.
lr '- srrno r < -r-291. l(.r)=l -L-r'. sR'-qo ,r > -r.
(DyA&qia Bpocra€, sriqo J. e (--; -11,, € [0; +-). OylrRqi.n cna,qae, .fiKqor€( 1;01.
3) y=(r+1\aCEcreMe Ma€ aBi IIapIl po3B'sa1ciB,
C*qreMa Mae aBi fiapa po3B's3&is.
1
300 l::::: At'tTEEPA MepsnrK A, r. ra iH. AxaaeMiqgri piBeHh l:iliii{i:iiil;itl [.atgi:1i.:llli AITEEPA Mep3reKA. r. ra iH. AKaseMi.{Hrn pi8eHb il{: 3O1
q
rl
ti
:::a;il*ii;;,fl:li:l:.fl
il
I
I
l'- l' ". [0;9) u (9; +-)lr>Ui
T
2gg. x) = t', ro6ro npu r * 0, l(r) = 1
t) f(-2\ < f( 1), roai n - HenapEe qvcnoi2) f(-2\ < f(1\, roai r - Br3Haqltrr seMor{inz Bo;
3) fl-2\ < fl-L), aonj, n - napEe qncno;
a) l(2) < l(1), roai n alrsHacrru EeMor*{,rsao.
foryeMoca ao BxB,{eHBt HoBoiteMtr
2s4- 1\ 514 - \lr5 = 5.2,5 = 5:
z, 1.6.0s z=! o.a z= r,gr
a) (.,/L)' 3('6)'=18 3 8=13-24=-11;
+, 1{,,/is) 'rJrn) - t..ta | .rn
"-rr= ".6262
295.1\x'=25ix=!5;2) t'=O,49t r=1O,7;3)rr=3;r=tJ3;4) x.'= -25,,j' € A (a6o I:e Mae AincE]rx xopeHiB),
296. 1) J :r, qefi lupas Mae 3Micr, nlllqo .1.>0,ro6rot<0,.1€ ( -; 01.
2) r,F, qefi srpag uae 3Micr, nrrqo t € R.
3) J r', qefi sr{pag -ae 3Micr, nnrqo -r'z> O, t: < 0, ro6ro t = 0.
a) Jx-8, aefi B1Ipa5 Mae 3Micr, n&Ijlo t 8>0,ro6ror>8, 1e [8i+-).q JVi, qe* Bllpa3 Mae 3Micr rp't x € ,R, 60.r':? o i I > 0, roMv ixnn cvMa
6in6ua BiA Hyn'.6) 1G - sf, qeil Bqpa3 Ma€ 3Micr, srtnro ' e ,R.
ll - | , qei BHpar MaF 3vicr trpx ). . 8. 106,0 'r {-@: 8l \ {8: '
€)Jrn 8)'
8l i , qer snpas Ma€ 3Micr,
f"f a*0, ["G*s.' lr>0: [x>0r
297. 1) TaE; 2) rax; 3) ra&i 4) Hi; 5) ran; 6) tsi.
2ge. | \m = 3, ratr, 6o 3t = 27;
2) V1 =L rall,601>0i13=1i, rl-n = -s, raft, 60 (-3)3 = -27;q 4,Ei =2, rax,60 16 > 0 i 2a = 16;
$ 4-16= 2, IIi,60(-16) < 0, a noDrHHo 6yr tria KopeIIeM lapHoro crereEsHeBia'€MHe wrcro;
a\ {-n = z, :gi, 60 2' = s2.
299. 1) {6 = 2. rlrcro 2 e apn&MerlI.rHllM Ky6i.{Hr4M kopelreM i3 'rrcra 8, 60 23 = 8i2-qnc,roEeBiA'€MHe.
302 llt AnTEEPA Mepsrqx A. r. ra iH. AKaAeMi.rHr,rn piBeHb ii::lliJ::.:.:.::::::i
2) {,6T = 3. .r{I'cno 3 e apr{bMernqEnM KopeseM 4-ro crenelrn s.rncna 81, 60 3 > 0i3r=81.3) 3 He € apnoMerr..rlrrM lropeHeM 4-ro creneEs 3.rl'c"ta 81, 60 -3 < 0.4) qrcno 10 se € aprabMerrqHnM KopeHeM 5'ro crelreHs 3 ql{cna l0 000,60105 = 100 000.
3) vo,0016 = o,4;
ry fo,s66s1=-6,1; " f#-m=;='i, r frJ=-'.
'; ",62s _ ./s' s ,2 .so1. n {Ear = "J?" =7: ,,i/trl-\l \l, 3 3
:t o,r.{:on=o,r.V z'.z' =o,E (-zJ z= 2l
4) -siF#=-8iF;= '( i)=,'q\[n'={n=la"=s;6) '"irAe- = rovtr). = 'oifi@ - ?.
3o2. 1) (J11) = 1li
q\,E)'=-z;?r (-3vl0l = { 3f lo 8l I0 = 810:
s, trr,[El".lrt".qe I €=9=g,"'l.z'=".1 -!2r '"- 64 8 4'
o, L gt* =! n,=,n.22
3OO. 1) J0,25 = 0,5;
7'4 110,125 = 4. 0,5 = 2t
sl i6'=i6i=s;
303. 1) (i4B)" = 1s;
sl (-{/ii)" = -rr;
5) f lad =i 45=15;
zl tlzta = a;
zr (Vs) =s:
b) iF= -7;
3) (V?) =7t
6) l5V3/ = 125 3=3?5;
2r (-VsJ - er
+rll.t,Eol=l45=9=11;\3 ,r 27 3 3
6) ( 2V 5l r 2r' (J-5) = 32 { 5r 160.
so4. 1) 0,3.$[boo-s V25o+o ( '{6)" = o, a . ro - r ' z r 6 6=3-1o+36=2e;
2) Jr4'-t-2Jr0J t t2a='4-t 2t' 10 2 t4-40-2=561
5/ i\ ? 5 Is t2 3=:t - + +4\ 2l A A a I
iiiifiiilil:.i:ii AITEEPA Mep3neKA. r. ra iH. AKaaeMi{i{ri piBeHb ii'.1 3o3
sos. r) 200 i6,oor - 5-63oor, -\-alz)' zoo o,t-{-0,2r-16 2=
=20+0,2-32= 11,81
1<ozr Veooo.l/zoE {ve)"'vrz -20.q r8) .rr.'oo 8 ,,r' ! 81 3 3
= s3l* 25 = 5s1.
ztr.t1 {i=-21 .r=-8; 2) ili =-2; "ea; U {i=-2 t=-Bz;\ l,lix z=o; iTi =2; sx=ror r=s];
rl i6r-z=o 3x. 2=o;3x=z; r=?'3'q lb' 2=2i 3x-2=16iAr=1Atr=6.
312.lr r:3 A2f + 81= 0. Hexafi r.a = t, roAi t, - 82t + 8l= 0, t = 81 a6o t = 1.orxe, ri = 81, r = t3; ,a = 1, jr = 11.BiAnoqiAb: !3. !1.2) tc6 +:.t - 56 =0. Hexeii jr3 = r, roAi t'+ t - 56 = 0, t = 8 a6o r= 7. Orri{e,
x' 8, r 2; .r" 7, x !7.Bidnosidb: 2t PJ1 .
3) ,rr': + rd - 12=0. Hexa;16-t, roAi t2+t 12 =0,.=-4a6o t=3. O,rrie,r.d=-4,r€ O;t6=3, r = Xeh.BiAnosiAb: lar5.
-25! 54=O,t= 2a6ot =27.
- T=\t--)/.+ ,
306. 1) Vr+6, r+6>0,r> 6.fllcqo.r'€[ 6;
U to tO. flKolo o = R, ro s,{par Mac aMicr.
s\ flE@ -1r, atu - 1)>0.
+-), Brrpa3 Mae sMicr.
2) ts = 12; t=!!ltt 3),r1o=1; r=11;5, 15 = -32: t -- -2,, 6l!6=-64',xeAt
ffiI'ldf:rg$i:.1{.ii}:r0':.:':di.tt$::!::::n:.t$:;.:riii:rq
ilrl
I
lI
l
I
I
;l
2)
4\
6)
2)
4\
i$ffi
i$jgiili
,finnro y € (--;01 u [1; +-), ro Brrpa3 Ma€ sMicr.
t\ !li, y > 0,, < o. sRrrro , € ( -; ol, ro Bvpa3 Ma€ sMicr.
' 5) V r', x' > 0, x' < O,.r = 0. .flI(a{o r = 0, ro Brpa3 Mae BMicr.
'Plx' -zx - 8, .r, - 2x - 8 zo. , ---\,,--- --\,,--.flKqo r € (--; -41 u [2; +-), ro Bnpas Ma€ 3Micr. - a ;
3O7.D s=4x-2, x 2> o, r> 2,, e t2; +*rt
2) v=!4 t, re n;
s) '{2' 4, 2x - f > 0, "(2 - ") > 0,
-----Y-f=\f- ' ' . t0; zt;o2
4) 9 = --_:]-, x, 4! +4>0,(t-2),>o,t*2,r€ (-*; -2)u(-2; +-).llx 4xt4
4)ta=i6ir.=!2i 5)16=5; r=1{,6; 6)xt= 81tx. At
7t27xt I Ot27x lt r' l, * l,21' - 3'
8lt.r- 2)J= 125, x-2=5: x=7i9) (' + 5)1= 10 000; (' + 5)1= 101; '+5=10a6o'+5=-10;'=5a6or=-15.
313,1, x6 25x3 54 = 0. Hexaii f = t, .ro(l t2
orxe, r, = -2,, = Pl-z = -Jz; xs = 27, x = 3.
Biano'iab: -1,E. 3.2) ,3 + lAx4 - 4a=0. Hexai ra = t, rori r, + 13, - 48 = 0,
r.a=-16,re A:xa=3, t = ):1h-Bilnoai't t{3.
s14. \,18 = a, sxqo a>0; z\,[V = -a,sxqo a so.
31s. 1) J;t=bl; 2) -o,4.{V = 0,4c|; a) ,E =)""); +, J^" = ^t=^,.316.D Jn"=n, sxr']o n >0;
4 \E6p' = 4p, s&s{o p > o;
5) lf,f, = cu - c':
atz. i) JoSl -:o = 0,8 6 = 4,8;
^. Et s\1100 10
t = -16 a6o t = 3. O?:*e,
1F= n, rrxt4o n <o;.,63e* - -o,or, s&rqo & < o;
,!,rr{t - o,stl= o,br?, a<o.
J6'.s'=6 e=b4;
,lra Ezr rr -s! 36
'l 36 6 6
309.1.) r'= 1; ,r = 1;4)rt3=0;jr=0;
/r 17t64x5 | 2 0i64r'- 2r'-il A''- ,,8) (2.r - lf = 8: 2x+l=Ja:2x+1=2.2x=1t x=f;1
e)(ir- s)6= 72e; t-a=\fV2e; '-a=Vtrr "-a=i/F; '-3=3; '=6,.r-s= -{F, r-3=-3,a:0.
31O. 1) Jr=9: x=81: 2t l/r=:: x=-:-:: 3) {/x=3: x=81:5 125
4) {i= 6; x= 216; 5\ \li=-2; xe a; 6) {/t=0; r=0;T {2' +7 = O; {2t = 7i 2, = 44Ai r = 171,5;
at \l2t+7 =O;2t +7=ot2x= 7; x= 3,5:g\ lfLrj 7- - 7t 2r + 7 - 343 2r = 336t r = 168.
304 ll:i ATITEEPA Mep3rrK A. r. ra iH. AxaAeMirHur pieexs ii!:.!lfilii:*
3r8. 1) .v6t..8 = .r52, = .rGZ = s;
zl ,6oo . Jo, re = \Eoo . oJs = .,66 = o;
q Jl:.Jt.1i26=,fu.2.%=,Ed = za:
4\ E3 tE.s" =tE 4 =2a.32=16 s-r44:
o f =n$=.ao='' -. vE fs fi rol -=-l-=,1J48 ! 48 V16 4
,Ez t27 /s.3 3 s .6 f5 /r r'' lt+z 'ltqz "lt zt .z.z 7' "'h.Jt2 -Va ts-Vs s'
i:i!{il!:iiliJ:111 alresPA Mep3rsKA. r. ra it|. AKaaeMiqHlri piaerr li:i: gos
r3. Bracr[Bocri xopeHr n-ro creneHt
319. 1) {6a.lx=+ s=zo.
sl !21o.7" = t.7 = 4.7 = 2a;
320. 1) i/0,064€43 = o,4.7 = 2,s;
",8=+=i='i's21. D 1!8. +E = 4!G =zl
,r ff=1ff=,.,0'=',sl
'E' . r . Vs' . 5' = 98" . 5' = B! . b = e . 5 = 45;
ela a6)1:::::: =:12," 73 =2".7 =8.7 =b6itl2" 7'zl .,[i-6. rfr..,,Ao = t,[ zr -ao - t6i = s;
z) Vo,oezs. s1 =o,s.s=r,r;+; i,6" rd' = 3" .1s' = 276 996.
z1 163osr. rr' = 6,3.11 = 3,3,
o, uEl ll -r' ,' a s -72 2zz.I 5'' 5' 25 25 25
zt Vo, ora . +4 = i6-ozro = o, o;
^'i ="[t=,E t- V128 !r28 !32 2'
,zs. I Jni' 7n -7n. 60 n zolD {rzs'.- = rn";;lf i6,ooooor- W = lo,tmun' =o,+^"n",60m>o,n>o:a,l tl,,t"* =)*"""1= ^6n3,
som>0,n>o.
2' \kli =,4;.sl '{"W = Xl o'a- ;
- .d-: -.
-7r '1/8r '{3' VB: sr * = i/', '9,.' ,t,'V*' t/ x
u F,tr" rF?^ t,",, - r^^".:Jm"n' rm n
na.4 .ld" ='\G:q 4"" = \E;
]zz. rl n[rE = \E,.rr VF = {,6t;
z) Vaa = iF = i4;
s, 4n" = llo;er c[6 = {F = {,Ar
e) x6.VI tEt.ict =.€. zz . i,6.1-ey = 3.1 3y=-e.
ro, fi. f'o =,Fm - rriu . ".v35 ! 35
szz. tl fllzi . ;uE = Pls' = r:
,,8 ,l'o = rrG ",i/5 I5
g dr" .5" .4* ni = I.t7' 4 = 23 . s = 4oi
+r $1- ro r[t'.-."
to-, *t " : ro' . I o. r,Vto'.3, \1 I0".3" ' l0
sr i/i - "/i7 Vg Jrz = ilst tz =tlu st
el l,E.,m tn nli"tw -ro - l6a - roo = tf az = -z;
t, v-"Frr6i=ry =4,6+n ='4.8=tz:
al J1%.Jis ,E .,.60 ={tr*8o..rEe'r=1181 . ,1 . ../86 = 5 . 2 . 6 = 60.
323. 1) tGr3)' = l-1sl= 13. z1 {-oy = s;
gZq. tt .t6"" =lS" =5r,, 60 a>Ot2\ iEtn = st":q lEE"-t' =lr""al - ba'b, 60 a > o i b > o;q ltFzg""W = Ba"bs =Basb', 60 a > o, D > 0.
8) {,G6* 10. {,GG_ro = iG.gI - t* = vior -t* = Va = r.
:r $[ e,' = -el= a.
a\ '4"" = {i;or 987 = Vs" =
"6;
sze. guoo '6. ro6ro d - 0.
t) {a'; 2) Vo'; gl 'Vo'; a) 'i/7; r) 'Vo'' e I '.Vf,;.
329. Vb, '106'10, € fi.
D ilt'; z\ {d; s) 'V;;; 4) '{6'.
:so.t) Vo'=o; d: o:
zl {a' = -a. a <o::t i,fT a; a - n;q 11"" = ", "=ots1 lQ sS =11,E-r', o,-s;6) V{o 5f =lva-5. dcR.
:er. r1 $6 = o', o 2 6t
2l a"" =-a', a<O;
3t Va' = Val , a>o:q dd = {-;' , "<o.
ssz. D l,l"t =+6.+lo, o>o,b>o;D <l"b=1
".11 b. a<o,a<or
4 { ab=X6.Ilj, d>o,}<o;qiffi=rl;.X6. ae R,be R)
5\ XGb = {-;. {j, a e R, b. R.
i:l:lttllJllt:.lj1i UTeSPA Mep3rcKA. r. ra in. Axasemivnrii pieenr i{f
D lxE =flr)
o "{"-u = tEi;
", E=,F =a.
3OO lrl:ArrEEpA Mep3neKA. t-. ra iH. AxaaeMi,{Hr4t piBer" lfiilillli:l:::i;i
a> 2-
PiBnicrr, BnKoEyerbcs, sErqo t € [3; 71.
s) XG- 6X' - 10) = {,6-. {6 r0, : e R;
4) i/i;1x,+2X'+3) =tt,.U t('-a {"-a), -
r > -1. PiBEsIrHs BljKoHy€r6cs, st(qo t € [ 1; +-).
'{6*q' = lpuq'l= p'q', srrqop>o;'tr;** =1n"nl= l-^").(-n") = n"o", .aftqo m < 0, n s 0;ab' 1t7*b"%4 = ab' .la"b'c\t - ab2 . o1, bs . ec),, = ata"cn, s&!ro 6 > 0, c < 0;
-qfr" . "E-" !: - -an'p" .'h"tlpot 8n'p" k'6 pto -o^,"1..k' \256n' k' 4m" 4 (-n,)k' -"P ^ '
m <O, h>O.
338. 1) i6t > l/Ft sxqo a > 0, 60 EepiEnicrs a ) lal rr.monyerrcs, Frciqo a > 0;
2) iF < Sf,'., flxqo a € E,60 HepiBgicrl o < lal sx!{ogy€r6cs, srtnroo€.a.
sss. rt tf' a=lol-o. a a=2a. ertto a -o;zl \la" +4V - al+a=-'a+a=o, m{qoa<0;
U \,[a" + l/V =o+ al
qr Jx lla =lol- o.
sss.U lxz -n= dx-z <Jx+2,
334. 1) t6{ = lbl;
o {68 = l"'l;
33s. 1) 1,2rV:0 = L2l*;q'{@-0- = a-v.
PiBsictE BrxoHy€rr'ca, slirlo r € [2; +-).zl :F - s(z - xt = lE4 lA - r,[(r.-3)(?-x)>0, f3<xs?,lr 3:0. lr-r, 3<,rt?.lt-"o, l*=t,
r-2>0,x+2>0,r' - 4>o;
lx z>o,
l"r+2:0,
l[; = :;,
.it
6)
7)
8)
r ti::iiii'-{.}:.:.::j:,lrSitfiiji!:tiixli
:lt$ri;ir::il*i:J::ilitl#-&i':fli 2[l-a<*< z'
l(x+1)(r+2Xx+3)>0, I ", -r,l-r+120' ll*r.0.lr+2>O- II 1v+2>O-lx+3>oi l**rro,
-1<t-1
-2
z1 -0,+{V = -o,t "l:l,[iF = n":
z\ {u- = a";
3)
6)
'3)
t[a- = a"l= "";'.3G-o" =1,-51.
9"' = la'l;
310. r) {, +a)n = r + a.Icnoci':lx+4=x+4i), . -n. J' . -4.l-x 4=.r+4: L2.r=-si
I,'- n. !,. n.
[]+4=r+4i l0,r=0;BiAnoqiAb: t4i +-r.
I xe Al:
336. I t {/aru = rnl - rn. qxqo rn 2 oi
zt !r^ = nl= -n. rxqo n < o:
{t6p' = 2&t-- 2p, snqo p > oi
q {zsen" =zpl=-zn, sKtr{o}<0;
B\ \,@ =b'l= "', s&qo c € .R;
o1 16-zra' = o,sla']= o,5r?, sriqo b < o;
11 tr6""5 = slt"yl= ax"y, axulo y 2 o;
el .,6, o1o%F = o, r lo'bul = -.o,ta'ou , sriqoa<0,0>o;s) -1,2*,h4x' = -r,zr,.al,u =-g,or'( r')-9,6ru, s&qor<0;
*,'la:.,,-:=*;' = 4*+, " . -f;.o,o.0.o.
ssz.t\ 1,8 5o^ = rl"' =so';z) i6, ooorf" = o,r a"l= o,1r', sxuro , > o;gl -r'[a'" = -s.zl" = r0 (-r) = 10r,
'1Rqo , < 0;
r; o,ri,fiooo ooo"" = -o,t tolz'l= -z', z>o;
3OB l:ij AnfEEpA Mep3neKA. f. ra iH. AxaAeMi'{Hr,ti piEeHb
x>-4.
tt ""o"ia: tr@++f = r+t, {,+qn =lx++=,+t,
nnllle snu]o ir + 4 > 0, r > -4.zy X{r-r'y =6-a,f, {6 s,)'=(1-3'f =(1-a,),,qe Mo)rirnBo, gl{rqo r 6 E.
rar.rl i/(G-z)"=J"6-rl - n/Jo -2. oo Jo '2,2) i/(1 -,E)' = Jh - .,8 = J-r + Jz. oo ,E ' r,
3)
4')
i/("8 "5I = q/.8 -,6r
i/rJe z)' = Vl"6 - ,l t/ J5 * z. oo Js . s.
s+2. r I fl(,6 - z)' JJs - zl = JG 2. 60 ..6 > 2lf- --zr V(G -.,4)' = {'va ,al = 1tfu = -i6=. oo ,,5. Js:
ar ((Jrr-a)" =dlJrr a = {Jrt -s. 6o JiJ,B;t;"r-
4) '{{J? - 3J = VJ? - s.
:iill:iiliil:iit: AITEEPA Mep3nrKA. r. ra iH. A(aAeMiyHrn piBeHb fl.! 3O9
6)tc<o,a=2r x=r;3a3.D s=a,,8 -x= xl-r=
= x- t= 2t, fiRqo t < 0;
z1 s=2r+\[ru =2x+ xl;a)r>O,U=gtt
et u=fr.2=fi,2.s=4+z=i+2, t>',=!a2= f +2, x
3aa. D !={V - 2x =lx -2x. 2ra=d=.d-r"-dj= x.
g&qor>0, toy=r 2x= x;s&qor< 0, aoi=-x 2t=-3t'
flriE{ot<0,ro6roy=-1.
- t/,"h6) U=-=-.xxOA3: r + 0..fKrr{on>0,roy=1;sKrqo t < 0, ro J, = -1.
3a5.*lV=r-a.
lr-4>0. lr>a-[l:r =x-+: lx=x +;
reA.
,, 9F
OA3: .t * 0.
0,
<0;
t>4,O-t= 4i
2r'{f =6 hlo-r>0. lr<0.I rno.i6: I I
lxl=e-x; lr=0-f1* s o. [1' s o.
ll-'=o-": llo,=e,.t10..r s 6. lJ0 < r s 6,
!'=o-,, [1"=:,II cnoci6:
zr y = iF. J"' vl' .JI r = J, , l'r ''.,>0.
3 I o :::::: AtIf EEPA Mep3rcK A. r. ra iH. AKaAeMiqHr4f piBeHb l::::ii:+:::i:::::::::l
lr+3>o-3) 2Vx" =r+3r l
l2xl=r+3i
l-= Ll'=:BiAnMiAb: -lt 3.
F. ".l2lx =x+3;
J-3sr.so,l-2x=t+3;
I',0,[2r=n+3:
I-3 s,r s o,
l>o,
q y={1' zf =,-z; t) v=Ji {'" =d"' =', r.>o;
sr u = .y',' V*' = lr.l'? xL' = lx ;
BtAro6;ab: pos!'s3RiB HeMa€.
3a6. 1y !F=x+a;
3s2. 1) .,6 - ./1t1../6 = 1.'6 - z.'6l G = -,81. ,6 = s,
zr iz-,6.1'6+r =(z-€).(,6*il=z.f +z-a-"6= 16-rat lb - ,t;1. lb l;l=lJbf iJ")'l= a - "r;ay lz s."i5l' = (-z * su6)' = a - z. z. aJ5 * (a,6)' = a nJE + 27 = st - tzJs.
sss.rr *= L2f,6- =rJ6,J6 J6 J6
- 24 zals a"6zt-=-=-5J3 5 J3. J3 5
^. lz JrkE-r) $Ur-n -E;=@;t(!trt= ,-1
erz. {"-#'iF-'f =2t x-sl+ 5 xl=2.
Bacrocy€Mo Meroa i'r"n"-i", r ftQfiir<,q lr< j. [*.3,r=s;tt1,,*t-u-' 2: {-zx- e: l*=a' -
", J3.xs5,'' lx-3+5-x=2:3){'[r-3 5+x=2:BiAnoaiAb:l,el3i5\.
ale. y = 1,@ + rf *1[:-F = lr + 1 + lr - sl.
SsaiAeMo nyni riAMoAytr,Er'tx BLpaBiB:
r - 1=0,.r= -1 i jr 3 = 0,.r= 3.fitrqo r ! 1,roy=-, 1-x+3=-2r+2.OT)+ie.
^' 2x + 2, t s l.
fl&nlo -1 < t < 3, ro t = t + 1 + (-r) + 3 = 4.
Orxe, Y, = 4, -1 <t<3.gr{qo t > 3,'roU=x +l + x-3=2t; 2.
OTir|e, As= 2E - 2' t > 3.
ll-ss,cso' f1-s<'-' o.
l"r+8>0. l.r> e, )r-.r-ar llr=-a;llx '-a: lr '-a:11"0. J,,0.
l)x=x+a: Io.t-8;
l-.1,Lr=21
BiAnosiAb: -4.f6'-10>0.
2t Vr" = 6ir - r0: llJrl= 6.t 10;
BiAnosiAb:2.
34e. 1) 3145 = 3 316 = 2"6;
ar S"Eoo=fr ro"E=.E'
350. r) aJ13 = ."6.rs = d1?;
a) e .,6 = ."66d;
-5
r=6r-10;
!r $.i!:;i::::.{.::::$
1l$z:r.tl$jiii,ti,yr,Lidri:il,:q "!.11:.:.:..1:.1:.:'' - 1 :!:i.:+:.r.t
^___!_rr,_5r-(/,.##;='u(fl;f )=,rv,,,r,,r,
CilNE:'=-:=-:icq{2 (Jrs - J12)(Jr5
= Ji *16
rs(,,!B*"/iZ)
Ji t "tiI3"t5's.*<s,10.r=0r
l"r5, ),r,, ".a.l2ir = 10: I.t = 5;
1
Ja Jb ltE - ,tE)(J; - .tE) a - b
foryeMoca rlo BxsqeHHi HoaoiteM]l
zt )Jna=)alz=+Jz:4J -o,o5G4oo = -o,oo ro.zJrr -Jrr.
zl -roJil = -'4a. ioo = -Jlaoo;Ij
4t -;J54 = l; 54 = J24.
I
I
,,
-,ELL=
Ji r,li _(J;)'*(.6I
gsr. r) uqb - oJ5 = s'6 - 4"6 = -."6;
zl r,/iz - z.',6 = ro"6 - z.'6 = 4"6;
el ali,-tuT+zude=s 6\E - a"E +2 7\E = BlE - a'J,+tttE = zsJt;
4) 8.,6 + .,[ 2s - + t62 = a. zJz + e.,E - f,
. s,!z = e'E + a',8 - sJ, = tt"E.
sss.ry [email protected]*a =.[7-ro =r;
a (\ffiG $ - 2.,6)' = o * zG - 2,,(o * z^,6)(6 - 2;4 * 6 ru5 -= 12 - 2.,Q6jl =12 z. Jte =n-a= t
iifli$illjtif AITEEPA MepsrsK A. r. ra iH. AKaaeMiqHnt piBeHb }i:!: st3
".o.'r fr=@jp=6.,,^. a- b lJi - Ji)(J' , "rt)
'la + ,lb Ja + Jb
^. "E-t Jz-t r JIJ6 J3 J5(v6-t Js 3'
.. Ji5 '6 v6(G-€) J5 vit' b J1o G(,6-Jz) ,6 5'-. ra ,45 ,/iT(,/i5-r)o,
-=
+=vlit-t:v13 ./13
^. "*2"!oa +a Ui * Ji\"o,
-=-+.=!a+JD:
,la +,lb Vd + Jb
I=
J7 -l;;tF'
-. aa+ali aG*'6) 4
" -;r - 5 = G - JF)Ta + G)-
= ;Gr"li
* '6("!;.Ja\(,E ,t.o - ^tr)
312 li{: AIrEEPA MepsIqKA. f. ra iB. AKaaeMieHxf piEeHb
ss6. 1) !,:-" =C;; =l^^lJn=^'Jn;2\ \Eo" = oJi+u = o" ualu$ = a't6 ,rG = a"b6.tE, a+0;
a, Jim z,"lJy -zx"Js. x o.
q uG'V =sl'1v'1J5" = -slx v'nE; = sxs1.t6;' r> o, a < o'
357. t mJi -.hn', n>oial prT = uF, p>o;
2) sn.,$ = JsVi = n[in", n<o;
4) lalxn=W, t>o, a >o.
4. ToroxHi neperBopeHHq Bllpa3iB, tKi Micrqrb KopeFi n-ro creneHt
3se-1\ 1.t86 = ilt- = 2\El
zl +En = a,Ezs z =t<,E;
U tEu - +lza = s+tz;
o fzzgo l/i' ro :''fl.o,
s; <Er],a" = l[e.6 n" -" = z":tli"" :
a1 t[ t =11 "-" = o"11;'
7:) d-b4aw = lt n . rd av = -zot"ttz""-;
s\ { !o8a,b- - t[-n. 4d'. a. b" . b = -s,a"o'{aab.
sss.,,-tvto = f,slz= z"Jz,
a *1640=;ic€2 5 =i\tT-=!r$=;lE,a, f sae |t[i ] rtz xE
+1 -r,z16e = 1,2{2" 3=-t2 21JE = -2,4\b.
360. 1) 160 = i[6 '5 - 216;
zl *,&s6 =l/t 2€=sV6-;
u Jin = "ul7 t" z = s'Jz,
at 16o ooo ooo = tot6;
b\ W =1P zo" ; =s u"W'et {6Jsa""' IE Bb' b ,'" " 3 b,'ltE;
sor. r) 2.,6 = 1Al =.,/ir; zt t{8={q"i=\6at=I'b2f;
3) r0f0.27r -fio'o:zr= rDzro, o,!ut, iffii /*,o ulloa' = lEzs ont, =:,!ii; 6, 2{6v = ilniv = illeul
7tblab dt-w .Ja,,", t,"{i-{X Vfo
:or.rr ]*ro=]r,6" r =!.au"ls={s;
2l
3)
4)
2lV=\Et=./16.7=^EA;rdG - +Ezr. +" = +E:r,o":
o,BltrooV = lEsn .too"* =18i7;
363. 1) ai6 + 3i[ stG = z<[i; 4 6!b + 2a,6 - 8!b = o.
:y r{,6+aV--{,f, +rplV =sr!; *e&E; 4) s&6 216 + 8V5 :i6 = oi,6+ 0i,6.
so+. rt s.t6--z{6={f,t 2J li +7!b -ar,tE = a\E,.
36s.r) t/625 V320 -vi35 r1+o=i6' s 12".s-i6'.s 92".5,=stJi z'tuB -ztrE + ztE=ri,6-al6 16=o,zl {san + :!-td ; {-an - t,s\lian + +lq+s* =
= ztFi - strFi + a1,E; - 1, E. 2{ sn + a\Fi = B1fti + o = s4lii.
soo.r) VEa si46+svi28+{t000 - BrrE s.24r+s.4(t== BltE 6{, + 201,8 = 27tr8tzl i6fii +eXE6a z+,EG + t4tzgu = s{i * a<,li - e+ri a<[i+t z.ziE== 111,G - 6{; + 24!!E = 2sd; .
saz.\.lzJs = t[q.B = xE ;
2) V3V2 = {Vsa = Vbai
s, 1{;$ = ,{{F =\F = \ti, a > o;
at tEtE = tl:[t ="4u, t>o;sr i,fula = .il14G ='i;t = .77,
6r y2vrv2 - VTE W,rze = vrze.
soe. rr lojo vi," - il," , ' o,
zt ula,f,a = \kn = \,ln,
s) i,6.,6 = {,F ='3F, b > o;
4) W" = xF6 = flW =.Vc = {6, . > o;
sr V''V,' = Jq/r' .e/, " = V",c', r'o;u, fi-,/"v, r/F=v"c. (/,c-vf, {a.={a. a .o
1
I
l
lI
I
I
ll
I
lI
.^. -- -lii::i::i.fl
ii:::::IJliii:::ii{Ni::ii:ii*l
l
314 iii: AIrEEPA Mep3neK A. f. ra iH. AKa.qeMi'{Hnn pigesu ::*:ili:!i:iJl:il:j i:ii:iiitiit{il: AI|EEPA Mep3rrK A. r. ra iH. AKaaeMiqHrt piBeHb ril:l: 315
sos. ry (r + Va + {fr)h - la)= r - ",zr (r *,6Xr. l6Xr - "6) = (r * G)(r - €) = r -..
az o. t (G *'[i) (di. {t)(et . et)(.v6i - pl;) = (G . J;)(<,r; . i6)(i; - {t) =
=(G + J;)(G -J;)= n-n;zt (l; - tri - !o)\{; .
'.ta) = J; - li.
gzr. n .fo l; = "17 "l'" ifr, a > o,
2\ J; t6=flF :lt = {f'0. o>o,b>o;B) {1; '.i6 ='d'"...v''' ="!^oo", n>0,^>o;
o, ,!4
=,{"_ =,4V = r1;. o , o.Vo 'Xa"c'E t!!A p!;a /o d.. vz\,r !z !r ,,lz t vlnr . td;-r,
-y'0- - -de,
- rJz. e, -
or V"/" V" = Vi6; 16 = 'ff V" +17 ,lo - dJ; o z o:
"'@ '@ f,-=vlg=d*=ra,.'19'v9'v3.'v3.et lm p,Et" '{"* ='{."b" 'fao' 'W =,{'w =XFt, =:["'a"l
n, t/o'a'Voa' - Vl_d %''"_' ,t1 =,F. a > o. b . o.Job {a"a" 'lano' ! b 'l b
s72.1\ {; lE='{'".'{7 ='17, ,>o;,t ,ly' . do' ='dr" fr ='il6 = ttr,st . "G.1t;=llF.{x.{i={"", ">o;n, E=E='$."'0,_ ,E v5 qF iF ^Ei .EbrEF=rF'F=vtr=ls'at t["+ '{"+ '{'t" ='{"'a" '{A qW =4"w 4}b" 4"'b" =
"fl|5t" =l7o", r>0, a>0.
azs. r; (r14 + o,rq/ios - {.600)*E = r+6+ o, siEG - i[ooo = s. z* 0, s.6 - r0 =
=10+3-10=3;6;-;
2) Vo.2s{V4 + 3V32 - 2(/108) = Vt - 3i/0,25 3, - 2ir-? - 1 t 3 2 2 3 = ti
3) (2{E 2{6 + {/ioo)(Vio * Va-) = ro n e = r+ (2.'6 = .,,6. s = Vao);
-f;37a. t t Ia{?
2 - r"Js, 51i, ; ). tB r.'6 + s _ a"6. L s/f . a =
-4 3 2-9.3+5.2= 24=9+10=t5+10=25;
D ""Jr-EtPp =s _ vzz r Vi2s = s _ g.s " z,
^. tV24 - V6l4,,ia - 3J6 4G:3E-
Ju -z ttz+a * Ja zJa + Ja - E"E aJ6 - 4,6
r ll :;,! ::::::l:::::::
Iil! :i : ::::::l::!t:-{
iili::4:.:l:*lil:
: r 4 :;r:.i!t:.!:
16 - olEz + zi/rrzs 16 - 6.2{6 + 2.516
.rs.r, l=t@ Var.,6".s_rVe _!r'Vs 16 Vs' e 3" -s'-t'
,, | =46 _ J=ra _E t _ z"lz_. tlz.V4 V64 4 4 4 z'
+t ., ^LL
= Jl!!- . r2f!l = -4i6r;V(-3) VB t/3. -3
o *=S=l!@=ura,{/8 V16 2
6) +=l!S- j -ftiT -g t {F -tr^.'V8 V8 8' a 4
,'etr n'<,ln"', r/n.=FF =-;=n"<|n". ".o,
'r ffi=#=',f =,ina,
n, I _r"iG_ (G.v*'
roy -ii-9-, r':-!Et::!j =tEt.V(d+tf a+o
szo. r, f2 =1$ =nvs, ,t
#.roJr:.l' =:tzs, -! ,<li=otts
u ft=f =z<8, n, -rs _ rsVzz' _ sVa" b.s'V3 _../".ll27 27 I
., lo {hooo ,--^ - 24 z+{te, s.z"dz', vro-
- -v-i o = vroo: 6) i; = ::r-;" = T = rroE,
,,1. *E ttu, " t;" xf' =m.d;. n .o.
i:l:::l::ltiiltl AITEEPA Mep3rcKA, r. ra ifl. aKaneMieHhi piaexr !:iil grZ
-----------il4\ -1-12+10= 1;
316 fil: AIITEEPA Mep3nqK A. r. ra iH. AKaAeMi,{Hnl pieenu li{:iiii{:i:i{ri{:i
szz.ttN!-j=t@Lr,_JJ -{{6-vbrlq vb) ..i1, '6.a 0.4 o,
", tE \l^ {. :l; :r ,n>o.n>o.m.ni'' L^-Jn tv,'l -'6)(v,zr-v,) Vln rV'
,, .,/i - q l'/,- rlln' 3) v, r. ,, , o,
'Jx+3 'Vr+3
^.G,li r,6,t/'" r) 6'' .^.o,-' ^ \l^" lF(.f'" r) ','(.fi t)
,. ,t*, ."1"_! d"tlf, -,[x\ q,a{i6 -v,) -"J;r, " o, b oi a - h,
"' rr,F t;6 ,totfa
^. tE ,'{oa'tlub + tb
o>0,b>0;
szg. rr =r = (vt)'
" vt * r
V2+1 ("8).*r,
^. 2 z (lDE * Jis * "61 "-2r *',. - '-"; ";" '-'= {zs {4s "6:
3, 15 rs(,6-r)_.,"6_,,.- V:o r{/o t o t
+ ----!- t(f '.{o) l,16*oa),!2s-t2o+t16 s+4 9''
=!+-l,Ett.3'
116($* $)'{6('it -'.i6)
tr
Gll; -'l;) tt; .6= ra6-6=O=v;'
9)
("6 !(i6.!"t(G 1)
m'O,n>O,mxni
(V, Vo)(@1. jg!:141={n *l,toa*tr|t", o't,
tE t'b
o, olo ali -.t*(J," -Jt) - Jo -Ja. , o.a u,Joa ..lab
rlii + tli r6(i6.1) 15r -i :: :- --b' Lo'Oib/oi
tla"t:' + va,t Va'b(1+ Vbl ndD
6) sLr,3 vgql--! i/27,r.v3 \i3
318 ltt AITEEPA Mep3rer< a. r. ra iH' AKaaeMi'{Hrr pieeHt il::li!li:!!:::iid
A, b _ s slJro -1./r -r) Vra V[*t V4{Vt6 v4,1r2 "J2 {\tla - t) :lz1t . t1 Jz 2
3so. 1r =1 == (if' q[t * i,6t).
la+lb d+b
zlvs vz) . "," ,,,.- {sr v63 rv49- g 7
Bt -"=.27.. . "11'0. 'l Trf.-'r,Vtoo-Jrorr lo I 11
n, ),-- rl(g. aVr * vE5l =.lg3d5'V25) o,r(s ra{6-uus).3 - V5 (3 - V5l(9 3V5 r (/25) tr
3ai. 1) i/a'D: = abi6E, a >o, b >D:zt +lo't = ollt, a > o, 6 > o;
tl +lo^o = o16, d<0,b>0;
3 .D +[-n" = \[-n n" = nld;=n"d;, n<o'2t il;trn -la,l. * 4,li = "'lb" tlb = ,Lb"{b. a > o, b >o;
3) 
I 1 lntn'3t nnl *=\l- *=lmnl
be6 = 96b", D > o, a6o -iGf , D < o;
a!-a=-ll-a?,a<O:at6t, = _l}t,. "t' = dVt", t < 0.
38s. r) c&6 = -t6c', c <o: 2\ a{i =d7' a>o;s\ abd6 = !t6a'b', a<o,b>oi
qt awl l= = piei ". =. Vro,a,. , o,\ld'0" \ a D'
g a1[4 =-d4, a<o-
,,[Y f v, {6JIrf.,t v,,
. l,'-xF \1" rb)({x - tln -t[t') lo -+EEtt[xJa 'lb (Vo - Va)(V, + Va) t" 'tlt
" +F t'h '6r (v" - "6)\+G
-to)- va tlb ----- iJ; atlb -
+lV y*Ei *Jt" -<,F,tl"t +tr"t -+6 -\Ei
4)
5)
6)
<li * <lt"
. :,1"t kE * "lt\a,
-:=
Va;(Vo + VDI V,
llt" , {t" **[a" *El7 24bc -2{VVa+t[
(.,tr - JiJktr. "6)ktr \E)(xF ttF)
4ao
6;4;=
386. 1) i6-t.&[el;6 = !fuIo 3' ft;ffi =
= frt.-tr.E flilF = {,Gs .ii')o-l;J" = v1?:6110 =
= i6or - geo = r;
zt {i+-a.ls 'E"b.,={;;-"T' \FEd =*Et-aTs a6;8E,+=
={u iTs.$srBG = 184" .8" i= {i76-s:o = dzra = +lte" = "ha
=s;
B) ffi-n'61-8G='@-T'tm-;m=='{Tb. rfiE.'{61 - &tr ='61. 8'4l''i6-ffi ='vtrj- {5 =
- ,So-r .ooo r:
q .F+iTz. Ja -{z = {dAf . 5 ;a= ffi;ll."tl tc-E =
= $* ta{z . +,E - t{z = <FF= n6 Jt - ETz = 4c6 rilzr 4 = 1ll. 4 =
=,tr =2.
sez. D \F -iFz - <,E* "E
= {F -lG iG;tr3I = {i -iTs 1,E;i; aG =
=i,FjF('*G) ={as-a8=ti
zt Jua-i tEs.qJ6 = t/(z,G t)' {zs+aJo ={24+r-4Jb i/25 ' 4J6 -
{t:AE:tl1"6r!t r) (v'-r)' j,G {"J'=-1) -#.' lG-1 q/r -r (Vx-tl(V.r+t)(Vx t)
32o '.tlil AITEEPA Mep3ntx A. r' ra iH. AKaaeMiqHri piBetb llf;:i-:I':li!:!::1
<li * {t^ 6 -'"G*tE.'. Vt+r=15-l.. "G+zz
( +G-z Voa gl- - t/a:' {;-"tE l"G.ze,G s Jarzz)-
, Va r ",Go -s (V, -a)(,6-r) V,a s'v" aV" -s-(16 -r(J, -3V,,el = t#-t(V;-3q/-r) =
. (tG - s voa s) _ Vo - qf,t "v" (vo Vat.(fi
' a)(V' - sv" , s) G'zz ,E zt
" ,G - zt v" (v, ,.6) ,,_."'""; 6 --G-n -'"
,, | " G
^ -@- - -l -'.- z"u " l, t to - ?,t; ) = ",tb - "J".
I Va' + zVac * V.' Va' - V.' )l. BH'(oHycMo roroxHi neperBopcsFr srpa3iB:
Vb"(rt. i6) '"6" _ .
({,6 . {6f <li ' <li'
b-" (i/t .l;)(tF.+Wt,lV) "lt"
**E;*J""
'F J"' (Vb v")R/b if,l vilil2. B!&osy€Mo Airo y Ayr{(ax:
{b" do" t t|i *:lV -"-16 * if tlt *<liitr lF (i6-*6XVa+V.) "n.-ValF=- va v" rvD-ic:
^ {tr {,t (,.6-.[)(,6.r./i) ..' "{fr.*[ ""-;; ';"'-]!=l/b-{':
a-b 11 rl6) -----------F- :l , - ',lio,tla'-!a't tl"t' t1a' 111' ,0,('a .6XG -.6) . li *:li
xtr (<l; - lb). l,F (d"' @)' 4;4i
;{iili.li'iltli AITEEPA Mep3rcKA. r. ra iH. AxaAeMiqHrr piBeBb fl:l 321
--- I I Rr r) V. Ji.t.389. 1r ii --F- , -tVr t Vr , Vr 2v' I
=# q-E -1trr,(V;-r,6)=Va-Va
r:t" :la\' tvo i6l{V: f) = ,, - Vr.
{i6 - {6XeG - c,6) t/d - t/b
lluu*o, Vo +S = 96+Va. toro:rcsicru opanr.'m'a'
.l_.Err (,ar'I =
(l/;- Jtt)(.v!:4 G.t'(,t*r)"F {" ' )t
*u"*o, 6*1 =
J' *1. Toro*{nicrr, rparrnL'a.
tx
^ | va - ga r (Va '6')l . tE ua
-'1tt'lffi ,li:Jt' df,'la 'vo--d,^ G u,'
r (.,/a V,l ('16 i,)' 'lo '6 .
' J"-Ju r6ira -ilG)(t;y; \{;.,bi'- +G !t, "ld -;,tb li la - Jo ' 1,6b - ""6k1" 'rE) .
' rlJ,,[" ,!ot-- trn -yrr -* -iv"-!bl"
".'c'
va{Jo 16l V,(l6,la) "l'b l!'b
' iy"'vor' ,,a -l;:T (v,-vb)v" 't-' vb
To.o)r{urcl6 npaBun6Ha.
gso. rr i,[l;E + iE] 5.8 . :r,u*uii * ,5^f2 t lli - 5{2 = ,.
r*' (i,[*rO-if GE)'=",
,. r,E 'r.'E,rJrl {t ,'Et , ti/G. *rrtt turt z tJz ,".
r+or 1-ry (1fi * s./z - iit - 5it)= '",t4 3,=f,f+* t4=o,t2 2"+2f 4x+7' l4=o'a'z(x-2)+2x(x 2\+7oc 2\=0'
(r 2\(r'z + 2r + 7) = O, t = 2 a6o * + %c + 7 = O.
PiBEsIlIrs r'+ 2t+ ? = 0 He Ms€ xopeHis, 60 2=1-?= 6<0'
o,*", iF ti"E n fi - sJi = 2. r{uc,T o 2 paqioHa-'rr,He 'lr-rc'!o'
a '6.,E
- ro i,6.'fa ro. n",.* 16'6* 10 i/aG- = '.
t-0'6-ro-rii(o,r, ro)'{o,a ro) -si/(a,l 'rol(e,a ro)'-(e,[l- lo) ,,.zo - : . z1G.fe * ro * a . ,i6.fa * 10 - "', zo o(.utoGrro-ffi ro)=,.,
)c' + 6t - 20 = O, x' - 2r, + 2t 4a + lfut - 20 = O, x,('c 2) + 2x(f, - 2) + 10(' 2) = 0,(t 2)G'+ 2r + 10) = 0, x 2=O, x=2 a6o rc, + 2, + l0 = 0. PiBHsllHs
rz + 2r. + 10 = 0 He Ma€ I{opeHiB, oo 4=r tO=-g<0.4
o'*", .,6'6 - ro = 'Gfu
= 2. qrc o 2 - paqioHanLse q'cro.
391.,iloepcr u, *o i,)O-ra,Z'v'ZO r+.2 q.
,qoBeaeHHs. ne""t i6o * r.r"E r So - l+'E = x. rliaE€ceMo ao Hy6a o6nasi qac-
({n *r4Jt. {n 14rE)" =,"'20 + r4,8 + 20 ra.E * si,(zo n ra.fz)(zo rrf,z) ({60;lt$. ijEo tE) =',,40 + 3V400 3s2.x=f.,40+ 6x=J.3, jr3 6' 40=0,,3 4r' + 4a' 16r+ 10r-40=0, |@ 4\+4:t(t-1) +10(x 4)=0,@ 4)(r'+ 4r+ 10) = 0, r-4=0, x=4a6ox2+4x+ 10 = 0. IIe piBEEEHT He
Ma€ riopeull, oo 4 = a ro = o. o.4
o,*.. 1E ttA po . u,E = 4. roro,$nic16 roBe FHo.([pr poBs'sByBaEHi BaBAaHb N 390 i N& 391 Mor{Ha Br.iKopscroByBaru OopMynrj(a + b)3 = a' + 1a'b + \ab' + b3 a6o (a + b\x = a3 + 3aD(o + 6) + b3.)
_ fory€Moca Ao Bl,tBqeHHr HoaoiTeMlt
s92. y=Jt.r; y=]o,re =o,a; a = uE,u =t,z; y=uEooo =oo;z1 o,z=.,E, '=o,o+ 5.=\l;, r = 25; 12o = .,E, jl' = 14 400; -q= G, xe s.
393. y=G.L\ A(16: 4), ./te = a, ran. fpsoiK OyErcqii npoxoAurr, repee rovny ,4.
2) B(49; -'lr, "6= z,
"i.IpaOiK OyHKqiI He npoxoairB qepe3 ro.Jl{v B.3) C(S,6i 0,6), .v6,0 = O, o, si. IpaOiIl OyHxrrii He rpoloanrB qepe3 ro.rRy C.
4) D( 36t 6), .faO = e, "i. rpaoik Syn&qii He npoxoaurb .repe3 roqXy D.
"no. r' .E' E!3 '{5
4 "ls, , 'm; s).,65.6=.,66;
q s"E = "Ei , "85; st ,Eo , zJi = Jn;
.,.,8=,F,i.r =ff=a.
= lu6 +]= "6*+;
J{J2-r)'=l/6 il r5 al .,6*a-.8-e 12.
395. 1)
2)
g22 ',t4: NlfEEPAMep3nqK a. r. ra iH. AKaaeMi'rHr4i piBett iiiili:ilitl'iii'i1 i:i::ir:iii:::irl::i: AITEEPA Mep3ncKA. r. ra iH. AKaaeMi.{H,fi piaens !:!lt 323
396. 1) qE=-:c-1; Y'=./1;A2= -x 1'
2) v, = ',li; v"= 2 x.. 4O2- \ a=illl+2, E(v\=[2; +*))4 v=di--+, Ets) =t-4: +-rt3\ v ={; -2, -a(y) = ( *; +*).
4o3. 1),finqo 1< r <216, ro 1< Vr < 6;
2l-72s<'<8, s<{; <2.
4o4. 1)O<r<256, O< i6s4;
aos. 1) i,/i- > i,/i;;D 'tl-n > rJ z6;
3\ 2 " tlU-;
4) l,6..@t. 6. {6 = f,tbls)'so.xa='vo+;el z{i = {u . slz = Jsa;
2) 16 <.' < 10 000, 2<i,t<10.
li$ffi
Bi]no6i0b:1.EtAno8tAb. poaB's3KiB lreMa€.
zl ,E=!;v, = 'l;t
1A,=;BiAnoBiAb: t.
q v =\rF t"+5, '': 4r. + 3 > 0,D(y) = (--; 1l u [3; +*).
4o1.1) y=(/'+L E(y)= [1; +-);
4 a = \,G 2, E(a\ = e*i zli$ v=li-s, n@1=P.
5. OYxxqir Y =f397, y = \lx.fpaoik Ol,EI{aii ryo,(oalIrL 'rep$ ro'rRu: B(1g; 2)i E(81; 3)jC'{10 000; 10)
l
I
39S. y lG. fpa$rts avuk(ii npoxoaxl6 'reoeJ roekt{:
A( s; 4; B(*;;); r( looo;-10).
399. t) y l,G. t. aryr R:
\ g = alx +1,, + 1 >O, t> -1, r(Y) =t 1; +-)ir:-,
Srq-:i'-1. x -2'O.x/-2'Dtut t -: 2r-'{ 2: r-)'t}rr - ---\,--- --\7-
a1 y=18 "-2,""-t 2>o, - Y Y 'r € (--; -11 !, [2; +-), D(y) = ( -; -11u [2; +-) -1
4oo.1) s = \l;+ 2, D(i = Rl
D g=\E'x,2-t>O,t<2,D( =( -;2ltl^
sr y=r/'-^.,r -3, O.x'3- Dlat=t -:3t 13: -):
t6 j,'o b ;(i?r 4i/; {' " = ilaq z :lzsz . rV; = {" "'
ffi,
', ,/i il? = {za +13 -/1:r3 vs a - +Er.
406. 1) .',6 =&/i% > 960;
D XE = \tr = ',X16 . "XEGI
3r srfa = !27 a Vros . a'E - tT z tT,"lq E!0,2 = {62s4,2=$zs >ro{o,orz =fo ooo.oprz ={rzo.
4o7.D1<J3<214) 4<V100<5;
408. 1) 2<v18<S;
47<4s<2i5) -2 < v30 < -1;
2) s<{/isg<4;
3) 2<1/21 <3;6) 5<-ve1 < 4.
3) -6 < -V212 < -5.
4o9. 1) 4 i ii{;0. qi,li qrcna, p$rarroBaHi Mi}li HuMI,: 5j
2) iFSs i {640. Ilird q'cna, posrarxoBarii Mi,x Hr.rMt,^t 2; It Ot li 2; Bt 4i b,
alo.Ilini qrcna, posrauroBaHi Mi}Ii'rrcraM[ ,/iS00 i iAo' 6t Et -4; 2t r;0i1;2;3.
a11.1) {6=i66>G=V2?;2) V12 ='.V144 > 96 ='{A%;
3) V3 =,V2? . V2Jz = VJ28 = 92slq tl'ln =:,tii , ttr =
"E = tE;
5) i6=16.ffi={Es;6' irmt 'VBz ='dz' - tz 'Ja slz = ,[2.
i;r::::iiiitiliii: AIrEEPA Mep3reK A. f. ra iH. AKaAeMiqHni piaeru lilr gZS324 ri::!: MTEEPA Mep3rqK A. r. ra iH. AKaaeMi'{Hnr piaenu lilllliiliil:ii;i
412. 1) G i 110; rE = i[ % < 1[40 = f o ooo, J-r.Vto;zt r1ta = "E; i6 ='gEs ' "t ='96t, r,/ie. V"E
'3y 98. i/2",2 - J,s '{8. '{z - ffi,+> .liE = e,E ="PIn, {G = "!" = \E',f iG.
q1s- \ "Ji; 'tE; thzl i6; 'So; iE;g) i.F; {,E; .6ral i,[E' '.i[x' i,6.
cr+. r) .,6; i4; i6; z) i6; i[o;
415-1\ a = -lla;
960.
2t u=4x 2;
{$ffi
326 iiti A'TEEPA Mep3reK A. r' ra iH. AKaAeMi'{Hnr pieenr :iii,:}illili:lil
fory€Mocr Ao Bl,tBqeHHf, HoBolreMr,t
417. 1 = 2o., 2 = 21 ; 4 = 2'. 8 = 2s; 16 = 2a; 32 _ 2\ 64 = 26.
I z , 1-=2". !=2". t "..
1 2.. L=z-.248163264418. 1) (-8F ( 1)r'= 64 1= 63;
z, sl ?l' =s. a =!.t 9l al I
gr s'' -a'=! 1=!,34124t 2" +6" =1* r =
9 * 2 =11,a36727272
srlll +t-2.:f s' i I '=8,5+t-0,04 4,46;t7/ 2 25
6)9.0,1 '=9.10=90.::iiti::illtill: AITEEPA Mep3nrK A. r. ra iH. AKaaeMi,{rinn pieens f!
, a=!;+31
s\ v = ilii2: +1 y =!2 x;
5\ a=\C4-z; ol y = {rl.
416. 1) y=-Vir; , g = 4lci;
419, l) a1 ar atll2\ tt1 : a5 = a':3) (a15 = o$'. taJ)d . dl di3 . o4tlt ---.-iE = -;-=oI5\ {r5 a3=azl6) a' ato otr - a 1:
7\a-ttat5=aI'8\ ar' a'o i ae = a12-2ite - a'9) (d 5)a = a 'zo;
10) (a,) a (a,), : (a-313 = a3. a6. a-24 - a3+6+21= a22.
42O, 1) 2s. 2 1', 2 " = 2 e \',+" - 2
2t..r.111 =' : =21=i.l' t3i
t,4)=2"=L,t
4t9t.27,=33 36=3':;:
, ?, r,3,'1" 'zs,'rl25r' 9 125" 9 9.9! 5" - ^,, ^,.t)['oJ llr] I'ltl t27)-% 27' sr{ -;ii 5r:J-
33^. 226.23 2" tl' 23 2' 16u, ;;r",l-fr," -to--"=2 t6.
6. 8r3HaqeHHr ra E acru8ocri creneHt 3 paqioHatbHl,lM noKa3HtlKoM
rr r ^^^.i^r a425.1t 4 =J4=2t 2t25' l2b': 31364'-3'="::,
4r -5 0.01 = 5.' I 5.r00 s.Jroo'--s f ooo ooo = -sooo,\ 100,/
lrz1 au =Ja': 3l b - ';:
!D
b) t..b) = a oi Gi: 6t ob' alb'l
Ed ro ^r
"asr o.rz; i .lloool' J/10" 19 loo
= l\ r25 ,r 'J 5' 5' 25
er lnTl"=li?91"="/tP'-l3l' 3 243 .ts.\ 64) \64,] \/ 64" \2/ 2" 32 32
427.|t y = t6, ,(y) = t0; +-);2l v = t La, D(g') = (0: +*\13' u = k - 3)L6, D(s) = [3; +-),60 jr 3 >O, '>3;l4) a=@'z-6,-71,, r(y) = (-*; -1) u (?; +-), 60 x' 6a 7>0.
.?424.1\ s = x', ,(y) = (0; +-), 60 r > 0;
2\ y = a3,, s = ai, ,(y) = [o; +-), 60, > 0;
3) !=lx+11 "rC ',-Dlll tl: r-).60r-r.0,.r.-1r(r + 1)it
14) v=@'! x 30)6, t(y) =(--; -51 u[6; +*),60r'?-t 30>0.
o, n.r,o i = ,/]!gq = ro
= 1= r?.' 1216 6 3 3
7) 27, =:127 = t127' 27 =27 3=8rl
426. r) 8: = J2" = 2l!-
2) 10 000' = l/10' = r0r
3) o,oo81 o'5=(o,oo81)ii =(#,)'/1\;
tt 1 =4, =,143 =23 =Al\4)
tt!429- I) a' d.3 =a6;
4' ao6 . a\5 = aa,.??1
7\ ai i |la, = az : a6 = a1r.
7O\ at.aE.a3 =aa'aa =ai.
1.. d"o" - ';r ^D ^i.Lzt _l_4
.?
',l':J '={#=;,
", "r".=[ t l'=Jt =1\32) \32 2
/ '\J : t: :2) \a,J ob; 3) d, ta3.-a? , -a6l
rr (,"/ tloi 6) \a a' =at a'=an1 -! l,' ill
8) (a '.1\4 = a1.', 9\ a3 iaa =a3 a = a3.
11) (ao,)o 3
/ r !\i r !13t \a6 b,1J =a, b'.
421. 1) 53 = trE
4)106= +--lv10'
A1 6 -es1i = 1y 3y1a={1r 39tr.
11422. tt t3, = Jlsi 21 3' = ^t, : 3t ro' .c' = Vc:
v3o :1
-ay x " lx6; b, BnrLno' 3m,n, =3{n'n":
6) (a. - 2bli = 4t" - zt'1" .
a2s.D yli . x 2) ta" =oi;,
4) V3o (3d)'; 5) ,12'" =2"1
tt llto - tt . t" ot", 8l Vr- b' = {d - b )s.
az+- t1 Jz =2it 2\ -{a" = ":l
4) Vbo' = (5a'); 56d6: 5) i/r t y tx - stt:
s) V6u = 6';
e) ,1[s = 4e'r;
,!3) \ns =n u
el 'i6F = o,ai.
illl:lfi!*illl UTESPA MepstqK A. r. ra iH. AKaAeMi,{Hr.rn piaeHu llt: 3Zg328 !tl: AflTEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hnr piaexu :illi:il:lill:i:i:l
f
t4\ o: . o''" . "2
. "; = .; ;'i: = "'
lot \otl . lo 6/ =,' ,'".
43O.1) b3r 'bL'=bolia1 t,t: =6"s =6i;
f ?\" !5)
l6',l = D',:
7) lrE tb 6 =b.'6 =bE =bi' 8)
g)o b, o 6t o"i6- "=ai 6-:
10r al o'' = a' 16 . bt'i = djd . ba.
oi bt
/ "\, r L
12) \o "b, J = arb 3l
14) (6o6f 5 bo.{=bo,3 bo,r-b01.16) (b1){r : (b o,a) 5
= D '3 .b1 b43
:; lzs"/ =\1./ =s'
b i .bi =bo -1;111 i
b,b1=b 1=b4.
bt.,lb=b,'t=bI.
bj .b a .: :,:'-.'_=o'"'=Dibt
r\ \oto.) =a)b'zi
1'rt,t,!131A) b' .bt b1 =b, 3 a =b1,.
15) (' o3f . (bo.3f.{ = 'i.3c
b03' bi.o4.
n, ll I " =,2 "t " = 7' =B4B:\ 491
..'-6,' . ... t20,,,zi ,zo.t'bt 12") 1.4' -l;l l;j =l.:r.J 4, .t4'=J2Lo 2" 22.
!!4,8f 33_":j-".
a, Bt
7) aD4.2t3 =2t'.21.3 =23 =AI
8) (6r3)a.2160,-606.(64f,=6i,G 60,6 - 60 ,1.2')
4)
6)433. a > O,
r) ('6)"434. m > 0.
I) m =lm")';r / r)'
5) a, = \rn,/ I
435. b > 0.
1) ,6 = (b':)3;
ar = ta.l :
," = ('"-/ ;
2) b15 = (b t)3i
o ,i = (6'i,) ,
*'=(-:)' ,
v = (,3)', a: = la"/ ;
zt l<,li)' , ar (Jo)"; ,1r (Va ) .
4l
8)
4',)
8)
3)
7\
3)
7\
2')
6)
431.1) a\" srd 3r3=J, =s; 2) (503)6 54.s-5!,3 5n.3=50=1;
( r), ," ^,1+sz. r' lars: f-ll'l \r, , "f =7, 7 . 7iI t49.r /
'''2) t0" 40i.5- .lot ]oi 2r S, l0: 2? b = I00r t0;
31 0,0016 4 0,04 ^-0,216 J t0.2', i-fi0.21)-, {{0,6)') ,-
o,2'-o,2' +o.o' { Il -t*25 tzs s*27.-tzz1,\.125) I I I4) 625135 25\5 \253 =(5{) { (5'9t5 (53)t=5' 53 . 5' = 5 3 . 53 = 50 = 1.
.. 32"1.4o- e'f \ 2t1 2t,.2t4 Zb ^, I'r 640'.t64?" (2')q(2")"." 2L6 |=2h-z 4i
^ t2 3' 7d 3 .2.3 7s6) -- r'"z' .8-'
I , ! l"t' |513i, | --t"? ^"-s' 2,.2'-zs.s:zse-2^ll:
frr; z;.J ' 3 2 256
ll 11 r: l" I r
r, | 8r'.8" | .l 2' .27" 33 21 | . 2'3.3'n"'l;l;l l,T,*1.] L,I;l ,,: ,;3',,,2" 2-3, 2, =L.
729
b) I I J r,2" =t1,2t0 .1,20' t,2r tt\ bJ
o'l'll.l i 1l-,ro1i.,roo,j l'o.rooll e,[ooo = ro:\r0/ l'7001 \7./ .17 )
,,e:=i="ii=r,2t 2'
8) 3601 . 6" = 60'3 . 61': = 6': = 36;/ r\16 / '16e) 14 "/ .16"' .\2") z, 2a.4.2,.4 2, - 4.
432. 1) 53.' .5 r'3 .5 ': 6
53 ! t3
'z.6 - 5n - O,2.
2) (7'orrl t7
/ afJ / a\,B) le?J = \s,/ = s: = 81;
lr l |l =rreri = t/tc =z:'1161
33o i::::: AIrEEPA Mep3rrK A- r. ra iH. AKaaeMi'rHni piEeH" iallill:'::ji:.::
@6.2')" 2
3*
iit;lii::jlllill: AITEEPA Mep3nrKA. r. ra iH. AKaaeMi,rHxt piBeHb iali: 3gl
a3s.r) I-; 0,04; .r,=(0,2),)r; l1l .tto,ztf, I -0.008: x=125:\ I,/
2t rx-2t) = 32: (,, ,,i)1 ,r., .x 2=4i x=6:
3) (r'7 2.rr] ,, -L =-t.xea.lr" 2.r
BiAnoqiAb: posB' trs: iB lle]{.ae.
499.1\ t Li = 27t @ ti)ri = 27t, ,a = A2l
1
I
.:c 1= 0,00001; .t = 1,00001;
44o. r\ aa 2Ob 4h - 5b\ a - 5b .
12ab 4 1ab 1ab
2l r' ,1 ,=tm.Dtm,_n+tt m_r.m'-n+1 m' m+1., m' \mn mtm lnt", tb,' _.J, - A(5, rlr) t'
7a' - a"b art1a bt ar=' b" _7ob" - be(b ra)- bs.
^. u'-t2!t-36 U 6f (6-s)' 6-go' te -, ={6-116. y)- t6 gx6 lt 6-g
--- -. 5a+3 6-ga 50+3 6-3a (5a+3i(a-3J+(6 3al 2a441- I I
2a'+6a a'.9 2otot 3) (a 3)(a.3) 2o(a t3)(a 3\5a'-LBa+3a 9+12a-6a' , -a" -g _ la'+g) .
2a(a+s)(a-s) za@+a\@ 3)-2a(a'-9\'a.4 4 ato 2\ (a-4')(a-2\
"' x. 40 '4 a' 4 \a - 2t' \'-\"-2t---a'+2a-a'+2a-4a+8 8=-- G-8@tD = la-zr"(a+41
o, 2p 5 2p" 2ptp-51 _ 5V_jL | _ 2p'"r,.5--p e'[t p" \p-s)\pns) (p+5,{p 5r {5 pl(s -pr
= 2j- :op -5p-25-2p1 5{p 5} _ 5 .- (p 5Xp+5) (p-5r(p+5\ p 5'I u-8 1 1 ur8 2-', 16-u" y-4 c \c 4)ty 4) a 4
y'-16+@+qv 2aQ+4)
a' t6+u'+8a-2a'-8a -16 16
--!J s v'l -ytty - u't= urt6 -n\
442.tt(3c-t_3c-1.]. 2. g.'z 6. I g.':+6c-l'l3c-l 3.-lJ 6c-2 {3c l)t3. lr
_ 12c (3c+1) _ ]:2(3c - 1)(3c + 1).2c 3c - 1'
332 iltiA'rEEPA MepsreKA. r. ra iH. AKaaeMi,{Hri piaeHb iLtiilillliiiii
2 I r\t2r tI 1ij=1ooi l(.r-r)iJ =100 t;
3) (,.-b)t=0; ' 5-o;r=5-
(i rlzal1 r 2a2l
--
-:-=l--
l:ta 4obt4b'? 4bz az) a'-4b" \.k-2bf t2b-a)t2b-at) a'z . ab'z
_ 2b + a - (2b - a\ . -(2b - a)(2b + a\ : -2o = 1 = 1
(2b-a)"(2b+al 2a l2b - at 2a 2b-d a 2b'
o,r d o o"t1l.o' a lota rl)-ora-1) a'-t ta-tf"'l, I-" r -i-71 ("L' -l'
'L a'-t) x+aa2 + a a2 + a + a2 + 1 . (" r)'
= 9!l2g:))g_]I9) - @ + 1)' (a - t\o' t o(d ' 1) (a lr(a + 1) a(o - 1, a(d - l)i
a-1
443.1, abt + atb;
21 2a - aat +\at = 2dt
A\ 2a + a\"bq" -6dasba3 -2a-saasbo3.
(^i)' ("i)' = ^i "i(s,;)- (.:)' = ,,: -/,? 1t ?
a3 + 2a3b3 +b3.
4\
(,r) _, 1,r,:.11,:l'=, _1,;_r,:.4 \4 I 2 16
(aq4)x + 6Dq1 + 9 -6Do;' = Dd;3 + 9j
(.t/ -r'=.-rr/ ,\' / '\'\a'l +\a" I =a+a':
r lt , \o,-16o"-(r'-1s'"*25)=" -roda -ds - toa, - 2s - -2bi! !1 ? ! '] l r ! 4 ? v ? 9
b5 4brb3 + b3 + 4b6 . b34 _ 4b6
/. '\' , ,r),U"'l tb'/ .l("' a'l=1,' .6')\6' -a")=a" -2a3b'+bx,
,,) [; _J[; -";.,1)G -1)=("; _JG.J_,; _'.
444, Ll L'a\" -2oao4bo' +\aD1bo' - 4ban = l'aas -tTao4boz -4bo1.
2) (nx'\'z - (no i)'z =n-n'/ ,\' / ,\'z
sr l"l -(sa ,l =a" -2sb';tt
4\ m 2m'12 + 4i3 !? 1 ! 2 !
5) b3 -2bcb 3 +b t = bx -23 +b B
ttti:{iii:::::iil AITEEPA Mep3rqKA. r. ra iH. AKaaeMiqHri piBeHl tl:l
i .i'z1 \+n;) tzn-,n; $n.) 16n J r 12 + 9'i
5)
6)
11)
12)
13)
8)
9)
10)
14)
-a06 - a')
6c+2
333
uv ('i)' * r' = *i * r,T v3 av\r . aon +rca + gy'z = g3 8a'+16g+8a'=uz +16y;
1 ?! I a1 1ll 1 I I I 1 !8) c3 +6cscc +9a5 9cr2c1 6cec4 =ca +6c6 +ga3 gct -6cc =ca-
s' {,,)' ,'J{,, - r)= {"1 r)i,; ,J=,1 -,,
,, ((":)'.(,:)')(,; Dt)=(,i .bi)(":-bl=. b
qqs. rt \0,) lo',i -1,, -r'")1, ')l, (":)" _(,:)' =l"i ,2)("i,bi)
, (-r)' [;)' =(-:-":X-i."]),) (,ii_(,ll=(,: al)(,i.B;).
,) (,:)' (,,1f =(,: -,i)(,t.yi,),6) (2'L,\, - (8s".* )" = (2'o., 3ao35\era ' + 3v4
35).
+ao. rr L:) lb)' l"; bll': -b')
, (-;)"_[:)' =(-:,;)(-;.";).r, (,',)'-(,' | 1,,1 , -;1. ,11
o, {,,)'-{rl)'=(-i ,"1{-l "r:)
o u-"= (ui)' ("i)' = (u; -";)(u;."1).
ur ro,'"'y,(u,i)' =(n'",' uri)(n"'*-u,i)
oor.,, (,i)' r(,1)' =("i *r:X":,:u:.o;),
,) (.,:)'.(b;i =(.;.ri)(,;,:u;.,;),,., (,'*)'. (r':)' = (,.' * r*')(o; o':r;*r;),
oon. rt (oi)" * ro|=,i Ll n r),
o ,:b: _.,i0; _ "ib:("l b?),
tl , \s)
'?i lm" 1/;
'/ 6
71 2, zt = z, \zt l;
ouo. rr ,3(,i u)'
/,\' t ttt \2t \b,I 4b'=b,\b, all
ll i \ '/,
\
4) c. _ci =ci\cr _il=".1.. rl,
e'1zi .ai -31 =ri(ri J,
sy "l(,1.f.
\0, + 2b. )
\at +*) ] l
\oi + atl
'l ' \-rl-, tl
+sr. rr ",'i -i'=o,r\a' - r/
^. a"la.+c'l .l(ai n .r/
I \ r\/ r r\ r
_ ldr - brlldr + b,l at b1Dt ,l/r r\ = _-iT;
a,b,\o, + b1) aibi
,) ,l ("" I .6)=,;(.1 _6)
,, oi(, -r, l) ,i(, ol),4) bq3(3ro; - co.5).
" ,loJ.("' ;;-,1 1)=,:r;(":b; _1)
u') ^;,;(^*^:,:,,).z1 1z"1iu - 121i = 2i; 2iu = 2i("i J = ri(r-' -,)',y ,03(ro3 * J.
: a+la'(o + 1)
= at - zbi.4)
6)
4)
5.)
6)
334
[;)'.r. =[; *a)(o aoi *s),
,"",'-(r'J' 1"" ,i)1"" -2:""' ,:) l"i,z"ll"i-rl'' r11.
[;)'.(,;)' =(,i.bi)("! "?bx .b;).
::ii: AnrEEPA Mep3nqK A. f. ra iH. AKaaeMi,{Hhfi piBeHb :i;:::::::::;:::::::::::::::
,,1:"1 ,o\,), =r": "0,", 8)
\ze za' )
o,')"-l';"\I" (.;)' L,l h" .')(, ,'".' .) ^.^.;-,iillijilliiili; a,nresPA Mep3reKA. r.. ra iH. AKaaeMieHrfi piaexu i:ilr ggs
tl5 \
'o''l).1-ul=1,rt [x, 6J .r;,l ' \ /1 \
t 1',la' r ?/.
= ,_ ld' + 71 = JLi
a,\o, $l \,; _t)\,, _z) ,,_t
_ ^ a' rt oi 6i(5; _ r) 3. 2lr2r:-:- -,,-, 'i = --__: = 3r.
2i.Ei _25 z, \s. _rl 26
1t' \+sz.ye!!!:-!.=ol.
1"1 . r)
o I aro.t _to.|r =
" ,"(.: 36) ,,;(.t 6)(,,; _ 6i , { : "lE) I , r = r L , m'\m" +oii
'1" \n" - 6i tn'16 6/
r r : ll ! \ I^.
8i .31 84 8. 13. li 2. "j
31 .2t _ 21 34 84 rl 21
( 3),ou".,. l n I
' l -l t ' l (o -'
' (rvr) ll= 1,'-- - l.- .2, t ) 4
,r u: -(S) ? =1r'fi *1"''"ri =zi ' z-",?
u n",, lr r;) e')"^ l2i) " =r.o. -r'=z' z',t t \/ ' \ / ,\':
:r lzl-z')lz -z )=\2,) e't' 2 -r'=i-i=i'336 {liAIrEEPA MepsreKA. r. ra iH. AKaaeMilHr4t piBe*" iiiiiitiii:$il:!
t r i t t\u r : r r ltui,.tr+Fa.3, l31 2t-8, 24IL - - - - l- -, -,
I =225+216=441i\ 5,+3. I '\ 24 -3, )
t t tli ,\t6
,, I r'
,r'lr" -,e'I - (rl)'(rll' = B" .8, . zb s 22si
1 1s' +e"J )rt,' r r r/, rr,d
", s".z la, z.lJ s,.2,\24_3;llzt , , -r- = -, , ,, | 3' 2'=2'1 8=216.
I lz,"g.l I t [2;-e.] )
o"n.,, tlr -ao'rra"5 + aq') _(au' - r"")
(ao5 bo5Xd+dorbo5+b)(ao5 btr5Xaor+Do5)a + 2ao.5bo.5 +b-a_ao.,bo.r _b------;t' . b*
4ss. 1)
\^r ,i). n mini - na - ms + min - ni -- 2n.nit
., (ao5 bo 5), + (ao. + b" "1.
- 2(a+b).a b'
e :2!::!:t!r ! :4i!: ! 2a + 2b
/ , \/ ' \
ar -_tllai*tl
.1, _ir;) j =b'" _1.1 b,:" 2.
t,ti il.r lr, 2\ /, ,,/ 11/ I !l\"' ul ',\",-a") la' -a'lla, a" )\a" ' ai)
"' T;l - 'r 'fr= ,ii ri,
a6b;\o' -brl t"\a, -t') o,b'\or brJ.b"
. G o',)\"-'lu,-o)G',-oi)\' '',u; o)
a'(a t)i.",', @-ar!
_,, orl, -,'.!', - u)1" - "',0'", u\=(,,, r,
":rl)(," . r,,,1r1)
a'to - Dl
a . tt - liui)' = a" + 2ab + b" ab = a2 + ab + b' .
- ao'5 + bo;
;
(,1 .blX,:-ri
. .. / ,\/ !\,,,, (,,'")',tz o':ltz.'_o"t 1 o1",2-o',=s,
\' 'i),, ("t ,r) l ::l=!:-4),; -"('l-bl)"; --""
I ,:b; _"bl ,1r(;^_",) ,(rl _,1) b'
ii:litlitil:jl:t A'TEEPA Mep3reKA. r. ra iH. AKaaeMieHnt piBeHb t:!li 337
{
. .1,^ ,, ",1(t'-",:) (.'-t)(,,i .r) r ^i+t-t ^L I''
^;Gi) *(,,- ,)= .l^: )456. ltCrporqy€Mo iiBy qacri") roroxHocfl:
( ^"."'
,?+,)l?l : :i-'=n'm':\m, +mn, mt+nr), m'+n' m n" nt mn n(n m)' J.i ,") .,-,,,= ,G:-,) =.F_,,)=
"("i ^r(":.^t) ,("i ^:)= f t-lr= ^m\n' + n'lI : :\
- n\n' - m'1 m ..
- r/r.. aoBeaeHo.
2) Cnpoury.vo iiBy qac.HHy roroxHocri:I ^a.s - ' -o5 ol\".2""'n a I l;d',r-d r', ao" t2 ool z a ao t 2ao ' - 2 - la + ao ' - 2ao' - 21
-
,oo' - t)':(do6 - l)a+au" -2-a+ ao" +2
(atr" + 1l(oq" - t) (a05 + t),(aoi - t)', zaa" -(aa" +11 2 2 .," (aq5+1),(aq5 -1).a05 - (ao' +1Xa0.5 -1) a-1'
22= . aoBeaeEo.
3) CnpoqycMo riBy qacrxEy roror{Hocri:t\,I oJtt., I I oi+bi oit;"t-tI ad b3) o3tarb'tb1 ar bt
1.1 a,bt at asba b3
4) Cnpoqycxro,liBy qacrrHv ro, ol+rHocri:
h' z"a + a')' \r \ / ' \/ ' ' \
a. t,)\a - a:b, - bl \at + t- l\a + a-t- - ol
o, a'b, 2aJb 2ab2 | o"b2 - b- - a, - a,bi - a-b + bI tt l
(0 bJ\a + alb' + b)
!??lq:1_2a, 2a,b 2ab, + 2b, 2a, (a _ b,) _ 2b,(a _ b,J
-lb blla t oii t tl n btla - a-b + blt r t\/ , \
z\"' *)\"+"1t'+r) tttl2a' _ 2bz. 2a' _2b'
1". "!ri t u)
AoBeAelro.
457. lr I. - + ---:-=---Y- -' ,,t ,t r ,/ r rl,'u,\,, _c I r's \,(, .v,1
2lt + D\
I1
t 2xiy'+a+r+2x'a'+at,t t r\/, ,\
x,y1\x, + s,l\x, a,l
c 2rx - ut Ji - zr' , yr ''.i. 1
x;y;1r.- s) (2t + 2s) :,iai(x y) z(r + 0 ' a
pi6no"i6o. L.
^. . irt + 3y" xG - 3y6lt r\'/r LlLj! !\l-" ..;l la6 -,6Jla6+/6,v v1
! t ! tt I I 11 11 1
_ t3 + x6g6 +3r6a6 +3a' + rz - t8gi -3tiv6 +3y3
,:)'(;.,;)I t t\l 2 2\
l" " _a "/L a 1o 4 t 46 t)i-----i = / r-
a 3 -r 3 (,-rL\/
' '\brl\ar+a3b3+b3l2
I t'
|,,\t"7tL, _ la'+b'l\a3-o'b"tb,l _ t _ t _ o.b.' t t tr/ I I ! tl , ?t- | | - I 1 -
\a"_t"l\o3 axbitbtl\ortb,l b'_a" a,.bB
tl3b3 arb3_ = _. AoseaeHo.
338 il::: AI|EEPA MepsncKA. f. ra iH. AKaAeMiqHur piBeHb ir:iili:::iti;:l:..::l
t, ,,"r = 19 = ?,459
Bidnoaidt: !: 0: ?:99
2) P(B' = Ol
10+20 30 24t PtDl=-=-=-.454532i
2@-.'G1 -bi) _
o-ttGtoii tt)tl
= 2a' - 2b'z .
(":- ,(,1 t"oi)-
(,; - ,;)'(": ., ,:)',(,1.r,;)(,;-,;)2- +I t r\'/ ' r\/ r r\
l*. - ,.J 1,.. + y.J(,. + 3!.J
BiAnosi}b: -: t,,i -ai
tsa. t, PrA.r=!1=?9=!,'n4ng
i::iiiti:iiiii::itl AITEEPA Mep3rqKA. r. ra iH. AKaaeMi,{Hun piEeHb Itli 339
45e. 1) P(,4)=#=*;214Biilnnaidh: 15 lo t5
2r PrB)=a=1.30 10
A43l P(C)=:=-.30 15
46s. \ \E;1 = {i - z; 2, - 7 = B - xi s' = 4i
Bianoailo: !.3
D J%- = Jr-'2x'lr
nepeBipRa: 1/2 ; -1\zBi)noatla: L.
2
s\,Ex r=J;-.2x-1=x 3i2x x=-3+1;x= 2.
rrepeBipKa: J, e>1= J 2 3t Ji = J- - "e .ae sl'i"'y.
Bidro8tAb. HeMa€ IlopeHiB.
4).,8"-1=tlF*sr 1s; 2, 1=x'+4x 16ir'+ 2r-15tz= 3'IepeBipxa: x1=-bi G11 =J-11 - ue uae euicty; .rc, = 3; .fi=.'fiBi0no6iAb:3.
464, 1) V.r-3 !,12x-3; x-3=2x 3t.r '6; .r=6.nepeBipra: {6 = d, - npeBr.L'rLgo.Bidnoaidb:6.
2) fi* s=r6lxr,r,r s r'r:S*=O;x l.l6 l 6
"=l. I FcMA{iMicrv.nepeBipka: i4 ; 5 {r ,, i-t I b
BiAnoaidb. nopelliB HeMae.
4 tlz" -zs =V5;+10; 12-25=2t+ 10; ''-2x-35=0; x\= 5;x2=7.BiAno7tAb: -5t 7,
4\ \F-s6=J2r-1) "-36=2'
1; x2 - 2x - 35 = o: ,\ = 6;x2=4riepesip(a: ', = -5; rlEb-36=J-10-1; J-rr=J tr ge uae auictvr r,= ?;
Jta "{l - npaB}1r'1,,so.BiA o6iAb: 7.
a65.1\ J2-r=s 2- t=t';x'+ r-2=Oixr= 2,x2=L
flepeBipriaf nr = 2; J4=-2 - aenpa.afl,Ho; r,=l: u4=r, r=r npaBunbgoBiAnosiAb:1,
z1 .lz+ t = x - 1: x + 1 = 12 - 2x + !; t' 3:. = O; x(r - 3) = 0; r, = o; a, = 3.
IlepeBipria: .r1 =0i 1= 1 HerlpaBrrnbHo; x,=3;2=2 - npaBl'rn6Ho.BiAnosiAb: 3.
s, ',h; 2-,;3,-2=)r\x2 sx + 2 = oi r'\ = It ', = 2.IlepeBipxa: tr = 1;1= 1 npaBvnt']jo; x,=2a2=2 trpaBxJlbHo.BiAnosidb: li 2.
q \Ex'z -Sx . 1O xi 2x" - 3x - 10 = jzi x2 3x 10 = 0; jr, 2t.x, - 5.
r€peBipxa: t, = z; rETzt' -a C2t 10 = -2: 2 = -2 HenpaBu,!6Ho: .r, = 5;
$.!'1.5 16=1 5=5 rpaBr",l'o.Bi0no6iAb:5.
:ilil:.:tilllilli AITEEPA Mep3ncKA. f. ra iH. AkaaeMiexr,rr pieelts i:i:: glr
4
460. Hcxaii y tiopobui r.6innx KyrboK, y.horo (r - 25),ryn6ok. PlAl m = L'''- n x-25
rrro ra vMoeorc ralaqi c."r"r"t" ? Mscvo pisgrgns: * --li z, =2, su;' 7 a-25 75js=50;r=10.Bi0no6iAh:10.
461.1) J2r.-l =21 \J2r-l) =2'i 2x 1'4t2x 5ix 2-5.
fiepeBipra: .,lz z,r-t=z; ,!4=z; z=2.BianoeiAb:2-5.
2\ lx - a -2i (i/t-4)" =23; r - 4 = a: x = 12.Bidnosidb: \2.
3) Jx-6 =-3: (V'-e) =t-3ti! 6 243i x 237.BidnBidb: -237 .
4\ {," -2,+s=*; (1t'-r'-sl =li 's 2'+3=a3: 2r= 3;x=1,5.BiAnosiAb: L5.
sr lz*fi'*z =a; (]z. G'.2 ) =s"; z +{V* =s; ",,F * =z; x'+r=a;xr=1:.x,-.1:r,.1.
lepeBipnai t, = -t;,fi * trEi = s1 ..li + z = l; 3 = 3 - rpaBrlnr,Hor r? = 1i
\q. tllJ 3:i 3 - npaB,nbEo.Bidnosidb: li l.
6) Vr'+rg =21!*1; f + 15 = 8(' + 1); "
+ 15 = 8' + 8jx'-8r+7 = O; '\=1;BiAno'iAb: \i
462-D $: 3=at ("[ r)'=n', '). 3=16;'-1e.flepeBip&a: .,its s =a; u/ie =n; a= I *
"puu""u"o.BiAnoaid6:19-
D .'lSr' x 15=3t 3a' jr 15=9; ga'' r 24=OtD=2898x1= i x'=3.
.--8. /" 6{-9-,o=3; yfn-rs=a: a a EpaBx,,r,Ho:rrEPrirPnd','.-''{"'-;_'"
x,=a: JB.9 a rb ai Jz? 3 rb 3:3 3 npaBlnbgo.
Bianoeiaa: 9: s.3
al i6s -G' * s = s, 2s +,,lVi = zt. n[V * = z; r' + 3 = 4t r' = 1: xt = r,
BiAnogidb: 1; -1.
34o lal: AITEEPA Mep3rrK A. r. ra iH. AKaAeMi.{Hrai piBer" l{i{litiitial
2r.-l=1 2ti4r=2; "=j.
= 5 .lrt o = o - rpaBr.rn',8o.
=0jr,= 5;
fi 2@i=x+2;4(r+ 5)=(t + 2\'i 4x + 20= t2 + 4t + 4t '2 =16; rt- 4;
IlepeBipKa: r, = -4; 2J4+5 = 4+2i 2= 2 Eerpairn6Bo t"= t; z,ln+s =a+z;6=6-rpaB[nbHo.BiqnoqiAb:4.
A1,!tS - Sr - t = x; J15 - er = x + t; 15 - 3' = (t + 1\'1; 15 - 3t = x' + 2t + 1lt, + 5r - 14 = Oi ta = -7; r,= 2.
nepeBipxa: xl =-7; 1tl5 - 31-1 -1 =-7: 5=-7 - HenpaBrnbHo: x,=2i2=2
BiAno6idb:2.
zl , 'E't*-zt
s;, s $,' ,-ai\x 3)!=2xt ' x-2t,z 6'-9=2zz+t 2li12+7t 30 = 0; r, - -1o; r, = 3.
IlepeBipxa: r, = -10; -10-J2(-10)'+(-10)-21 =3; -23=3- setrpaBr{nbEo;
'"=3i 3 - Jr./' +3 -2r =3;3=3 - rpaBr{n'Ho.BiAnoqiA6:3.
el "tz.',18 3, "" =o; u6-g" "'=-t'+2): a 3x "=(-(x+2)r'i8 3r-r? .r:+4,r +4i 2x'z+7x 4=01 D=81: ,,=-n, t"=i.
IIepeBipKa: t, = -4; -4+2+ J8 + 12 16 = O; O = 0 -
|*r*fi 91 1=o',=o He'pa!&r6'o.
BiAnosiAb: 4.
466. 1).[0-3r =-r; 10 -3r=.r'; r'z+3r-10=0; h=-5x,=2.fiepeBipxa: rt = -5j Jto*fs=s; .85 = 5: s=5-npagurEHo:r,=2: G=-z;2=-2-EenpaBrrnr,Ho.BiAn%iob: -5.21 x=Jr+5+r; r -1= 1G *;
1npaBunEno; r, = ;
x' - 2r + 1. = t + 5i t2 - 3r - 4 = 0; r, = -1' di=z; r=ta.-t = 3 _ HenpasunbHoi.r" = 4; {= J9-1;
5) '-!6;'-11a-20 =s; '-s=\6"-rri 20t x, rox+25=Bt,-tla 2oi2r', - 45 = Ot D = 362i \= 4,8; x,= g.
nepeBipka: 't = -4,it ,4,5- JA(-4,5\, -lr.(4,5)-20 = 5; -14,4 = b Henpa,llrnbuo; r2 = 5; 5 -v6.5' 11 5l[ = b; 5 - b - npaBr{nLno.BiAnoqiAb: 5.
467. 1) G:r+1= 0; G-z = 1; 3a BlragaqenEsM apreMenrqEoro RopeFrs
Jr 2 > 0, orxe. pisHsHs' Be Ma€ xopeHis.
2l Pli+t"lxt=-2, sa BraHaqeBH'M apr,abMenrqHoro RopeHs i6>o; {GJ>o;cyMa HeBiA'€M[r,rx q]rcen, .rjrcno HeBiA'€MEe, orrne, piBHfinHs He Ma€ Rop€niB.
s) ,&J-Jf -.r =5: oAs: 1x-4>o' x'4'1t - t - o; ]*' l Po3B '3KrB
seMa€'
PiBHtHHt He M6. konaHiRl- a-
a) Vr-6, Je r l: o.[a: r- '-0' fr>6' r- 6.16 -.r j 0i ljr < 6r
Ilepesipxa: 1f,11uftl = 1 6 = 1 HerpaBurrr,no, or'{e, pis'rr'n, He Mae
s) .,60*"6*r =r, 26+Jx+1=zit .,&*r = -r. piBIIssHs ne Ma€ xopeHiB.
46a-D {; +zda' -3 = o; aai.{isa: {6 = r.t+2t'-3=0i2t'+t 3=oiD=25jr,= 1,5; ,, = 1.
{6 = 1,5; .r=-s,3?5; Vi=L ; = r.rlepeaipxa:: = s,azs; iFg,g?5 +zifi a,gz5)' s=0;-1,5+4,s-3=0;0=0 -rpaBanbno; r= l:4I+2a,Ei a=o; o=o-npaBnnEgo.BiAnMiAb: 3,375i 1.
zl G+iG-a=o. Ba:uisa: i6=r; r>o;,4=(G)'= t,itrri 6=0:t.= 3i !r=2.:3 I{e saroBonl'ns€ yMoBy t > 0.
nepeBiprca: ", = -1; -lJ-t+S+t;4=4-npaBsnbHo.BiAnoqiAh:4.
$ nEr\ 5, * a = Zt + 2', 2* + 5t + 4= 4x'z + 8x + 4i 2r'I + 3t=U tzt + g)=O;.r, l,5i .r, 0.
fi€peBipRa: ,, = -1,s: Ez,zs-z,s*s =-3+2; 1=-1 - EenpaBunbEo; r,= 0;2=2-npaBvrll,',o.BiAno6i0b: O.
l) \,'+tO-rt=Zr; a,&l tO = Zr + tt; 9(r + 10) = 4r, + 44!+121t
9,r I90-4,rr t 44x t l21i 4,r/ - 35-r - 31 OiD.72gtr,. .t; r, - -4.'4nepesipxa: r, = -l; Sv6-ll =-2: -2=-2 - np"urronor r, - .91,
,[!l-,o 11=-?1, -11=-!1\t 4 222BiAnoqiAb: -1.
342 ::tt: AIIEEPA Mep3nrx A. r. ra iH. A(aaeMi.rHrr pieexu !iliiiLi:!!:;:ji
nepeBip(a: +6 + ri/i6 6=o: 4+ 2 6= 0; 0= 0 - trpaBr{rbrro.BiAnuiAb:16.
3) 2r-7J; 1b=0. BaMil,a: Ji =t, t>o; , = Qi)' =l;2t, - 7t - I5 = 0i D = 189; f, = -1,5; r, = b.-1,5 H€ sa{oBonl,Hse yMoBy t > 0.
Ji=s; '=zs.nepelip(a: 2 25 - 7nE5 - 15 = O: 0 = 0 - rpasr{rEHo.BiAnosiAb:25.
ql !; + el'G = t. 3ardsa: VI = r; t > o; l,[r = t":tr+3t 4=Ortt= +ra=1,-4 - Ee 3aAoBonr,Hs€ yMoBy t > 0.
G=1:,=t-Iepegipka: {/i+aVr=l; I + 3= 4i 4= 4 - npaBunbgo.BiAno6iAb:1.
zG-t b a-. Bauiea: Jx+t .r,r.o.V.r+1
i:iililrillt::l: AIrEEPA Mep3rel( A. f. ra iH. AxaaeMiqHxt piBeHb !i;l: 343
I
I
32t-5='i1t
"- 2
2t'z-bt 3 o. 2t,t
5 !7- 5t - 3 = 0i , = 49: t,.,= 4 ; tr=3;
-; He sa,qoBonbBn€ yMoBy i > 0.
1Ci =z; r+ 1= 9;, = 8.
IlcoeBioKa:2v6*l -5- ,3 ; t=t-npasribHo.J8+1
BionosL1h:8.
o) "'-r+g*nf'-'+s=12.3aMiga: ,lV -t*s =t, t>o.t,+t-12=O:tt 4;t,=3.-4 - se saaoBo"'1l,Hse vMoBy , > 0.
,Q -a+S=S; r'-ir+I=o;.tr(t-1)=0; 't=ot
x2=1.
nepesipRa: r, = 0: 0' 0 9-19'-0-g 12t 12= 12 - npaB,lEHo:,rr = 1;
1' - 1 + 9 + Ji' L + I = 12; 12 - 12 - rpaB'r6Eo.BtAno6i0b: Oi \.
7) lrF -+'*t 2:!S--s=o: :lA4 - z{;- a=0. saMilra: {t--t;t,-2t-3=Utt-3itz=-1.{x-z=s; x 2=zlix=zgiV.1--'2 = I r 2=-1it=1.
BiAnoBiAb: L: 29.
8t -1 - + -3 2; oI3: x * l. 3a-MiHar iF = i: I 0.Vr-1 Vr+1
I 3 - 1.1,3/ 3 -2ti'?-ll' +--2.0: - -'.- 0!r-l ir1 (i r)0,r)-2t2 + B! - I z, St = O, [r1zr s1 - O.
ft-lxir1) L(l -Jt(r rl)/0i [i*Lr/ Ir
G= 0; *=0; {t=1,5; x=5,062b.
t+1+3t-3-2t2 +2
BiAnoqiAb: O| 5,0625.
s, .F-*z.F==s; oaa: r-1'o: x- ( -,!r-1 I.r+5 x-l/;* 5 Gl r
saMirra: ixr =ti t>0: { . =-:
(, 1Xt + 1)
it=0:r=1.5.Lltl:f*-1:
5) u (1; +-).
---+-\--'-\,,--+.-J-_-:_'
,,1,-8,. '' 7r- 8' o; li-8r- 7=ottt lit,=7.
- l{OpernB lreMa€;
Fl! =r, tt 5 as. x 5 4sx - 49 0. -48r ' 54 - 0.li,r-l rLI r-lI8
Bianoeiaa: 1L.8
l0) 'gf -1{' ' l, o,A3, x+rixt 7.Vr' t v*+t
344 tll ArrEEpa Mep3ncKA. r. ra iH. AxaaeMi.{Hrr piaexr iltlil:ilillli
x+5 -r+1 6 -
-=0:
=(,r-l r-1j,, =,:,l--t.
{Vx ) r (V') -rI "r-\' , Vr-1
('[ l)(it-1) ..(Vr + rl
(16)'*r 16*r=a;(u'E)'-trQ*z. q-o, ({,J' -+E z=o. saMiHa: i6=r.t,-t-2=o;tt=-1;t,=2.{x= 1tx I - Hc Ja,qoBo,rlHs. o,{3: Vi=2: x-8.BiAnosiAb:8.
469. r) r \t 12 = 0; oA3: , > 0. BaMiHa: ."li =t; t>o,t'z. ! 12 Oitt-3t12=4.-3 He Ja,4oBonbHflc yMos! I >0; G=a; x=16
BiAno6i0b: 16 .
z1 1w+8=sdi; Vr'-gi6+8=o. sardsa: i,6=r;t,-9t+8=0;tt=ltt,=8.{[=L'=1; iG=s; r = stz.Bidno6idb: li 512.
g G - 4- = t: oA3: x 0. samisa: J:r i; t 0.
i-"=0: : ' 0i tr-t-2=O..tt lit,=2.1t-..1 - lre saaoBorElis€ yMoBy t > 0; '.lx = 2; x = 4Bidno6idb:4.
a) rt+5.-3{El;+2=o; oA3: r+ 5 >0; iu> -5.3aMiEa: d"*s=t, t>o;
t, 3t+2=Oit,=\t,=2.dG+S=L r+ 5=1ir=-4 dx+5=Z; z+ 5=16; .r=11.
BiAnoqiAb: -4t 11.
s, J- , , 2 I: olIS: n r l, -r , 27. 3aMiHa:
Vx+1 Vx+3I --L-r- o, t-3-2J:Z--JLL 3r-t+3)-0.
/+l r-3 (lrl)0r3)lt+t-2=o. [t, r;t,--z- lt 2.
Irr. txr.rt*0, li,-t:i*-a: Ji=r.
<,6 =t.
{r+1,(t+3)
r>0.
-z+4=4i r(r 1)-0;
{i =-z; t= 8; i6=1; r=1.BiAnoqiAb: -8t l.ol i6 o'F*z{6 ,1 8 = 0; oA3: 3 - ' > 0, r < a. 1fi4-*y +2i6 "-s=0.garulga: &6-= t, r>0.t'z + 2t - 8= 0; t\- -4t tr= 2i 4 lre sa,qoBonr,Hn€ vvosy t > 0; S-=2;3 iu=64;.t= 61.BiAnoRidb: -61.
z\ *'-t*a*nlV -r+q=6. SaMiHa: .,t; -t*t=t,t,+t-6=0; t1= -3i t2= 2;
3 He 3aAolonbEflc yvoBy I > O: G tt+ Z;,'
i
i:iltiir:lilii:i AITEEPA Mep3rqKA. r. ra iH. AKaAeMi.rHhi pi8eHb lt:l 345
r1
IlepeBipEa: ", = 0; 0'-o+++.,6'-o+4 = 6; 6 = 6 rpaBlrnr,Eo; r, = 1;
f r+4+ J? -1+ 4 =6; 6 = 6 - rpaBsnbso.BiAnosiAb:0,1.
*, it" *3 - lL " ,.r.613. L2 , e,I2.r-3 VBr 2 2x 3
E'*2 E*z rSaviHar -1"" --: = i: .l-'' : -; I 0.
\2x-3 !3ir+2 t
t t 5. t' _!1L2 _ 6, f' u -z=o. o_n.t 2 r Lt+o;- 1.. -o'1- 2"' - ''
10x + 11121+8-2t+3
-=ui
2x-33x+2-8x+12 -
-=ui
2t-3It=2.s.Ir + L5.
flepeBipria: xr = 58;11= 15 HetrpaBrnbEo; t,=2i 3= 2 + 1;3 = 3 - trpaBtnEEo.Bi0no6iAb: 2.
2\ ..8 +1- .,rGi=2; .,,6r*r=z*uG*r; 3r + 1 = 4 + 4.,611 + r + 1;
2x-4=4Jii; x 2=2Jx+1; r.'-4x+4=4(r+ 1); r'-8t=0;jrt,r .8r = 0:./, 0i xr 8.
fiepeBipxa: x,-O;."E ."E = 2; O=Z o"r,put"n""o; x"=8;.lE-.tE-212=2-rpaBrnbno.BiAnoqiAb: 8. '
+zz.\ 'li-s +lEoi =3; uE s -s-u4o-ii x 5=s ou4o-,r+ro-x;2v.24 -6',Eo - x; x l2 :vrio-r: r'- 24x | 144 gllo 'xli!'z tsx | 54 =0:r-=6:r, 9.
rrepeBipria:;r, = o; ',/i+ ]a =s; 3 = 3 - rpaBnnbgo;
l" .|*, - J) " o,u' . -r.
[i"+z t ,r+z tt_= .
-__=0:\'l2x 3 2 2x -3 a
l?!t? ,. 3x +2 ^ ^.Vz* : - 2.r-B ' -'
5.{ + 14 [5x +14 = O,
2x 3 l2r 3+0rBiAnoqiAb: -1,Li 2.8.
Ix = r,1,
lr * r,r.*, o,
"[ - '{ = ar a : npaslnbao.BiAnoqiAb: 6,9.zt Jxi t.!' t + fit=a.Jx t:
8.lT- = 22t 4J'l = 11; 16(t - 1) = 121;
., 7 - 16 - 818-1 +.:c 1;
rcx=taz:'=#.
47o.| J22-x-.110 t=2: .tE -=2+.t!o "i 22-x=4+4J10 r+10-';i8=4J1o-; ,Eo '=z; to-r=4;x=6.repeBipxa: Jzz s JLf4 - z; 4 - 2 = 2;2 = 2.BiAnosiob:6.
D .l;i .rEx - 3 = 1t .tEi = 1 +.Ex - 3; x + z = t + 21Ei4 + 2r - 3;
a, r = z1lzr4; 16-a'+a'=4(2r- 3)j.n' 8'+ 16-8r+ 12=0;t, I6t + 28 = 0. D = 744i \= l4i x,= 2.
flepeBipxa: r, = 14; Jl4,z "Es-e =r: -r t HetrpaBrni"io: r^ 2r
"lr*z-"84 =r' 1= 1- rpaBr,n so.Bidnosidb:2.
3) ./E + 3 - G + 1 = 1; uE" * s = t + "l;
+ 1; zx + 3 = I + 2G+i + x + 1;
2x -3-2-x=zJt l; r - l-2vGJ: "r- zir I 4(.r + 1):x2 + 2r + 1- 4r - 4= 0; t' 2t - 3=O; rj =-lt )e,= 3.
nppeBipKa: r, = -li J2 r l)r3-J-lL=li I t trpaBxnhHoi!,= 3t 1= 1 - rpaBnnEgo.BiAnoqiAb: -11 3.
4\ 2.rE- - 'h i=y uE-'=t+rt xi aQ-',=1+2$ '+7-'8-4x-8r.r 2Jt x; -sx=2rt't:gx 4\7 x)tgx'z 4x 28.oi
D = 1024: tt = z, '^=4=f .99nep€Bipna: x!=-2;2'E+2- Ji +2=1; 4 3=1;1=1
reDesio*a: EII.E ,=n\/16 ,{ 16
3i6noui6o EI.16
a) Ji-t+'t+1=r; "4-=1 ',Ei; t - x = 1- 2Jr + 1 + 1+ t;
z,Gj = zt ri 4l r,r)=4.r, -4! 1.$t t,',=+, '" f.^ i E f----i:v.r L vlr l- vnn.nFRinke: r = : .ll +.11+:.1
"6=, - p=, ='; 2.f, -f, = t; -r = tBiAno6iAb: -2.
qzt.tl .,Ex+S=Z+nlit: s; zx+S=+++nEr S+s"-s; A-r=a"lTt s;36 l2r + x, = 16Gt 5); ,'z 60x + 116 = 0; , = 3136; r1.= 58.. x,= 2.
346 !ii: AITEEPA Mep3reKA. r. ra iH. AKaAeMi'{Hnr piBetb li::iiii-::!itiiii:i
-_ft;lt;'.=-9,,/r' 1" -,/r-*-t HenpdBr.,bH..'2\2Y2
Bidnoqidb: He vae HopeHiB.
al'Ea -E + J" + s = s; nEa'at = t Jx. + 3; 13 - 4r = 25 toJr + s +.r + a;
tO,G + g = rr + 15; Zuli + Z = x + a; 4(ir + 3) = r': + 6r + I : r' + 2r - 3 = O;
11- -3t ]d2= 1.
fiepeBipxa:.,c, = :;.,4s+rz+J s+l=5; 5 = 5 - npaBllr6no; t, = 1;
u6+G=s; r=r trpaBnnbgo.
BiAnoqiAb: 3i l.
a7g.\ Ja-r.+'E+5=4 J4-;=3 J:r+s: a-r=s 6Jr+5+t+5;6J,+5 =u a+'+"; onGls =ro+zx; s',lrTs=r+x;9(.t + 5) = 25 + l0,. + x't 91t + 45=25 +loa+ x.', t'+ x 20=O;1'1- -5; t2= 4.
repeBipKa: x,= s; Jl,+s+J-s+s =3; 3 = 3 - npaBlr,'lLHo; ,', = 4;
Jl n *n4+s =a; g = B - npaBrrnEHo.
Bidn%idb: 5: 4.
4 "6x+t+.,Fi=a; Jr"+t=e -.!2 7;5t+1=36-12Jl t+7 r;
:i:::t:iliiiltil: AITEEPA MepsrtK A. r. ra iH. AKa,qeMiqHran pieexr il:l gaz
- ,ro"uor""ol t, = t9;-9
12\li - x = 42 - 6r; 2.Ji- = 7 - xt 4(7 - x, = 4s - 14x + x'zi 28 4r = 4s t4x + i;)t'z lox t 2l Ot x, 3i xr" 7.
flepeBipKa:,, = e; G 3 + 1 + J7-3 = 6; 4 + 2 = 6; 6 = 6 npaBr.rrlro; x,= ?;
uEtz +t+"lil =a;6= 6 - rpaBrnb*o.BiArcsiqb: 3i 7.
al J*+s+&+5 = s; .Dr+s=a Jx+5: 2' + 3 = g - 6$ + 5 + (.t + 5);
6J;+5 =g+ x +5-2r g; o'6+s = rr 4 36(r + 5\= 121- 22x + r'36x + 180 = 121 - 22, + x,t t, - 58x 59 = O; \= \ r,= 59.
Ilepesipka: x,. t:Jztz Jl5 3:3 3 - npaBllnbHoi.r, = 59:
"E rs*g *"69*b =3; 11 + 8=3; 19 -s - HetrpaB'nb'o.
BiAnoBiAb: -1.
474.1\ x'-5x+16-auF -sr*m =o. 3a*i,.a: lEililili = t, I > 0;x' -5r+ 20= t', 1' 5x + 16 = 4= t'i t' 6r + 16= t' 4;t' - 4 - 3t = O; t' - 3t - 4 = Ot t\ = -1, tz= 4.-1 - se 3a.qoBonbFs€ yMoBy t > 0.
Jx" -S,+ZO=4i f -5t+20=16i1.' 5t+4=0; ,1=lr,-4.IlepeBipxa: rr = 1; 1'? 5.1+16 s.'[' 5.1*20=o; 12 12=0;0=0-npaBrnB-IIo; r, = 4; 16 - 20 + 16 3.,[e zo+zo =o; 12 12=o; 0=0 npaBnnr,Ho.BidnosiAb: li 4.
4!'zta 5lx'1 2 0.3a,Mil,a: ,Tz r.t>0.x" 2-t'l x'=(+2t, + 2 + 4 - 5t = ot t, - 5t + 6 = o; t\= 3; t2= 2,
uF -z =a; x,,2=s.f =11; r,, =sfi;.["" -Z =z; a' 2=4; a"=6; y,,=1uQ.
tlepeBipKa: r" J6l 6t4 516 2 0i0 0: -r" uto, o=0, r.=-"fi,tt-4-5v[t-2=0:0=0: r,=Jtt, tt,4 bJt r 2 0i 0 0.
Bianoeiaa: rll:l:r !18.rr 'f,'-r'* s * r'= 3a171 1t'- 3*-5 -.r -3.!.5 -12 = 0..
Bu*i.'u, G' -a"+r = r, t> o.t2t t , n.t - a.t 1.
4 - ne 3a,qoBonbnse yMoBy t > 0;
.{," -e," G - z;', - zx - 4 = o; \= 'rt,',= 4.
nepeBipxa: ', = -1; VG1)'!31-1) + 5 +(-1f =3 (-1)+?j 4=4 npaB'n6so;
x"= 4, J4' -3x+5+4'z=3.4+?; 19=19 npalgnbgo.
BiAnoaiAb: -l: 4.
at .,.6rrsrJ6=r2+8, tr2. Ba*i"a: ..6'iliilE = r, r>0;1t'z-9t-26=t'' 3r' 9t 36+10=t?;3(ir' 3t-12)=t' 10'
" t" to fi' lor33
3t + t'z - 10 = 0; t'z + 3t -10 = 0; tt = -5, t2= 2.-5 - He 3aaoBonr,Hs€ yMoBv , > 0.
nEt'-s*-,6=z; 3x,-g,.-26=4i3x, - 9r-30=0; r,-3Jc 10=0; r.,= 2;
flepeBip&ai r,= 2: .FCI" g( 2>26=12+3( 2) \ 2l;2=2 trpaBur,so;
34s lilj ATTEEPA Mep3ncK a. r. ra iH. AKaaeMiqHefi piBerr l:jaltitliltllil
",=rr.,8.r' o r zo =12+3.5 5'i 2=2 - npanmrso.BiAnosiAb: 2i 5.
2,"+a,-zJV+st z =5. on3:''z+3, 3>o;
".1--; --3- J4,ur- " .E i .-,. saMiBa: uG.+3.r-s=r. r:0:22
x'!t :.J 3 t;2x 6x 6.2t";2x'? 6x=21 - 6:2i'z-6-Bi-5=0;i2t2 3t+1=0:r=1: t, ==i tr=71
'['",z, a l; x'':x : I;4x' l2r lJ=0;24- -t2 + 4J22 -s - ,lrt s .hcD: ll
Tlep€Bip(a: x1= -4t 5= 5 rpaBfrlLlro; r"= l: 5 = 5 rpa8]rrlbrro.
or J*,f, . tliT tz: 'rlx" t'dV 7r. tttii -'d'' -tz=o.Sauina: rVr3 =l, t>0.t, + t -'72 = 0. t, = 9j t,= 8.
I ne sa{oBo,lEsse yMosy t > 0; 'V7 = 8;
repeBip,.a: J:r,ztVttou * tEozE,ltou = tztBiAnoqiAb: 1024.
475,1) x'-4x sn7 tuzo*to=o. sultri'u, 3!F - 4* + 20 = t, t>0.t'-3t-10=0;tj= 2;t,=5' 2 - He sa,qoBonbH.se yMoBy t >0;
x2 4x+20 =5i t' 4x+20=25;x2-4x-5=O.1't=-2t x2=5,IlepeBipnai rr = 1; 0=0 - rpaBrnbHo; t:=5;25 4.5 3,85 4.5 + 20 + 10 = 0; 0 = 0 - rpa3nnr,Ho.Bi?nosi1b: \t 5.
il z'{'" z,,n.4+3,r-r.: 2"8 3, lt" (r' srrll)'15.B"*i*u, .,frllllli - r, r>0.2t=-t,+15;t!+2t 15=0i rr = 5;t,=3.5 He sa,qoBon;sse yMoBy t > 0.
uF-ar*rr=a; f - 3, + 11 =g;.r': 3jr+2=0;repeBip(a: ', = 1; 2.,[' - a . r * r r = 4 + 3 1 1'; 6
zuF-a.z+n=++2 2 2';6=6 npsur6ro.BiA o6iAb: \ 2.
4 Jr""-6'+40=,'z-3'+8. SsMiEa: J2x" 4, + 40 - t, t>o;
2r2, 6x + 40 = t,i z" ax + a + n = | ; "" - s" * e = | - tz, t =
t: - n,222
2t = t' 24: t' 2t 24 = O: tt= -4i t2= 6i
-4 ne sa,qoBon6lrse f >O:.lir'-Ar*+O =A; 2x: 6x+40=36; x'? 3x+2=0;x1= 1; 12= 2.
IlepeBipRa: r, = 1; J2 1'-6.1+40=1'z-3 1+8;6=6 npaBvrt'Eot x2=2i
Jr.2" . 6.2+40 =2" -8.2+8i 6=c trpaBrr'Eo.Biano6i0b: 1i 2.
:tiliiltliiiiai AITEEPA Mep3ncK A. r. ra iH. AKaaeMi.rH!.ln piBeHb itair 349
x3 = (23)10. x=21o=1024,
\- 1; x,= 2.
= 6 - rpaBrrbHo;
Bidno6idb: -61 4.
Ir'+t-sruor<1.476. f(r\ = 1,' lr 1, rxqo x:1:l(') 3pocrae tra rpoMi4i1!&x ( -; 0l ra [1; +-);l(r) craAae Ha rpoMiniRy [0; 11.
477. A = hx + b - 3aranBEr.Ii Blrrnsa, MaeMo clrcreMyi
| 2h+b=b, l2b=2. lb=1-lzr+a= :; lz**a= a: lr=-2.BiAnoqi1b:V=-2r+1,
478, V = at' + bx + c aaranr,Elri BLrrnnA, Ma€Mo clrcreMy:
t\ tt' * tO, + .[r' * z" - tS = 123. Sal,liEa: '[V +zt ts = t, t>Oi f 2x-15=t''zitc, + 2r=t2 + 15i
'x'z+ 1Ot = 5t2 + 75i5t'+75 +, 123 =0; 5t'?+ t 48 = 0i
D = 961.. tt= 3t t,= 3,2.-3,2 ne 3aAoBonBns€ I > 0.
J"+Zr-U=S; x'z+ 2r- 75=g; "
+ 2r - 24=O; at = -6t x,= 4
nepeBipKa:.r. 6i5 r-6)^+10 l€) t.//(-6,*11 6)-t5=123:123=123 npa-
rrvnblo; x.2= 4t 5.4'+10 4+ J4' +2 4-75=123; nA=f23 rpaBlrnbgo.
4so.rr r.r r.G-4=6; oI3, {' l-9'"r.[.r-4-:0:
u(r t11" + a; = o; (r - 1)(r + 4) = 36;
x'z + 3x - 4 - 36 =0; r'z + 3r - 40= 0;
\= -8; ',= 5.Bi6no6iAb:5.
2r-3:O.2t ,l2x +3 'lx- 2 3r OA3: i.- " x. O.x z -Ol
1@r+ sXt a=z; (2, + a\Q 2\=gi2''2 4x+3'-6-9=0ibe' r l5=o;D = 121, t,- 3t t,= 2,5.Bidno6idb:3.
fr>0-3) J). J1 r .rl oA3: i r.I0: Il.
lxa!JrQ+q=x; r(1 - tt=
1
2
Bidnoeiat o. | .'2r-t l2t 7-o-4) ." - -Jr-4: Oll3i I x-4-
Jzt 7 lr 4'or18a+2c=2,c= 2,
9a+3b+c=10;
{alsI 4" alr=, D=-a'+ t 2.t'93lr=9,l3
4" 8BidnBidb: U=-x-+Zx-z
47g. t) u =.8 t, t t .0, L* > o,\lr x /
11 '= o' I'= 1' ''. (0, 1t,[x+oi lr+0:\ s = '[V-; )rs )e >oir.3- x=ot..r:(x I.)=0:x=0rr ltrc [0:1]:
3) v= z-1*9,2--!*l'6.x+6 x-2 x+6 x-22tx-Gtlx 2\ x,2+9x+54 ^ 2x +8x 24 x +2+9r 54 -^
k 4 6ttx 2) (n 6Xx 2)
2t'z+16x+32,r':+8ir+16 -l'+6)lx-2) -"' (x+6Xx-2r - '
tx-4t'z .o.r-{ -i 6)J{2:rF,.rr+6)(x-2)
_at-_^olt
, 2=.1E"'15.+28, x2 4x+ 4-2r2-15t+28i* 11r+24=O;x,= 3; 2r18.BiAnoeiAb: A.
- t fr-s>0-5) Jr 9 r./r= #; oA3: I ). 9..h-9 lr>uiI' j--G-n, * ..9--6-"-9: e^ rs-0,9 15!l135
0'' Jx-g x-9 jr I ' s
144 ^^15
BiAnoqiAb:9,6.
et -!!:-J2x+s= Jr + 10: o.tr3:Jr+10
=o. [, 2 JiT-ts,rn=o.lzx -t z ot
r+10>0. .r: -1.5.2"r+3:0i
foa-:a+r= s,
1" = 2.
lgd+3r+r=10:
9a-2=2,
9a+3b+c=10:
4I
4+3b-2=1Ol
x-2 Ja 4x2x - 7)
Jr' -,
l
12
-
144_j- J,r I0 J2,r-Bi - 24-x+tO=2x.3tJr+10 -t+lt1a!.^ , tz -- o, L'"".:tu .oi xt=-li.t" 26.
'+lo t+toBi0no6iAb: l.
481.1) \ft2t + 3Xr -4) = r'4t (2x + s)(, - 4) = / - 8, + 16;2x,-5t 12 r'+8r-16=0; rz + 3:t - 28 = Oi t.\ = 7tx,=4.flepeBipKs: r,= t;.,!1u+ly tE=-7-4t ll= 11 {erpaBlrnbHo; t, = 4;
u@+a1a-a=a 4; 0 = O - rpaBEnlno.BiAnoaiAh:4-
::Itl:a:ttiil{i: ATTEEPA Mep3nsK A. r. ra iH. AKaaeMieHti piBeHb :::::;: 351
I
i
I
I
35o ii:i: AITEEPA Mep3ns( A. r. ra iH. AKaAeMi,{Hur piaegs !ii::l:lillril::t
z1 1@ zyz" 11+z="; ,ft" - s' + to = r - 2, 2t' - gx + ro = x' 4x+4ir, . 5r + 6 = 0; xt= 3t t2= 2,
flepelipHa: ", = a; "G ztto rl+2=3; 3=3 rpaBvnbHoi ',= 2;
1@ 2yt - s1 + z = z; 161-g a 2 = 2; 2 = 2 rpaB,,nBiro.
BiAnBiAb: 2: 3.
al O*zlJr" t zo=a"+n; O+z\nlVl"-m -6('+2)=0;Ir 2 o, lx 2.
tx-2)lJ.r' -ir-20 -61= 0: l .-l'l x' x zo 6t Lr' -x-20=36t
lx= z.x=-2- I
^ lx=-7'x" x 56=O: I
lr=6.IlepeBipKai x= z; ( z+2)Jl+2 2O--12+12 O J-14= 0 - HeMa€ BMicryi
x = 7i ( 7 +2\J4s+7 20 = 42+12:, -30 = -30 - rpaBnnbEo;
;r = 8; (a + z).,6a 810 = 48 + 12; 60 = 60 - rpaBrrnbEo.BiAnosiAb: 7,8,
.lt t' + tr,F - s' - s = x - r: tx+l)(Jx -rr..5 l) .0rl' = -t,lir.l U, x I. I| _ tr I,
lJr'? sx+s=l: x'-5.r+5=1; I'' 1"-4.IepeBipRa:, = -r; (-r + r)rf-rf +:+S = -1+ l; 0 = 0 npaBr.r,rBrro;
x I: 2vl 5-s 2: i = 2 - npae,{,rsHo:
r - 4: 5Jl6 20 5 5i 5 5 npaBx,rbHo.
Bidnosidb: -l|' l;4.
aez.9 'lt
*,.J,\ zt =,*t; t*'.[V*u= 12 +2r+1; 'Jit24=t'*2t:"("r-24-*-2J=0, l'
o l-. o^ l'=:'L'lx' zt xt2i x'-24=x -a"r'a: lr 5.
rrepeBiprca: , = o; Jr * on6; * z+ = 0 + 1; 1 = 1 - rpaBrnbno;
, = s; JI;;J%;A= s+1; 6 = 6 - xpaB{xbdo.
BiAn6iAh: Ot 5.
2) \E;;.8= = ' t;1+"'["' u=,"-2"+t; ,(.h"-u-"+z)=o:f"=o. l'=o. [,=o.I 'F-u =, -2, (' 24 x" ax a: lx t.
r-----i.:::fiepeBjpxa: r. = 0: Vl 0V0' 24 0 I
,=7,,81716 24=? 1; 6=6 rpaBrrlLgo.
BiAno?iab: 7.
+83. r) Jz' +l + "Gl =2Ja; zt+t+zJ@x+t11x-4+@-s)=4xl2J2! - 5x - 3 = t + 2t 4(2x' - 5t - 3\ = x2 + 4x + 4;
352 ill: AJfrEEPA Mep3rrK A. f. ra iH. AKaaeMiqHrai piBeHb
ax,-2Or 12 x,-4x-4=Oi7x, 24l 16=OiD=1O24i xt=-!, r"=n.'4
repeBipxa:.r,=-;, V ;',r ir-B;=rV ; HeMacaMi.ry:
," = e; Js + ^11 = zJa; 4 = 4 - rpalsn6*o.BiAno6iA6:4,
4'[v 2', u$, a =,fs - *,', z z.[x + zxsx + 21. 31 7 = 8 - x:zu@ + r1s" + n = -t - 5r 4(3! + 13r + 14) = 1 + 1Or + 25r,il2x' + 528 + 56 - 1 - l0x - 25e - Oi L31c, + 425 + 55 = 0t 13x, - 42r - 55 = Oi
D = 4624.. x. = r, *.. = E.' 13
lepeBipxa: r, = -r; '[ + G = '6;
3 = 3 - rpalrnE*o;bbFiEs6Es91672bt6_ '' :' 13 \113 ll 13 'lJ 13 Jra Jls JrB Jlt Jlg
BiAnosiAb: -1.4 "tE' 1-$r-=Jr-7; 5x-1 z.!1sr-tysx-4+u z=r-t;7x 2 2\\5!'-13x -2i 4gx, 28x r 4 = 4tt5r? - t}x 2):
4gx! 28x 4.6Ox,- 52x-8illJ, 24x 4=O: D=400; x. - 2,, r"=2.' 11
flepenipxa:,, = z; "E
- "ll - "E; 1 = 1 - npaBsnLgo;
2EoTt2.r. ='_: .i--l-.i 2 .l--I -HeMa€3vicry.' 11 vl1 Vll vUBidnBidb:2.q 2,8 -1-J;-=\E4: 2&' r=.r7a+lia.a@z li = t - g a 21p - 1gr + g + x 1i lzt - 4 - 2x + 10 = 2.rF - 19, + g.
fi'+A=z,,lV -tor+s; 5r+a-.,f' 19**9; 25.r, + 30x+9=.r,- tox+ 9;
24t, + 4Ox =O:3"r) 5r_ 0;r,tlc rt, =0, I, IL3fiepeBipKa: r . 0: 2J 1 JL = J-, - He Mac rMicry;
*=-1, zJ-a ,[9=./-* -HeMaeiM,cry.3 !3 ! 3BiA no6iA b : rlel.N.ae KopeEi3,
4a4,D Jt I>4i o,[3:r-I>0i.r>1.,-BiAnosiAb: (17; +*\.2l "G l<at OA3:r>1:x-lrt6ix.Bi1no1iAb: (1i 17\.
-------u
.il:':.:itl!
t::::::l::::l::::5T':'.,q
1> 161 x> 17.
17 ' (rrq..l---:1 17
q It I > -4; oc*irr,Iir KopiEE ap[ibMerr.:.rnr.ri, ro r , .ruc,ro, sfie Ba,qoBonbHseOAB,r€[1;+-).BiAnosi1b: 11; +-\.4\
"!;- < 4, I{opeHiB EeMae.
fr- ,'^ t-\r4a5.1\ J2x-4 >Js --r: oA3r l:" I -* 1-'l're tz;sl.lr-.r>ui lrss:2t 4>5-ri3x>9;x>3. tTrrrrt>)"\i+
RiOnosiAb: te (3,51. 2 A 5 'ii*ltili{1i:l AITEEPA Mep3nrKA. r. ra iH. AKaaeMi,{Hr4i piBeflb l::t: 3Sg
l2 yci rAE r0 s.,r. l
I*'0.[r+1>0; 5
-4 1,6 4
8 -4
BianoqiAb: ( -; 1) u [2j +-).
qA6, D ' > J24- 'xr
OI\g: 24 - 51t 2 O, :( =
4,8ia) fltsLro ir - 0. 'ro r' 24 - 5.ri x t 5x - 24 O, \ /--=-\ '--- -
", = -8,; r" = S; r € (3; 4,81; -'----*-\" : :t:noj on,.o i o. Hcllaa. po3B s3KiB. 8 0 3 4 8
BiAnoqidb: (3t 4,41.
zt G<'6+r; oA3: ,r> 0; x < r + l; 0 < 1 - npaBlrnlHo.
BiAnoeidb:te[O;+*\-O Jx" +' < nlViOA3:t'9+r>0; t(t+ 1)>0; ,.r=0; t,=-1;r € (--; 1l u [0; +*).t'+t<x'+1tl.<1.BiAnoqiAb: t E ( -; -11 ut0; 1).
q nF a,*t , Jz' z;
lr':-lr+t:0. ls*.6 lO-tr3: I ire I i+-' l2r 3:0: | 2 )
x' 3'+1>21 3;t2 5x+4>0t\= 1; r,= 4: r e (4; +-\-Bi.Anosiqb: (4: +-).sl .,6: r' > G, - ro;
ls s" o-On3: I "r€( -i 41.
L.r'-16>0i8
'ic> t'1 - l6i x' + 5, - 24<ot
Bi1noeiAb: |_8l 41.
el J" z,*z.'ti"\z,-ttlr': 3r+2>0. t llon3:1,, x(l__;rlrrl2; -_).[2x'-3.r+1>0: \ 2]
x' 3L + 2 <2r'- 3t + l; t'- I> Ot
s).,,/i'+a'+:<z'+r;
firrrro2x+1>o, "1,23r'+r-2 >0;r:,= 1;
eionoaiao: I ?t + -) .\it l
a; .li '-' a . z' + z; ogz,:,. € [1; 6].fiI{rro2r+ 3<0; r> 1,5;7x r' 6<4r,+i2x+ 9; 5r,+ 5ir+15=0;*+x+3>0; r)+.r+3=0; D= 11;EeMa€ nopeHiB; r € ( -; +*), BpaxoByroq{ OAA r € [1; 6].Bi0no6iAb: 11; 61.
4e7.1, J2 r>r.; O,[3:2 :]r>0irs1:a) rlrli{or>0,.to2 x>t2,xr+t 2<0:t:t = 2; jd2= 1; x e [0; 1).6) nlirrro r. < 0, ro jr € (--; 0).Bi0no6iAb: ( *;1\.4 Jr.+7>x+1; OABir+7>Otx> 7ia) sftqo r+ 1> 0; r> 1, ro x + 7 >x2 + 2x+7ir'?+r-6s0; r,= 3;x"=2; re [ 1;2].6) sxqo r + 1 < O; r < -1; rel7) 1\.
-Bi1noqiAb: | 7;21.:t J*' r.x: O,[J:r ] -O:r., I:r =lrj' € (-*i -11 u [1; +-) |
a) nlturo r > 0, ro a, - 1 > x,t 1> 0 HenpaBr'rnbrio, HeMae po3B'.{ariiB;6).rxrqo jr < 0, ro r € (--; 11.BiAnMiAb: ( -t ll.q ulV-zr>s 4 oA3:.r, zrc > o: xtx - 2\ > o: t = ot r=2t,. € (--; 0l Lr [2; +*):a) nEtrro 4 ir > 0; r <,1, rox'z - 2x>16 8! + x,; bc>16,
I 2 f t Ix> j: r)2-. raaoBoi6H'c on3r r. Lr;:
.1
].6) nnqo 4 jr < 0, r > 4, ro ir € (4; +-).
sia,..ia,, lz?, * *).13 )
sl ,["\ ' 2,'; o,qB: J., + jr 2>o;r,= 2;
,- 2i x e ( -; -21 \-r [1; +-):a) nnqo r > 0, to x, + x - 2 > !.t t - 2 > 0;r> 2; x> 2 aaAoBonllrse OA3.
:ttii::{iiltiii ArrE6PA Mep3neK A. r. ra iH. AKaaeMi,rHran piBeHh lr::: 3S5
12"
BiAnoeiAb: [ 1;0,u 9;1 .It
OA3:r'+3r+3>0;r€fi.
r'+3x+3<4r,+4r+1:2
'3
l1 e - " :n[:7; o,(3: 1 J" > 0; rL = 1; ',.flrtrqo 3 - , > 0; t < 3; I 6jr+t:> 9(1 jc'?);
9 - 6r + ir'> I -gr'!: 10t' 6t > 0i(5r.'- 3t) o; J.(sr - 3)'0;
=1; re[ 1;1].
7! - :.' 6 >Ot x, - 7:t = 6 <O; ).\ = l: x,- 6;
=N-=-Vttt1t
'.'."""""'.'a:,i,1.tr.a..| l.:a i a.. --....
"i " """'4""'-
'3
:..*..-.\--Vz;-2 1x
D J2t{+7 sr+2ion3:2r + 7 > 0; ir > -3,5:a) J]Ku{or+ 2>0tt> 2;%c+7<x'+4x+41x2+2x 3>O.x,= 3:r,= 1ir€[1; +-).6) sKrr{o , + 2 < 0, )c < 2, HopeEiB HeMa€.
BiAno6iAb: 11; +*).3) J3r r'<l-r;OA3: 3n t'> 0; r. = o; ir = 3; ,c e [0; 3]..flllnlo 4 ,> 0; t<4, BpaxoByr.rt OA3, J'€BianoqiAb: tO; 31.
[0;3].
354 aiit:AITEEPA Mep3ncKA. r. ra iH. AKaAeMi'{Hnr pieeuu :i:iji:i!il:.il:iiii'i:}
6) sRqo r < 0, ror€ ( -; -21.BiAnosiAb: F*; 2l u (2; +-).
6) v/ ;'-;r. 5 ' 8 2.r: oA3: -I r 61 5:0; - F=\ ,-.----\
-,r' 6.r=5<0:.r, 5:.y, l:.rc t1; 5l: Y Y ,a) r1.llro 8 2r ? b; r. : 4', .ro I 5
-t:z+6:.-5>64 32x + 4r,; -5t, + A8x 69>0,5x? -38,r ' 69 0i .r.r. 4.6: x, 4i r E t}i 4j.6) flHqo 8 2,r 0: "r 4. ro,r < (4; Sl.BiAnoqiAb: Gi 51.
s 4. TPl,lrOHOMETPllgHt OyHKqti
1. BracrllBocri TpraroHoMerph,{Hrx OyHKqit
488. Pa4ianny Mipy Mo}t(na o6qHcnur?r ra oopMyJroro
-.,. r! 25" 5n
180" 36
4) tr ' 1600 8rr.180. I
-. r 40" 2,r180" 90
-. n-21O' 7ft180. 6
4 2!3!: =72".
5)3.1800=5400;
n.100" 5rr
180. = t;n.300" 5r1ao. 3
3) 1qq = 20".
6) 2,5. 180" =.450..
3)
6)
49o.
489, 3arrictr n cd,q niAcraBrrv 180..
t) ti8'= tt"4) 1,2 . 180. = 216.;
497. 1) III .rBeprb;2) I .rBeprb;
3) Iv 'rBeprb;4) III qBeprb;5) II .rBeprE;6) I qBeprb;
7) 600" = 360" + 240", III qBeprbj8) ?50" =360' 2 + 30", Iqseprb;9) Iv 'rBeprE;10) I .rBeprb;11) 400" = 360' - 40'r-IV.rBeprE;12, -470'- 360'- 110', III.rBepr6;13) I .rBeprL;14) III 'rBepr6;15) II qBeprb;16) II 'rBeprbi17) -1,8t! = -5,652, I.rBeprb;La, 2,4n=7,536=6,28 + 1,265, I qBepr6;19) 2,6r! = 8,164 = 6,28 + 1,884, II.rBeprb;
II .rBeprb(90";180')
( 180'; 2?0")(1,57;3,14)
III .rBeprE(180";270')( 180"; -90")(3,14i 4,71)
IY qreprr,(270";360")(-90'; 0")
(4,71t6,28).
49-1. AoB}ri4Ea Ayrn nona o6qrcnro€rbcs sa OopMynoro I = Ro.
t1 |.tz = a" 6*1; 2)2.12=24(c.M);
5n 123) "-=
lon (cu)t 4l2fi t2 .24filc{t.
492, 1) I = Rctt I = 3. 5 = 15 (cM);
2\ I=J19 =4,sn 1"*1.
3)Z=0,81!(cM).
493.r=3,14pa{.
U!-t,rz; |rt,s; z)-t,52 >-z; -!;. 2,
a1 r,Os r r; 1r 1' 4) 4,71 <4,8.+<4,8.
20) -4,25; II .rBeprb;
21) III qBeprb;
22) IV'rBeprb;23) III qBeprE;
24\ 7 = 6,28 + O,72,I '<septs.
498. 1) II .rBeprb;2) II qBeprb;3) III .rBeprb;
4) UI s8eprb:5) -380" = -360' - 20", IV trBeprr,i6) 700" - 360'+ 340", IV qBeprB;
?) -800'= -720'- 80o, IY qleprbi
.j.Iia:i:i:::j:iji: ATTEEPA MepsreKA. f. ra iH. AKa[eMi,{Hxi piBeHb ii:i
4s4. 1) o,7a5 -, rt X.t Z1 O,r. O,SZ; -\, -!
357
IpaAycEa10" 12 36. 80" 108" 105. 720. 824 240.
PsAiaEBaMipa ltyra
n18
n15
!5
4n t 711
i5n7 4n 1,8rr
4n
356 Itl: AITEEPA Mep3rcKA. r. ra iH. AKaAeMi,{Hri pieerr :i:}j!{Lll{:i:}j.:-:l
499. 1) (0; 1);4) ( 1i 0);7) (0; 1);
5OO. 1) (o; 1);4) (-1; 0);
2) ( 1i 0);5) (0; 1);8) (1; 0).
2) (-1i 0)i5) (0; 1);
3) (0; 1);6) (-1;0);
3) (0; 1);6) ( 1; 0).
8) II .rBeprb;
9) III .{Bepr6;
7nlO) - = -Ztt . lv vaePrb;33
11) 5,5n - 4n + 1,5tr, IIe Eanencnr6 ,{oqEiil qBepri;
I2l ij = 2n + -:. I qBeDrL;6ti
13) I .IBepr6;14) III qrepr6;15) IV 'rBeprB.
5O7. 1t80": 2) 190'; 3) 45"; 4, 2800.
5OB- 1) 0= 90" + 36O"n, n e Zi2) a= la0'+ 36O"n, ne Z;3) o= 30" .360"n, n. Zi4)a-135'+36O"n,neZ,
5O9. 1) o= 90" + 360"n, ne Zi2) a= 60" + 36O.n, n e Z.3) o= 135"+360"n,neZi
sro.rr x q= ,l: , ]', 6=x. ],. -ir 6=0.ir3 x3 [r_3,0: lx 3=0.
P-o3!'frrrcMo I piBHsdHs MeroAoM riA6opy: r: - r 6 = 0; a, = 2; r, = 3. po"r,"uu.",U piBHrHHe. orprMa.vo { = 3.BiAnoeiAb: 2.
\ ?r-l _4 l0 9x. r3r-t{r i} 4r t0 9,(.x x-2 " -2x )t!.2t x\x 2)'
3:t'-6x x+2 41 10 9:,r- ,k-4 =,@ 4:[a'' rr,+z=ro-s,,l'1, zy + o.
PorB n)l{FMo I p BHenEq: 3n 2r - 8 0: , t00: x 2: r.. i.PoJB slr.Fvo Il p'B-AHHn: x , Oi x , Z. 6
BiAnoaila: !.3
51'l " Hexan 40 - nirbllicr! MerIKaHqiB, rqo nporflrlarr 2 polir roMy. ,4^ = g8 200.
o. ql , ,50.] :
qa.\,,o piBJnHH,, 88 200 4 I , , ,i;J ,
'8a 200 = Ao 1,1025jA0=A0000.Birro6tab.. 80 000 MernaHqiB.
512. 1) 2 cos 0o + 3 sin 90'= 2. 1 + 3 1= 5;2) 4ts180' 2ctg90'=4.0 2 0=0;
9)
3)
4\
5)
+2= 3t
1+1-7 = -4:
=r*1=r1,44
6) sin0"+tgn-sh4= 0+o (-1)=1j
5O1. Hexan I Ityr - 2jr paaiaE; II xvr 3, paaian; III Itvr - 5n paaiaE MaeMo piB-
Etl',.t'. 2t + 3t + 5x = ni to, = u t= 2,10
'3nTH\r -:: IT K)l .^: lllr{Yr'itu2r3trr
BtAnoaidb: : i -.5102
5O2. Heran I llyr - r pa,qialIl II ICvr - 3t paAiaH; III Rvr 4' pa'qiaE; IV l(vr - 7a
paAiaE. CyMa BsyrpiruEix RvriB 'IorrpnryrErlra 27r pa{iaH' MaeMo piBHtHIIE:
r + 3t + 4t = 7r = 2n; 15x = zn; x = 2].15
2n 2,t --. 8n "' l4t1lKVr -r; IIHYr- -:tUKYr- 15 15
2nBidnaBidb: :l5
5o3. soBsiusili Kyr Mlroro&y?sq(a " +: = +. cvMa 3ocsi nix RvriB' v3'rIrx15 15
ro oAsoMy trpr l|oniEin Bepu' i - 2r. n=2n: *4=15 ' n= 15'15
Bianoeiab:15.
'r 36 n504. KyTnpuorHoBi prBBo6erpPHororovts)rHYKa{180'-36"r:2=72':3ti" ,16"- 5:
2n
5
3irJ 11ir + 2 10 9r.x1x 4 = 1(r 4t
2T 8n l4n5' 15' 15
2n 2fi
l; 1;sin,15o + cos45.= ta + fa = Jt:
sn.6o.+.os30 ,:i ,:)'=l i=l ,,,
sin45"cos45'crsso. = * ; n = *,
3trtcosn + 4cos + 2cos2,r = -5 + 0
6sin.1 zcosl + tgI -7cts!=g
z"r",l *".",1 = :.1 4l' -l €l'4 6 \.2) \ 2l
5O5. 1) 90" ra 270';3) 270" ra -90';
2) 180" ra -r80';4) 360' ra -360".
7)
8)506. 1) 400'= 360'+ 40"; -320'= -360" + 40'; 680" = 360' 2 + 40'i-1040'=-360'3+40';2) 510" = 360" + 15O'; 870'= 360" 2 + 150"; 1230'= 360' 3 + 150';
-210'=-360'+150'
358 i::i:aITEEPA Mep3nr( a. f. ra iH. AKaaeMi'{Hui piEeHb :::::::::::::::::::::::::::: iii::i::.::'ii!::ii AnrEEpA Mep3nc(A. f. ra iH. AKaseMieHhi piBeflb ii:l 359
6
"t'( ,(^
E=:
514.
ror shrts, n","n [email protected].] l'.ut. l=1..'' ---'3'- 6-'6 2 lJ3.l 2a 2
513. 1) sin 270'- 3 cos 180" = -l + 3 = 2;
21 "."6s" * "i,'3s" = 1* 1= 1,' 223\ 7 te2 45" - 3 cts 45' = 7 - 3 = 4)4) sin 180'cos 120" tg 60" = 0 cos 120'tg 60'= 0;
"tnl+cosn+ts] I t+1 -bl-2sin1 2 !62
6)
7')
8)
1) Il=.:[email protected], zsin 1= z l=t; sin 2d. 2 sinoi6) 3 2 6 2
- "t;'11 - "*" =0: Scosj' - "v": cosBc' 3 cosc.6t 2 6 22\
515.
li1) sin4.n sinn=0; qsinft 'n 9=zJzr sin4P' 4sinp''4422\ qq L= rgr o; 41gI=4.t 4i ts4pr 4isp.'' 4 ' '4
516. O6nacrE sra.reEr, y = sin r: y e [-1; 11.
O6"racrr, axavenr y = cos t: y € [-1; 11.
O6nec1l 3Ea.relr, y = tg rr y € (--; +-).O6.racrs sEaqelrl, Y = ctg t: Y € ( -; +-).
1) ; €t-1i U, pisuicrl, MoxnrBa;
./isz) -4- = -u'9/. prBEicrb HeMoxr'lqBai
3) -V1J = -1,06, piBgicr" EeMoilc,::lBa;
4l 1= 1.05. Dilnicrr, HeMonrnrBai3
- 1t -_-_5l - = u. /60, prBErcrl MoxJrtrBai
ot 9-rl. DiBEicri, Heaaoxnr.rBa:887) piBnic$ MofinlrBa;8) piBnicrb Moxn sa.
360 ll.::iAJTTEEPA Mep3rqKA. r. ra iB. AKaaeMieHxr piBet" ll.t*l:jtii:liii:i
. 'r " .-" JE 'E Js zJs ,E.srn4 cos-.crs3 Z Z Z=t.l t,*"1 "t"! r.tc!= o+1+o= 1;
6cos0+4.sin2r' 4sin'? 2ai =6+0. n lf]' =u- f.' n
lac517. OcKinbns Y3 = 1.t2, ro 3flaqoHsa sin Ct, cos o }re Moxyrr qopissrcearl,l !.12 " '-.'----- "' z',
3IIaqeE .s tg (,, ctg c! - MoJrtyrs.
518. 1) -1 < sin a < l; -3 s 3 sin c{ < 3; Hai6i{bme - 3; HafiM€nIIIe - (-B);2) -1 <cosd<1;3<4+cosc[s5;Han6inbue-b; IIsriMeIIme _ B;3) -1 <sincr< l; -1 <-sin&<1t1<2-sind<g;Eai6inErEe_B; HaftMeII-rre - lj4) 6- 2cos s; -1< cos d < 1; -2s6 2 coso<8; Hai6inbrre -8; 'IaiiMeEi[e
_ 4;5) 0 < sin'zs < 1; Hari6irEue - 1; IrajtMeEltre - O;6) 0 s cos", o< 1; 0< 2 cos,o< 2; 3<2 cos, a < -1; Hai6inEllle - (-1); EaiiMeI{-llle-( 3).
519. 1)-1 scos q< 1; -5 < 5 cos([< 5; Haii6inbue - b; EanMeII e- (-S);2) cogo - 2i 1< cos a < 1; -3 < cos a - 1s -1; sai6inbme (-1); IIanMeE-Ille - (-3);3) 0<sin'2d<1;5<5 +sin,d<6; Eaii6irbrre - 6; EafiMeHr[e b;4) -1 <sir d< l; -3< 3 sin a<3;4< ? - 3 sina< 10; lafi6i,rbure _ 4; sai_MeH'tr€ - 10.
52o. l, sin.r = r: r. T: '- =n , zn - 5n '
gtr. z Z
,7, xxl --4ft= 2i2) sinx= li *,=-I. *" .-n+2n 3n n 7n
. 2 2i xs=-2 4\=-.
521. 1) cos .r = 1; xt - 0; tz = 2ni ri = 4n2) cos r = -1; ,r=nix2=n+2T=3n;as=tr+4n=5n.
522. 1'iinz.I +
"o"2 4
44 srn +cos 1+0 1 2
sin a + 3.1 1+r 1r1222",nfr-11*,r,3\4 12) '4
. /n n) Brr
,, "'"1 3'ul sin 6 =_L=o./n nl /r n\ 3n Isrnl +cos , aln -+cos +1,\36r!36i662^. I 1 n\" I n n\"3)
i st' ; +
"," ;J -|."'" ; -"'';,l = "r., f , z"r' [":" f -"". I -"',, fi =
=2"i"[.i'i-"i",' =a"r'["r'i = ^ i,: "E
Va.n[J-11 ,"0*"1 J-.n^] ,6"rnn.,Jzcosr 9rr ^-523. t )
,ni 5n ol"rnln nl rnn",'n I JB J3"\12 6/ -\3 6) -4 -6
= t'rtu '*,t;
_ "r"; ; !5 _1-+_, JE
cosr - Bsin4 1+ 3 42
2)
./^n) r fl\ 6,/ 6 -3
-"(t ll ,.,"1 r.1* r.lJ\ 3) ! 3 6)
iliJitilitliii AITEEPA Mep3nrK A. r. ra iH. AKaaeMiqHur piBeHb ,!j:: 36i
524. 1) sin x = li x = - + znn, n e Li
2r sin r t: .r ft -znr, n -Z-'2
525. 1) cos I = 1; t = 2nn, n e Z;2) cosr.= 1; x=n + 2nn, n e Z.
526.9 tgr.r D(lg'): x ' - rn.nr/i
A = cLg kt D(cl'g t\t t t n + n' n eZ'BiAnosiAb: se tcEye.
527 . 1) cos x. = a + 3: -1 < a + 3 < It 4<a< liael4. 2l..
2) sin n = a' + a; a' = 0; rt = 0;3)cosr=d'-1, 1<a' 1<\i
" ' t. ], =2. [" ' -,t2, J2..
", I Jz,,El,Lr' t: 1r a'>oi Llle,Q:
4) sin jr=a' a-1;1<a' a-7<1;fo' a-s l. , \,'-----\,--;a ot_,, .jppir;fa' a -z<o.la'-o>o;a € [-1; 0] u [1;2];5) cos n = d'? - 5a + \ 1 < a' - 5a = 5 31:a sa+5: t, I;-
5a-4 '0. o _ lrr 2l! l3r 4l:Ld'? 5d+5i-1; ld'-54+620:
at26\ lFt -
i a+2." 02
1
531.1) y=Z_"i.,, l' srnr:l; I s2 sinx'3:
1. 1 . r, ,,.11, rl,3 2+sin,r - L3 l
Z\ y=: 7 : I .osr\ l:-1 :-cos,r. tlO. I cos.r:2;" 1-cosrI I [] \-t <+-.r€ -:+-l-2 l-cosx ' 2 )
9532. l)y !;:-;: -laroEx' li I / .cos.r:1:2:3 cosri4:
l 1 1 I 2 11 I- -!_t
< aL rLt_:tt:4 3 cosr 2 2 3-eosx " L2 )
2J g I ., -1 :sin,rl liO<srnr 112;
1 1 lr )2- s;n,1--i a'l2t - ).
524. 1)sint=a 2i-1<a 2<!;2) cos r = a' + 2; ocllinEnrl a'9> 0;3) cosr=a'-3; 1<a' 3<1;a'-3<1. fo' +so.
lo' e--t, lo'-z-0,
".1-z; "E)ul"E;z);
1<a<3; a€ [1; 3];d:-2 0, ro l asxx rHaqeqb r JJe irH) c:
533. npu noBopori OC,AD, EaBKo,ro roqna O
na &yr - nporrr roanr {nroBor crplnril, Bln IIe-
peiiAe B.npnMol(yrHl{n OC,BD,, to(i OD2= OD\toc,= oct,
cosl -a t" OD OD, = -q. = -sino;\2sin s =.-(-sin (:r); sin c[ = sin d.,qoBeAeHo.
534. npl, troBopori OClAD1 HaBKono roqrtlr O Ea K!-r'rrtrpo1h ronhHHrr{oBoi crpirxx BiH nepefiac B npfl-
. Monyrrrr& OC,BD,, ,roni OC,- OCJ OD,= 04.cos(n + rr) = ts = -OC, = :OCt- t^= cos 6.,cos d = ( cos c{); cos c[ = cos o. AoBeAeEo.
535. 1) -A(r; y) e I qBepri; jr > 0; y > 0;2) A(ti y) e II qBepri; r < 0; y > 0;3, A(x: V) E III .rBepri; n < 0; a < 0i4) A(x) vte IV.rBep"i; r>0; u <0.
4\ si,n rc=2a a'=2i 1<2a a' - 2 < 1; '1 < a2 - 2a + 2 < 1;
o" 2a-2't. lo 2a t 0. ra lr'z' 0. !'=t' , ,.\o'-za.r.-r )a . 2atBzo: la - 2,r3-0: o'R:
529- OcIlirLRr 2 sin ct - sin'd = sin(2 sin cr); sin ct > 0; (2 sin c[) > 0' ro2 sin rr sin'a . 0i 2 sir c' sin: o.
53O. SEaiiAeMo ssaK pi3El-rqi cos 10" - cos 10' cos 20'= cos 10'(1 - cos 20')'cos 10" > 0; (1 - cos 20") > b, ot*"' cos 10' cos 10" cos 20' > 0;
co.s 10" > cos 10' cos 20'.
ra iH. AKaAeMiqHl4i pieeru :;:;1!::::;i:i:i:i::i;i:i
536. ll/lx) 2h-_ ri Un: x--5:r.=5- flrvprp qHa eraHocuo roqR}i O:
I xt3
" t'
" , r1;= 2-t : r'nannar
z) f(4= lx": ,(Dr R; crMerpu.rHa BiaEocHo roqlrr o;
r( r) = iF l' = -i,F, lenapra;
sl f @) - dV; ,(Di -a; crMerplrqtra Biagocgo rorrxr.r o;
r(,)=i/Gt=tr?, rap'a;a, f@\ = 2r7 + 4x5 - 3'; ,(D: R; ctrMe"p@Fa Biasocno roqr$r o;f( x)=2(-x\1 +4(
')5 3( r)= 2t7 - 4x5 + 3r = -(2x1 +4'5 3r), EenapHa;
i::iiiitiiiii{i: AITEEPA Mep3neK A. r. ra iH. AxaaeMiqHnfi piBeHb i::i: 063
5) ft,rt = -;l-; DU): .t t 0t x z 2i x = 2. cl{MerpL{'IHa BiAHocHo rot{Rlr OiY' - 4v'
55l(- t\
-
.-i, napFa;'' t-xl'-4(-x)' x -ax'o) /(r) = i/rl; D(r: li; cxMerpr.rHa BiaEocEo ro'{ti' o;
fr xr=t4l fi. *0''".
2. 3HaKr4 3HaqeHbrp1,lroHoMerprl'{H1'!xOyHKLlii
s42. 1) sin( s0) - 2 ts(-4b.) + cos( +st = -f,+ z.r+$ = ri.* =t.{,a stso + zsrn[-r) - r"*[-;) -.-"f-;) = s. o -2. 1 + a. r + r. o = z;
.,( n\ ./ nlLb+srn'l--l-cos-l II 6/ \ 6l,.r.lrl'-l@1"\2) \2) r,5+0,25-0,75
2."tE2
rJiJz2
543.1) ssin(-45') + cos( 45")+2sin( 30".) + 6cos(-60") = **9-r.!ru l=2222
- uE tz=2-Ji:
""'" '"Ei 3 s 6 ,-2, sjn'z(-60.) + cos'z(-SO") = Yl +L\2) \2rt zt"J ll.,*1 -o1 rssinl-Il-q"osf 1l=z r-rr (-Js) Fs.r-r)+4.Jq=-t 4t -t 6) \2) i6i --'-'-'
2
=zn6-a+zJ5=d5-a.
544. 1) sin100' > 0; sin132' > 0; sin100.. sin132" > 0;2) cos210" < 0; sin115" > 0; cos210'sin115. < 0;3) cos285" > 0; cos(-31q') = cos316o > 0; cos285..cos(-316.) > 0;4) te112'< 0i sin165">0; tg112..sir165"<0;5) cos318'> 0; ig(-214") < 0; cos318"tg( 214") < 0;6) ctg300'< 0; sin220"<0; ctg300'.sin220. > 0;7) sinl>0! cos2<0; sinlcos2<0:8) sinS<0; tgs<0; sin5tg5>0;9) sinS>0; cos4<0; tg5<0; sinScosStgs>0;10) sin(-118)<O; cos118'<0; tg118"<0; sin(-118")cos118" tg1la" < 0.
545. 1) sin102" > 0; cos350'> 0; sin102.cos350" > 0;2) sin134" > 0i cos131" < 0; sin134.cos131" < 0;
a) sin lsz" > 0i cos256.<0: "ll-.]jl. s,cos 256"
4l cosl42'< 0; "inzz" O; "1"1=?. O;sin?2"
5) sin112'> 0; cos(-128') < 0; tg198. > 0; sin112.cos(-128.)ts198. < 0;6) sin( 245) > 0; tg183" > 0; ctg(-190") > 0; sin(-245) tg 183" ctg(-190.) > O,
s46. Ilsino!gc- 0i zt "in'-9.0, 3.1 "in'o.0,cosd cosd4) sin s - cos o > 0, ocRinL&Ir sin c{ > 0i cos d > 0i - cos a > 0; sin o + l-cos d) > 0.
[r:tlliltilll{i AITEEPA Mep3rcKA. r. ra iH. AKaaeMiqHni pieexs iill gos
sxs(-i) "t"(-;). 2""<'r. n"''(-;J ='6 G * z. ca * a (@
=3 2+4.::=4i
537. 1) 38" € I cBepri;2) 119" € II 'rBepri;3) 196' € III'rBepri;4) 302' € IV qBepri;5) 217'€ III .rBepri;6) -74' € IV csepri;?) -98' € III 'rBepri;8) -285"€ I.IBePri;
2n9) -- € lqBepfli
tor 91 e rI qneori;5
7,tlll -
F tll qBeDTr:
t:r !! e Iv qseorir'4
rrt -4 e lll onepri:
l4r !I e r qseDril4
16n15) - o e lqBeprr.
539. 1) sin 186' < 0;2) ts 104' < 0;3) €os 220' < 0;4) cts 340" < 0;5) sin( 36") < 0;6) cos( 78') > 0;7) ts( 100') > 0;8) cte( 2s1') > 0;
I54O, l) sin(-30') = -sin30" = -!;
2) te(-60") - -tg6o" = -!5i
534. 1) sin 110' > 0;2) cos 200" < 0;3) tg 160' < 0;4\ ctg 22o' > 0:5) sin (-280') > 0;6) cos 340" > 0;7) ts (-75') < 0;8) cts (-230") < 0;9) sin (-130') < 0;10) cos2<0;11) sin (-3) > 0;12\ cte L,7 < O;
13) tg 1> 0;7ft14) ctgt < ui
1n toa<o:' "62n16) cos S
<U.
4',
,.."(-:)
9) sina > 0:7
ror tE9I > o:"a/ r 3n\r11) cosl-
12 J < u:
/ r e"lt2\ .to _-t>u.' "\ 12)
3) ctg(-45') = -ctg 45' = -1;6
a) cos{ 3Ol = -cos3o" = ;.
541.1) cosl-60"t- re(-45"1 .os60" tg45"= t, ,=-fr,
2r ctg(-60)sin(-45")cos(-4s'l cts60"sin45'.os45"={ 9 + f
964 !1{: ATTEEPA Mep3rlrKA. r. ra iH. aKaaeMiqHnl pieexu ill:l:i{;}ii:i!i;i
I
I
M
Jz
f
sinB547. ll sin P cos P 0: 2) " ,'0 r 0:
4) sin 0 - cos 0 0. ocKiibK sin 0 0: .os p 0.
,1 lEl . o'srn li
54a. 1) te 130'< 0; ts( 130") > 0; ig 130' < tg ( 130");2) tq 110'< 0; tg 193'> 0; tg 110'< tg 193"i3) cos 80" > 0i sin 330'< 0; cos 80" > sin 330";
ar 8n4l sjn 60" 0: sin -" ' 0: srn 60' , .in i:
ud ,n5) .le 1' 0: .os 280" 0: .te:' cos280':
:l tJ
6) ctg 6 < 0; cte 6" > 0; ctg 6 < ctg 6".
549. 1) sin 200' < 0; sin ( 25o'.) > 0; sin 200" < sin ( 250");2) cig 100'< 0; ctg 80" > 0; ctg 100" < ctg 80';3) cos 250" < 0; cos 290'> o; cos 250" < cos 290';4) cos 6,2 > 0; sin 5 < 0; cos 6,2 > sin 5.
55O,1)sino<0; sino sin(r =si c[+sin(r=2sino;2) cos q < 0; cos c, cos & = -2 cos d;3)tgc[>0;tgCr-tgq=0.
551. 1) sin B < 0; sin P + sin I = 0;2)cosP>0; cos0 cosB=0;3) cte li < 0i -ctg B ctg B = 2 ctg 9.
552. l) sin o 0: cos c 0: o . ll qBcpli:2, sin d , 0: tg o 0: a L TTT qBFPri:
3) sine=sin.r; d € I qsepri a6o a e II qsepri;
4) ctg cr + lctg la = 0; (1 € II qsepri a6o ct € IV'{Bepri.
553. 1)coss>0;tgcl>0; d€ I'rBepri;2, sin a 0: ctg L/ 0i c, - IV qBepri:
3) Lcos nl = cos cr; o € II .IBepri a6o (r € III 'rBepri;4) ltg c4 ig d = 0; c, € I .rBepri a6o o € III'iBepri.
554. l) /(x) = sin'? r Dltt Rt ll r.) sin'{-rl sin ir' napHa.Le{ -x) Ls r
T lv)=:b-. D\l)t x . Ot /{ x) =:- --. r,aptsa.
3) l(is) = tg ' + cos x) D(f)t x +71h, k e Zt f( r\=tCCt) + cos (-ir) =
= -tg r + cos rc = (te ir - cos a). <f'yHllqin saranbHoro BltrrsAy.
4r /rxr-f "o"'. otn, I cos"r' 0; xtn-2nn,n'Z:I +.os r
I - cos( x) 1- cosir/l -rl -. naDlta,' 1+ cos( x) 1+ cosr
5) l(i') = '3 + cos jr; ,(t: Il; l( ') = (-'f + cos ( ') = -ri + cos 'rr. ovl{xqis 3a-
ranBEoro Blrrns,ay.ir sin.r6r /rxl= ^ : D{/): I cosr'0; cos,r- Ir'r /nh.hcZl
1 cosr.rsin(-r) x sin,r
ll-x)=-= - . napHa'I cos(-xl I .osx
rr /rrr . (r - 1) ciii D(/): x - 1. ovHrq' Jaran6Horo Br.1c*av
r-18) /(xr=
r sinr: Dtni',oi 1-'1 {-:rt s'nr x1 n:11I. "enapHa
366 lli anrEEPA Mep3neKA. r- ra iH. AKaAeMi'{H}ri pigeHb {itliiltii:ii:!:i:
555. lf /rr, = tg .r - .Lg xi Dlf\:.(?nk,*c Z; x t\+nn,ne/;It xt tg.r - ctg n ttg -v ctg r1. n.nrp"u.
2
2) /tr) "in"*r8'. Dtht x , : . nh- h t- zi .in , tgt=0;srnx tgx 2
- sin,r - sinxrcosjr 1r lsinx*O. lx, nn.n-7.stnr-- ?u. _ /u. I
"_^ :::: "_,
cosl l'o'r ' r': lr '| znm'm' Li
" 2 -'" - - ., -. s,n( "r)- te(--r) (sin/+Ls.r) sinr r{sJ.-*rr,r.z /' ' ' = sjn(-r) - ie(-r) =
Gi" r - ie ") = si", - tg r ' "ap"s'
cos( r)3) /(f,) = :.''' : Dtn: !. !7i /'-x) ("-;t = "i*, . nao,,,.
tt 1,n= t!''r, Dtni x-li , , | ^*.r-2,DO se cllM€rplrqHa liAEocHo roqrll{ O; ibysRr{in 3arar6Horo s}rlnsAv.
5.1 l1r)=cos;r+f; ,(r:.R; l( r) = cos(-'l * i = "o" "
* l,u\ f@ =*#+a; D(n: r+ tt; ' + nn, n e z:
.. clgt r) l\-x )2 1) crs). (.r' - l) . HenapHa.(-.!)'-1 x'-1
556. 1) G' 36=VtJrL; x, 36=2x- t;f ,2r Bb=O:11= .Et',=7,IlepeBiprca: ', = 5; vE6-36 =J 10 1; ./:rt=J tr; aeMa€ sMicry; n,= ?;
"4t- 36 = vt4 r, fis = "{3.Bi)no7iAb: 7.
4 \85-3' r=r; '[r-ar=r+rt
rb- Bx=:t, +2r + Lt f + Ex 14=o:x, = -7; x2= 2.
lepeBipxa: r,= z; -1Es+zt-t--7; 5=-7 - seirpaBu,,IEso; r, = 2;- u/t51-1=z; 2=2 --EpaBo,nbEo.BiAno?tAb:2.
UUr.rrr' 3! s, .( -2x 3(x h. - Jr^ 6,r,6 ' -5rr6x B xt2 t)i r 2-'oi r,2 =o:
lx' 5r r 6 = 0. l.r I a6o.r. = 6. -->Z-- \Z--\,'-
[r-2=0: ltr z. -2 I 6
BiAno?iAb: C*: -2)u[ 1;6].
-. r'?+3x- ^ x'?+3x+2(r 3)- ^r-3 r 3
J{ ,5r.-6.0. I,r --baoox, ,.--=-y-}---V- .
l,-s+o; ir+s. -6 i i aBiAn@iAb: [.6t 1l u (3; +*).
l'=-t'3)rjf 1xr.- 2)\x. 3) 0i(.{-1)(.r 2111 31^,0; l;r,2,-i\/-='\a-V .r 3.
-3ttBiAnoqiAb: e*: 3) u ( 3; -1) u (2; +-).
:tlliiitiitlii:l AnTEEPA Mep3neK A. r. ra iH. AKa,qeMi,rHran pieenr flir
x'?+5r 6 - .r:+5x 6
l a:u: , 3 =0;
367
4) (r + 2)(x - 1Xr 3)'< 0i (' + 1Xx - lxt 3)'= 0;
--F\r-=\,,'T\,'+-2 13
BiAtuosi)b: l-2', rY, \3).
l-fi rypncr 282a
4
2-rf, r!?ncr ! 2A28
c4g 4
IIepEe piBHsnHs:2a247; i-6
,4pyre piBHnrrtrE:4x+4V=56
560. 1) sin4m" = sin(S60" + 60') = sineO'= @;
l, = -2,
l-='L'= 3.
12'
13)
14)
15)
-. 23r. - (., n\ . t rl n "Es,n 4 -srnlon-4J s'nl--] =-srn4 =--:
","4="'"[r" ]l ="i".-^l . -.r"r--. 6,3 ! a) -"\ 3) -"'3 2'7n /- r) ( n\ J2.cos-=cost zr =.os _ t= :,4 t 3) \ 4) 2
/19'11 l9r / n\tcL -3 | tc a = - tcltt'r ' 5J = - tc; v3.
558.
{28 28 7
MaeMo ctrcreMy: l;-i 6'I4x+4a=56t
4 4 I 24/14 xl-24x 14x + x'1Po3B'sxieMo lpyre pil""""", j 1a_,:-i=or
-"'" a;at'l;i-"
" =0;
-r2 - 62x r 436 _ n. lr' - e2r . 336 = 0, I*, - 56 a6o r, = 6, s6 Ee 3a.qoBorbHrc
6x(14 -.jr) l6x{14 - x) * 0; lr. , 0, .r * 14:
. l.r = oi!'MOay 38,qarrl; I -lu=6'Bidno6idb: 6lrM/roA.; 8 EM/roA
3. nepioAnqHi OyHKrtii
559.1) sin390" = sin(360'+ 30) = sin 30 = l;
2) cos420'= cos(360'+ 60') = cos60" = l:2's) ts 780' = tg(360'.2 + 60') = ts60" = J'i4) ctg 405' = cte(360 + 45, = cteL,d = 1i
E5l cos{-?50") - cos750'= cosl360" 3 ' 39'1 sG36" = f, r
6) sin( 390") = -sin(360 + 30) = -sinso" = -l;2
7) !e( 2lo') = - te(I80'+ 30') = te30'= -*l38) ctg225'= ctg(180" + 45o) = cte45o = 1;
s, cos300' cos{360" - 60") . cos(-60') -"oo'= j,
l0) tsl50"tc(180'- 30")= ts(-30') f 'lln r- rr / nl t vb1l) cosj-=cosl zn-= =cos ^ =cos-= ^ ib \ o./ \ o/
368 llt AnTEEPA Mep3rrKa. r. ra iH. AKaaeMi'rtrlri piBeHb iijtit:lil::titi:i
t;cos4050 = coa(360'+ 45o, = cos45" = l::2tg( 325") = -tg315" = ts(180'.2-45)=-tg(-45")=1;
1sin I I l0' =sin{360' 3. 30")=sin30.. ;ite?65" tg(180" 4 + 45') is45" = l;
7r (- n\ E Icos-=cosfzr+t] = cos- =,i5r! / nlcre4=ctcl'r r
4J = cts:= l:
.l 9,r' In fit rr "E4 . -srnlz'r + 4) siLn
4= - '; I
2)
3)
4J
5)
6)
7\
8)
n, ""[ 'Sl=-",*'!*- .,u(r"-;J ",";=-fs61. a)
I
iiltltiiliil{t{r earesPA Mep3nrK A. r. ra iH. A(aaeMi.rHrn pieenu lld gOg
T
569. Hexan Mixc ABoMa cenaMn r l{M, roAi lenocrreAucr Aorae qro Bi{craE} sa
a rpaRrop * -a
*o. Benocsnearcry trorpi6Eo sa 1 roAr{ny 6irBue.
r 5r-3r 60rvracMo prBHssHq:
ti. 6=1, 60 . -: 2x 60: r 30.
BianBiAb: 30 kM.
4. BracrlBocri i rpaoiK]a OyHKqit y = sin x i y= cos x
szo.rl af-l;-rl; r=-"f-*l' r=o serpaBrr.rl'o, roqriaA H€ Ha,',e)(,rrr,t 2 ) \ 2)rpa4ix]:
". -lsn. ,E uz s* ,E ., i .'"2t Bt-t 2.i 2 cos4:; *.l." ;j, ', ', , -"., B Ha-1F){,r6
rpa0lry;3\C( Lnr 1): 1=cos(-4n); 1=cos4r!;-1 =1 HenpaBrnbFo, roqfta C Ee Ha,,re,{rrrL rpaabi$y;
12
563. flItqo f(r + '1:) = f(x T) = f(x\, ro " -
repio,q OyH$qii l(r).
rr rrrr cosx: /r'.rr .o."'9I="o.lrn 'n)="o"'. Aou.q"no.4 " 4 \ 4) 4
2) f(r) = te lxi( 2n\
/{r. + It tg3|x - ---: ] - Iel3.y 2n) = Lsl2r 3,rl = - ts{ 3x\ tg3x.
AoBFAcHo-3) l(r.) = cte
'rir; f(r + T\ = cts n(' + 3) = cte(nr + 37t) = ctg n'. AoBeaeHo'
4) fi.rl = sint5r 2r:(t \
/lx-r) sin s r-ll zl sin(5ir-2r4,rl sin6.r 21. AoBFAcFo.\ \ ,t l
s64. lr /r.rr cos 3.r: /{x ., n .".3[" - ?)
cos{3ir + 2r) - cos3ir' AoBeaeHo.
2) l(jr + ")
= cos 3(n air) = cos(3r - t2n, = cos(I2n sr) = cos-3.i. Aose,qeso.
565. l(:r) =sin r; l(j' + ")=
sin(t + n)= sin r.; r IIe e 'epioaoM
abvtlllqii.
566. l(r) = ts jr;/ nr (n )
[t.t . rt = tE,! )) ,t,i r, .,s*, - I He . ucpioaov SvHRuii
567. 1) l(r) = r'? + 2; rpaoilc napa6o;ra, <eirxur EarpsMne{i Bropv, r.oopalrlrarrBeprrnEr (o: 2\; f(r) e [2i +*);2\ f(x) = rz + 2a='2 + 2x+1 1=(' + 1)'? 1; rpaoin rapa6ona' lBirRIfunanpsMneHi Bropy, xoopar.rHarrr BeplrI{IIlI - (-l; 1); l(r) € [ 1; +-);31 11;i=2./r+3; < BirRa, lapa6onr, BeptU'Ea Mae ICoopaI'IHar' (o; 3); l(') € [3; +-);
, 4\ f(r) = 4 3G; <sirna' rapa6on', Bepn'FIa Mae rcoop,lurlarr (0; 4); l(,r) € ( -; 41.
568. r) "6.* V7 VF v? {z "F
z,
,) 1616 Vt - 'S' a V* = 'VF lF = .'F VF = s,
",:14=e-rc2=:trt =g=,' VsJt 'i's" 2 {2'' V2'
37O i::t: AIfEEPA Mep3ncKA. f. ra iH. AKaaeMi,{Htn pieeHs iii:ilil:ilii::::i
roqlla B Ee Hane}rlrr6 rpaoiKv;
-[ltn 11 1 n] 1 r r I\ D\ B
:dt =cosl4r--]: =cosBt ,=r; ro.rfta, sane?I{I,rb rpaoiRy.
,rr.,, o( l, r'1, -r "r"l ll, r=.r:roq,.aA Hanc,,*nrb rpa{i*):t 2 ) \, 2)
/n 1\ 1 tr 12\ Bl-: : =sin : -=1\2 21 2 2 2
3) C(nj 1); -1 = sin n; 1 = 0
n, ,l?!s, _ lJ, -1= ","?pa,I 6 2) 2 6rpaOiKy,
572-1) 3n -2n: -n:.0,2n:6n;7n syni OyHkqii;
2) Han6in6moro sEaqe'na'$yurcqir Fra6yaae "r" -+, ;, +,
3) EanMeH'roro 3Haq6EHn oyEriqis Ea6yBa€ *" Tt -;, +.
573. 1r Hvni dvHk'ii: 5n: qI. r ' 3n. 5n. 7n.2' 2 2' 2 2 2
2) san6inBuoro sHaqenH.s OynRqin Ha6Fae trpn 0; 8n;3) EanMeHrroro 3HaqenHs Oylr&qis Ea6yBae npr r; r; 5n.
574. y = sin r € opocralo.rorc IIa trpoMiflr&ax l); 4).
575. y = 5in , " "o*t orc sa npoMiniEax 1); 4).
576. y = s6s 1 sra{.. Ha rpoMiBrcax 2); 4).
577. y = cos r 3pocra€ Ha rpoMirriKax 1); 4).
578. rr cos t.6rT .os r.68,r. o.tsinbHH Ha ]'1,r"l 6u"*o'" "o**.,2) sin 20" < sin 2l', ocEir6(s Ha [0; 90'] y = si1r rr..r...3) cos 20 > cos 21", ocdrbtiu Ha [0; 90"] y = c6s r..rr^...
:::l::all::il::ri:! AIIEEPA Mep3neK A. f. ra iH. A(aAeMi.rHri piBeHb ::it 371
HenpaBrrnbHo, Toqlra C Ee da,re)r ,rrB rpaoixy;1(n\rr-t = srn[4n
6), ,= - 2, ro'rKa r] Haie].'rrL
l0't 25r I 3nI4) s,nl- > srn 18
, oc}(r,lbr{H Ha lfii.2 I
y = srn .r cnaaac;
tor 25n I 3nl5) cos-9 <cos t8, ocxrnbxn f,a itr: 2 I
y = cos r 3pocrac;
6) cos 5,1 > cos 5, ocKinExn Ea [4,71;6,28] y = c6s 130o"t""'7) sin 2 > sin 2,1, ocKinbxr Ea [1,57; 3,14] y = sin t cra{ee.
n 4n lnl579. 1) cos;>coE;:, ocftinbl(r Ha
l 0r ; l
y = cos r cna,qa€;
5r! 1711 ln Iz) sin I >$n Id-, ocxl.nbKH 3a Ltitrl y=s)nrcna4ae:
( zft\ l' an) 7n 3'lrr) s,nl
so.J >s'n[-loj: -$n30 > srn16, oct(r4hlcn as
Y=sintspocra€;lon l1n i 3nl4) cos Z->cos t, ocEtnbKr Ha
I tr;
2 I ,, = cos t 3pocra€.
580, 1) Ha npoMirrc&y ll,57i 4,711y = sin .' cnaAse; sin 4; sin 3,6; sin 3,2; sin 2,4i3in 1,8;2) sa npoMirGy [3,14; 6,28] y = cos t spocrae; cos 3,5; cos 4,2; cos 4,8j cos 5,6;co3 6,1.
581. 1) Ha rpoMbracy I-1,57:' 1,571 a = sin x 3pocrae; sin 1,5; sin 1: sin 0,9; sir 0'2;sin (-0,2);2) Ea IIpor.blCICy [o; 3,14] y = c6u
" "o*""' "os 0,1; cos 1,4; cos 1,8i cos 2,4; co8 3,1.
582. 1) sin l23o sin 132' > 0, Ha npoMir{rRy [90'; 180"] y = sin 'r cna4a.i2) cos 4,2 - cos 3,4 > 0' Ea rpoMitrKy [3,14; 4,?11 y = cos t 3pocrae'
gl co" 51-
-" 3 t o, sa apoMixKy loi trl y = cos r crarae.'49
583. 1) sin 190" sin 191'> 0, sa npoMirtliy [181'; 270'l y = sin r cra{ae;2) cos 1300 - cos 110" < 0, Ea lpoMixrcy [90"; 180'] y = s6s .t saags..
584. 1) sin 58" > cos 58';2) sin 18" < cos 18";3) cos 80' < sin 70'.
585, 1) cos (r = 2 sin 25'; sin 25" - O,42i 2 sin 25" = 0,84;0'84 € [-1; U; piBEicrb
2) sin cr = JtcosSs'; cos35'- 0,82; .,6cos35" = 1,16; 1,16 e [-1; 11, pistticrb
/-\546- l ) , = sin l x + : l - 2.' \ 6.)
nocmnoBHicrr, tro6yAoB[:1 Y=sinr;
t'nlr.z. y = ernl,r + 6Jr
nrBop!.r Ha 6i
372 ill: AITEEPA Mep3rrK A. r. ya iH. A€aeMirBri piBeHb ii'::i'iiiili::i:.:i
ysns Ea 2.
,\ u=-;*",,-i).locniAoBnicrB ro6y,qoBr-r:
,., = *"['-*,), trpaBop]n{ sa
sez. t) , = -3"r,'(r - 1). nocrdsossicrr noey,losa:
,., = "t'('-;), op"uopw "u f ;
3. y = -B "t"[" -;), poarsr ysaoBxc oci oy.
zt r=-"("*1) -r. rroc,riaoB'icr' no6yaos,n:
1. Y=cosr;
,. o = *"1'. X),,riuoow',u {;
::i!i:iil:ii{lil ArrEEpA Mep3rrKA. r. ra iH. AKaaeMieHrr piseHb irl:
f _\3. y=stnlx+il-2;
t D-/
I r, ol12l
1t
6', , = - i -"(, - t), crncxas', ao o, y 2 parr,.
373
s) y =,6""-; _r-...--; D(g):cosr_l>0.
;I
l
#ffi6)
a)6)
#
I;;;:;:i::: D(v): B; v = c.s r + cos irr.a)cosr>O.,,_"6icosI-0'-'.osr: 2)
6)
a. r_"."(,*l]=r. *u" ,," r.
588.tr,,-/r->rz, _ , vsrn x, : Dtg): sin y,6. r.. [2^n; n + 2nn], n e Z; g = sin t.
seg' t) v - (.["",-)'; D(r): cos r ] 0; y = qos .r.
,(y)j -cos,i:0i'=Iroo'n.2,
cos.r a I: r = ,--^4. n EZ-
a) ,r. o: ,, = -,:': r'1: ,{J)i,er
u, -. 0,, _",1 I lill,i;::i:,,"t
'"' r - srn "r = 0
Dlg); -sin" > n. __-",^=nn,
1
37a i_l:,:, artaa""o Mep3aqK A. r. ra iH. AKaAeMieHrr, piEe,rb
liiji:iii:_::l_i::iiji
375
al j/ = Gin'-; r(v): sin,- 1>0; sint>1; r=f,+2nn'nez;
b) y=bgql; D@): cost+o; x+f,+nn,nez;
a) cost>0;Y=1;6) cost<0;U=-1
590. 1)y=sint+ l;D(ulxe Rla\ E(yr: lo; 2\l
6) syni OyEriqii: x = -! +2nn, n eZ:
tn :n-lBt s ot x Fl-!;- 2ftni; ' 2nn )' n e zl
rf y spocrac. rxeo rcl |,znn:|tznnf.ne z: u cn*a.-'
L
"""{" *'l; ' znn: !r' + znn l' n e L;
A) y.",=2 npn t=!+2nn'neZ; y '=0rur x=-L+2nn'neZ;
,, r="'"[,-l), D(y),re Rl
a) t(u): [-1;1];6) Hyri OYnKuii: '=f,'"'''-z'
"'tv'o; x e(!+ z^,;! +znl, n.zt I < o; 'ce( | * zn':f,* zn')' " 'z;
r) y spocrae, snrqo '.l-f,* znn;! * zn')' ''z; v " t ''***. , . f 1! * znn; -It znnf' "2;
376 iril AITEEPA Mep3neK A. r" ra iH' AKaaeMiqHnr piBet" illilt'i:il'tiili
A) y-",= l npri t=-?1+2nn,neZ; y-t, = 1rp4 t=-!+2nn,neZ.
3) y=sin2r; D(u\ re R)a) t(y): [-1;1];
.no, nym QyExqr: x=n,neLi1,.
B) y .0, srqo 'clnr;';-nn)-n-zt a-o,sttl'of--l
rt y 3pocrac. -- -+-rr," nn,nczi g cral\ac,L4 4 )
,.1f,*nn i{^rn).,.r,
ot '.1f,*n,!*nnl,n.z;9... = 1 rpn t=!+nn,neZ; V.,"=-1 upn ,- !+nn,oez.
4r u = -f sin,r: Dtutt x e' R:'2
", t,,,, [ !,1l'6) Hyni Oytrxqii: t=nn,neZiB) y > 0, s&rqo r € (-n + 2firy 2Mt), n e Z; A < 0, aRt\o t e (2r1ry jt + 2nn), n e Z;
f- Ir, , ipocrac. xel':"znn:'" tzrnl.ncZ: g anaaac,
f - - lxel :+2nn:L+2nn),nez:
ol v*-! npu x=-I+2nn,nez; v-,,, = -t wu r=|+znn,nez.
(n lx.l,- + ftni n +,rn ). n ezi
i:liilli:iill{ii: UTeSPA Mep3ncKA. r. ra iH. AKaaeMi.{Hr,rr pieexs i{:J 977
1591. 1) r/ = cos .:r 1; D(y, x e R:
a) x(y): t 2;01;
B) y<0,sriqot€ (2nnr 27t + znn)' ne Zir) y 3pocra€ rpr r. € [-n + 2fi,zfin'l' n € Z; ycnaaae' mflqojr €
A)y,,,,,,=0npta,=2fin'n'z;a,,,\= 2 npi x = 1t + 2nn' n e z'
zr u = cosi x-l']; Dru;:, -R." \ :1)
a) E(y): [-1; 1];
6) syri OyEkIIii: x=f,+2nn,neZ;
B) y > 0. snrqo,.( I r """'i*2",),
n ez; a < o,
",.*. ' -[i znn,,! znn\.n. z,\b
r) y spocrae, '.1-! *z^,, !*zn)'".2; v." t",
'.1 \ * 2n,,4 n zrnl, n. z',l3 ri I
r) v.", = t, r= -\ +2nn, n eZ;
zt y=""'|, DQrxeR.
4\a=3cosx;D(a\tceR.
\ ,[, \
"'\'/ 1
\'/t(v): [ 3; 3];
HyniflHxuii:, -;,",. ^ /'
y o. ex,xo x.\-'r -znn:')'r,,)., -z: v o.
l- \
',.." ".1; z"^,"r' z*,)., -2,r) y 3pocra€, x e I n + 2nn; 2nnl, n e Zi y cnaAae, r € t2nni n + 2nnl, n eA) y.",=3, t = hn, n E Z; C,,,",= 3,r=n+2nn,ne Z.
5s2. u 2ain(zx nl r, -o,,,,*- n." | 3t "nocniAoBHicrE ro6yAoBr.r:a) !, sin 2.ri
/ n)br y=slnlza+-J. yniBoHa :
z;
o r=r"*(r"-f). po3rsr y3Ao',,. oci oyy 2 pa3r;
.r r=zs"(z'.lJ -L yri,,s sa r oatrE,rr'.
(, -\se3. y=-3sir,l;- 6) 2t Dtsttx- R.
IIocniAoBnicr6 no6yAoBr:
ar Y=sln_
- (, rl nul , srn-" \2 6) " " 6
:::!iii:::iiirti* AIrEEPA Mep3nrK A. f. ra iH. AKaaeMi.{Hxn piEeHb lii: 379
l2nni n + 2nn7,a)
6)
')
$$,ffi
r = 1- 1 = !l\ 12nn. r .7.
a) ,s(y): I 1; 1l;6) Hvni Oysftqii: t=fi+znn, ne Z:B) y > 0, sl{qo r € ( 7L'r 4nn1 T + 4nnr, n e Zt Y < 0'FKUro r .- (n' 4fn. 3n - 4rnr- n I zir) y3pocrae,t€ | 2n+ 4nni 41Lnl, ne Zi v cnaAae,:r € f4nnr 2n + 4nnl' ne Zi
A) y.", = 1, r = 4nn, n e z: v,,,u, = -I,r= 2n+ 1nn, n ' z'
378 li::: AITEEPA Mep3nel< A. f. ra iH. AKaaeMi'{Hlri piBeHh :;:::;::::::::::::l:::ai:l
3) , = *""(; -;), posrnr ysaoBx{ oci orl v 3 pa3r';
, = *",'li -i) , 2. yropy Ha 2 oA{'sqi.
Ma€Mo crrcreMy piBIIsEb:
l+x *_"^ t-Bc u '"' ;=ro'1v , 1
i: -___- = t0; lx l5r" u+ lu 15u+2-15
PosB's*ieMo Apyre piBEsHIIs:60(16A t2l-9O0s ,^- 900y.120-900y-150y-20 ^ -150y-100 ^tbvl '* 1br+, =u:
-u+2 =u:
1,, _ roo t.. _?1s0e - 100 , 0. ' 150 1' " l.r = a0'
ts .2 / o: ' n. Ir-|' Io"-r5r Ly+-1b:BiAno1iAb: 40 *M.
5. BnacrraBocii i rpaoiKn OyHKqifi y = tg x i y = ctg x5g7.a=tgt
tl "(-;,t)'
r-ru(-;)' 1= 1; Eenpasrnb*o, ro,,*al ,,e Ea'e*c'rb rpaabiriy
4yHrcqii;/-\/-\2r Bl-;'-Js]t -ft =tc[-;], -.,6 = Jt, EpaBr{nElro, ro.r&a B rlanes.'rErpeoi$y OyHHqiii3) C (tr; 0); 0 = tg r; 0 = 0, npaannrso, ro.{xa C Ha,re)rcr.rrr, rpaoiEy Oylrxqii;
,, "[z'. Ja). Ja -,-zt. Ja , , '!l G Jjo,'[u,t,-B=tc;' - l =te['I-6J; -3 T."*"',"".roqRa , HanerltnrE rpaoi(y OyErcqii.
598.u=ctg,/- \
l) Al^:l]r 1=crc;: 1= 1, npa!nr!,'ro, rosxaA Eanex'{rh rpaoiky o}'Entrii;
/o- \ /.-,z1 r] {;ol; o=ctgl }]; 0 = 0, rpaBunLso, ro..&a B Hsne}crrb rpa@iIcy O}'s-nqii;
-^f 'v5) '6 rnr "EIt c[-u;fJr t=""[ a'J, !e=-n6, uenpaauarso, roqna c lr€ Ira,r$$&rr,
rpaoixy Q]'Ercqii;
,r "(f; '.,4),
J" = *r*, la = "t*[^ - iJ,,6 = -f , ""nn",""r.8o.
roq&a
, He lr8lrexinrb rpsoiky O}.IrRqii.
599. 1l Hv,rsMu dvgftrii u = crs -r c 1, -I, 3n, 5n,2' 2' 2'
2) ne ra.rexarr o6.nacri BlraIIa.reHEs ibyr]Iirliii O: '1t;2it.
600. 1) HynsMs Oysxqii y = tg r e n; 0; 3n;
2) He ua,relxa rE o6,racri Brl3ua,rcHnr Oysxrii y te r: -Tt -X, |, tX
:iiitli:iit:jll::i AITEEPA MepsIeKA. r. ra iH. AKaAeMieH r piaexr l{! ger
r = 6Oy,
oo-15 6o' = ro.
l5a +2
x'-3x+2594. 1) l(x) = :- . ;
Jx=1a6ox=2,
BiAno,iAb:2.
r'z-3x+2 -l(x) = o; -'- --=u; [x'at+z=o,lir-1+01
Z\ f(x\ -,"[x'zli, ocrcingftg .r2 + 9 > 0 trpllr€ B' ro Ovgrcqis EvniB He Mae'
BidroBidbi Ee icHylorb.
s\ f(r\= x',lii; D(y):r-1>ojr>1.f(xl = 0; xJt I=o; x=oa6o.:=1; t = 0 He saaoso,'lbHn€ D(y)'Bidnoeidb:1.
4) Itx,= J-lx -2t Dtattlxl- 2,0: lxl> 2: r c l -: -21\- l2i +-)'
,!i'l i = ot lx 2 = o;lrl= 2; x = -2 ^60 x= 2
Bidnosidb: 2i 2.
/ 3\a
uru.r,It',"|=,il3"/\2,.r0) lziJ .ro.
I"i ,ili r. uri rzt -r:u] =\zl .3{/ =\21\3'?',
1032t= _:
2',.10" 10 5
!\stJ = 21.
380 :.iil AITEEPA Mep3rt( A. r. ra iH' AKaaeMiqHnr pieerr {ill{ll:i{:}}ilt
'60"15
l!*n*,!*n).*.2\, 2 )
606. 1) y = -ctg r, crMerpis y = cts rBiAHocEo oci Or.
2') v = cls r + l, rapanerrr{e nepeHe-ceHIIn BHu3 sa 1 oArnlrq&.
60 l . 1) Ha KoErsoMy 3 rpoMir{tldB
tg( 38") > te(-42");2n 7n
2) tg-. < tg-,
y = ig , 3pocra€' or}ce,
3) tg 130" < tg 150';
4) tg 0,9'r < ts 1,2n; 5) ig 1 < ts 1'5;6) Ha lior*{HoMy 3 rpoMiJ{KiB (rk; tr + fift ), & E Z v = cig n cnaAae' or]rle'
ctg 24" > ctg 28';r 3r!
7) ctcT - cts?:9) ctg 0,4r < ctg 1,4r;
602. Ha (oxcsoMy 3 npoMi,rcxiB ( !*"u,|*^n)'o'7' u=te' 3pocrae' Ha t{oxi'
HoMv J npovixKrB lnftl I rh, P - Z 4 clg 'r claAac o-}t(F:( nt3) y . rtcl .r + -]. ndpa,rpnLsp nppFHecFtsFF Br iBn tsA \
8) cte ( a0") < cts (-60");
10) cts 2 > cts 3.
603. 1)ts1,2;ts0,9; ts0,5; ts( O,4\t 2) cts 3'2; ctg4'6; ctg 5'3; ctg6'
604. 1) te 1,6; tg 2,5; tg 3,6; tg 4'1i2) cte ( 0,?); cig ( 1,4); cts ( 2'4); ctg ( 2'8)'
605. 1), = tg t' clrMerpis rpaoiriay = tg :i] BiAEocso oci Oir'
2) a =tc t + 2, n^PanenEse repaEecei'EE lrroBEt oci Ov IIa 2 oAIrHErrl Bropv.
u=te'+zl
li/!I
n1 s = "tc|,, po:r.sr yonosxr oci O, y 2 pa3u.
99607. l)sino ;1980':
-ts80"-3.78:3.78a I li lli piBHicl6 /p vo}t{nuBd:
21 costt= ctg!; ctg+ - cts10'= 5,67; 5,67 e l-It 1l; piBHicrb IIe Moxnr.rBa;"18 -tA
:r coso rgf : 1gtr = tg20'" 0.36:0.36 - L r: Ilr pisHicrb vor(,lrBa."q "q
608. 1) sin 78" < tg 78', ocrrinbKn sin 78' < 1; tg 78" > 1;2) sin 40" < ctg 20', ocl{inbK]I sin 40' < 1; cte 20'> 1.
::::i:ii::l{iil::i: AnrEEPA Mep3ncK A. f. ra iH. AKaAeMi.rHrar pirenr liilt 383
1) tg 110" > te 90";2n 5n3) tg- < tg
-;5) ts (-1) > tg ( 1,2);
o, = *(' - ;), napanerr.senepe'e'
celinn y = tg r BnpaBo Ea t.
2) cts 100" < ctg 92";3JI 5n4) ctet > ctg
-:6) cte (-3) < tg (-3,1).
ii,l
4) g = te r, crlzc( YsaoBri{ oci O,y 3 pa3lr.
Iy 3 pa3lr.
382 i::::: anfEEPA Mep3ncK A. f. ra iH. Al(aaeMi'{H}ri piBeHb :::::::::i:::a::::::::::::::
ooe. rl v = *c(, + 1) + 1. rlocniaoBriicrb ro6vaoBll:
^, a=ctgt:/n)It6) y=ctgl,rr -], $aparFnbHe nepeseceHHfl BnrBo Ha
4:
/ E\
Br I ctclx - ;]. t, r.ear-*" ""penecelrHn
Bropv Ha I
zr ,="t"[s' Il." "\ t2)IJocniAoBHicrE no6yAoBr-r:a) !-cteI'6) y - ctg 3r, crucx yeqosxociOrygpasn;/ _\st z=ctsl sr l:l" -\ 12)naparlenbse nepeEecerrEf
nBrlp3ro Ee -.
n "Ls 2x-!. nocnjaoBHicrb no6yAoBr.r:
g=tg,;iU Lg 2x..'tvc!r y3rcs}l{ oci Or Y 2 Pa3x;
u lgl2x ^ I, napaienbse nepeFeceHE{
ftBflpaBo Ha
t
( 27t.r61o. l) v = 2rcl.r''; J.
flocniaosHicrb no6vaoBx:
a, a =te 'i/ 2nl6) v=2€l.r+;'J, napaie"lb'e nepcHec.IrH' sriBo Ha
/ 2n\Br s 2tslx'?J. n*'* v"o.'* oci ou v 2 pas'l'
2l
a)6)
B)
{:,1
zfi
.-i
+!+nn.,ez.2
tg'z * > o;
or r. ry y = (ur"te")' ,
- lx*nn,neZ.L ut:1" lctg r 2 0;
g=ctgr.
2t v=tsx+telrlDtut: x+I+nn-nez:
a) r>o;y=2text6) x',oty=O.
s1 y = .!,ts";; o1yy. y=nk,hez.
L:2l
ctsxl
^ur. )x*n+nn nez,lctg r * 0:
a) y=l,nllqoctgr>0j6) y = -1, snqo cts: < 0.
;:i!:iiflifiltli AITEEPA Mep3ncKA. r. ra iH. AxaaeMieHr.rr piBeHb ll, 385384 ii:i AITEEPA MepartK A. r, ra iH. AxaaeMiqHnr piBeHb :!:lli::::::i::ii:il
T
612. 106 no6yAyBarr rpaoiK 6vHKqii, Eeo6>riaHo:
l. 3Haiire o6na.rb BrirHaqFlrHt OvHXqii:2. BlrKosarr'I Heo6xiAEi reperBopeEHn' po3Kplrrlr MoAynb' spaxoBvrotrt rpoMr'{rfttl'
IIa sr$rx niAMoAyrl]'lrn ii Bt'Ipa3 Ea6yBae AoAarErx ra BiA'€Msux 3HaqeEL
Llr q (Jre*l i 1sx--oiDtat: nn::' nnl'n-Z2)
erqe oci Or - 6e3 3Mislr, Elrxtqe oci
Or - crMerpis BiAEocEo oci Ox.
i\
2, a = cte r ctg lrl; ,(y): jc + nn, n e Z.
Po3rnsseMo ir > 0. I = ctg ir cte x; a = O.
IpaOiI.oM rDyHRqii;a npoMir{Clv r. € [O; +*) e rpsMa, slia 36iraerEcs 3 Bicclo O''p.""""""..'t < o. v=ctg* ctg( x)i a=ctgx+ ctg t; y= 2 ctgt fpaoiKoM
OyHl{qii Ha .tpo*i*"v t l (--; 0) € noraHrellcoiAa, po3rsrHvra $AoBtrc oci Ov
fpaoircoM OyHRrrii € MHoxclllia roqox is xoopA EaraM
1t u '"' ' 1*' z "n'n' '' otl, ''"!,,.2.ts r' ltg,. - 0, l' ,
"^. ^ .2' z
po3r.lsHeMo te' > 0.,.(."u, !, "o, u. t). a = ffi' v = t.
rpaoi]{oM e rp.aMa, napanerbHa oci Or.
p*rr'n€Mo tg ' < o. xe(!+nn;n+nn,u.t). ,= J81, o=-t,rpaQikoM € npsMa, xaparerLEa oci Or.
5) u=te*+\Ec\: D(a\ = R. a = rg ' + lte rl.
Pogi'nrHcMo tg .ir - 0. .r -ln^r\t^r,^.71. u Lex I re:tiu 2tsx.LzJfpaoilloM OyExrtii € raEreEcoiAa, po3rsrHyra B3AoBrrc oci Oy y ABa paslr.
Pos!,lslreMo tg :c < o. " .(! t nnt n * n,, o . z). v = tsr - tc ,; v = o.
fpaoir{oM rbyH(qii € npsMa, sl{a B6iraerEcs 3 Biccrc Ojr.
s) a="te* J.tc.";;D(g):r+n+nn,neZ.y = cte )e - lcte xla) ctgir>0,y=0;
6) V = te x.
D(y\: !+t+nn,neL.(;."",".',")
Zl v = [.te\; -ctg'x > 0 Bllnoiiv€rEcg 3a vMoBIr, rqo ctg't = 0'
r ! ^^., -z: Dl!:)'nn.n-7t npu x L nn'n-7t a'o'^2'2'2
386 :;::::: AnrEEPA Mep3neK A. f, ra iH. AKaaeMi'{Hhi piBeHb :a:::j::::::::::::::::::::::
6ry ictgrir Dtyt:! ' nn.n-2.Cro.rarKy 6yAy€Mo rpaoiK OyHKqii y = tg n. t{acrnlry ryaoixa, slca 3Haxoalrrscssx*{.{e liA oci Or, lino6par{a€Mo cnMerprqHo oci Or.
:::::i!iii::iitli: AIrEEPA Mep3nqKA. r. ra iH. AKaAeMiqHrt piBeHh l!,1 347
lt*
. rsr ,x-F--nn,n.L, l-,1 "^,,.t,1J a=Li | 2 I 2ts r'
ltg,. - o, l' , "^. ^
. z'
r613. Hexafi a, = -4; a,=5.a,=o,+6d;-4+6d=5',6d =9; d= 1'5;
e,= -2,5i at- -l' a1= 0'5t tt|= 2i a6= 3'5.BiAnoqiqb: 2,5t -1; 0,5; 2; 3,5
614. Hexafi b1 = 256: bi= 1. bi= b1
.l 1- 1q'= 256,
qr=- 4 aoo q,=
4'BiAnoqiAb: I) 64:. 15, 4i 6164:
617. 1) I+cts'5d=--: ;srn- 5ar
_Cl
^. 3 3 C
lq3
3) ctg' 1;
4)
5)
-(t- sin'o) - cos'cr - I_ ----;----:+l=- " tl ctg'c+l=-(l - cos 0, sin c - sin? cr'
i sincr cos cr L': / cosc sin a \':ii:.' . | :ra.::_:, =sin.o rcosru =1;\ cos.r I / \sinfl 1 I
- sin Cr sin' (I sin) n sin/ a1-ctg?d{l-cos':o) - cos'c sin':c I cos)o sin'a "
'sinc I?) -+ - ts'20 = 1;
8) ts, p + 21g P.cts B + cts,P- (te,0 2 te p.crs B + ctg, B) == Lc'1 9 + 2 + ctc, B - tc, F + 2 - cte, F = 4,
ore. rr lll -l - vr3 I | ,13--!, t4 , t.'4' 4 ) 16 16 16 16He BrzrioHyerlc.fl ocHoBHa Tp{roHoMerprrriHa rorollEicrr, sin2 lx + cos, (r = 1. Orse,piBllocri oAHoqacEo Br(onyBarncs IIe MolcyrL.2) 2,5 - 0,6 I ,5; 1,5 ' 1.He BrrftoEyerBcs ocHoBEa rprronoMerpaqHa rorox{EicrE tgs. ctg (1 = 1.Orx{e, pi4nocri orllo.racHo Br.rKorryBarscs He Moniyrb.
6te. r) l2l',131'=1*-s -13, 13,r.\5,/ !5,/ 25 25 25 25
PiDHocri Btrt olryBerscs se Mor*{yrb (arB, no.ncHeHH.s Ao saBAsEHn N! 618 (1)).4 1 45 5 52l - 7-= +ls 4 94I I
PiBsocri Br.rKosyDarrrcs He Moriyrr, (ArB. roscHerrl1n Ao aaBAanH.tr Ni 618 (2)).
620, PiBEocri BfinoHJ,.BarIIcs se Moxcyrr,, ocKinr,trlr sin, d + cos: (x = 1.
621. 1) 'firiqo tg dl > 1, ctg ol > 1, ro tg s ctg cr > 1
2) filrnro lts dl < 1, lcts cd < 1, ro tg c.. ctg o < 1.Ane tg o ctg q = 1. OrBe, HaBeAeHi yMoBr.t Blrr{oHtBarrcs He Mo)r{yrb.
622. ll I 2rgq . Lg'a' I -2tgo r tg'n = -J- . l" J-,cos'Ct cos'd cos'ar
2) (sin? s)' + 2 sin'? c, . cos' o + (cos, s), = (sin, d + cos, ci), = 1, = 1.
3) sincr(1-cos) + sin c[(l + cos) , sins sinocosc[+ sinc{+sinctcosd _' (1+ cos)(l cos c[) 1- cos' cr
2 sin d 2= "i;t;
= "i" ";
r\ cos0 sin0 cosoll rcosl .sindsinc'' .ino-f*"o"o
"lnaft*.o"f
coad+cos-0+srn'ctsin (x(1+ cos d)
cosd+l 1=
"i""O + "."a = "t";
iiilll:*l:liii;.1AITEEPA Mep3rqKA. r. ra iH. AxaaeMiqH.,rt piBeHb ,al:! 389
.qa;256.4=1t
16;4.
615. IIpoa]'rirnBtricrE Itirbrcicrb sacyItirrbLcicrBaeranei
l-it podirflnl! Ha 3 Aerani6inEme ---1
na 1 aeH; 90 Aeraneii
2-i po6irl Ic 90 Aeranen
Hexaii Apyrdi po6itEr'Iri Br{roroBnsB x Aeratefi 3a AeEE, a trepEtIi - (t + 3) Aerui
ra aegb. ncpu{fi po6irnrR rpaurcBas 90= .*"i". u apv,,ii - 9:0 a"it n"pt";npa(loBaB sa I nesb Me$u,e. r + 3
90 _ 90 - r. 90 9.L I O, 90x . 270 90x - x' 3-r O.
a xt} -' x x+3 (rr3)x'-3x t27o n. f-r-s'.270=o. {-l} x) Bx 2ro=0.,D bt-4oci
r.(.r - 3l lr.{.r + 3l 7 0i I
D=g-4' 1 (-270)-1089;- t-38 3,33 ,
JD = 33: x. = ;-;" = 18. I'e 3a.ooBonblnc vMoBv 3a4aqi: x,' z ;- -15'
15 aerarefi qoAHF BuroroBnsB Apyrnii po6irl{rK, 15 + 3 = 18 Aera"'rei BnroroBnsB
neplllHii po6irFsk.BiAnosi)b: l8: 15.
6. OcHoEHi cniBBiAHotxeHHn Mix rpnroHoMerp[qHrMn OyHKqicMxoaHoro r Toro caMoro apryMeHTa
616. lr iin'o:2) (1 - sin'2cr) = cos'? (1;
3) 1+1=2;4)1 (sin'34 ' cos' 34)r I l=0:
st "o"3 og'c,.os.i sind6l
-
= srn d- 1 coso7) 1g' di
. cos'a sin" dal .os'd r =cos-d lcos g zcos (,;sin'.l I
" / 1 ,)sr -"'o [ .i, cre aJ ' cos'c-r {l-ros7cr)- -sin7.r;
ro) 'i":q !e#=rcos" F $n' p
"x11) 1' sin't = 1 sin'- = cos- '
12) sin'zo + 2 sin d'cos s + cosr o + sin'z& - 2 sin d cos cr + cos'z=
=2 sit\" d+ 2 coE2 ct= 2(sin'c, + cos'?d) = 2 1= 2.
388 lrj AIrEEPA Mep3nrK A. r. ra iH. AKaaeMiqHni piBeHb i::itiiiiiiiii{::i
l
I
I
il
5)(1- sinoxl + sin cr) cos'zcr' - 1- sin' cos" cr - 1- (sin'+ cos'o) -
cos cr(1 + sin q) cos a(1 + sin&) cos s(1+ sind)
sin'+ 1+ 2cosc, + cosd': 1+ 1+ 2cosc(1+ cos s) sin (} (1+ cos Cr) sin q
, 2+2cosa - 2tl+coss) 2 ,
(l fosslsind {l cosa)sind sin0sins sin P
-. cosd cosP sin o cos B + sin 0 cos n . coscrsin0 -sinocosp .
" "*o "o"g """".*0 sinssinP
sin d sin B
tsin o.os ll + sin p cos o) sin d srn 0 singjlnll rsorsBrcos s.os ll{cos o sin p I sin Gcosp) .osocosp
^. taSa (1 ctg':3s) tgSq ctg30sr ffi ,rr;-**....-= "cos o /sina cosa) coscr
9)
-.1-+-
=-:sin a \ cos(l srnc / sln s
cos rr cosd.srn(Isino l
1or _jiny _siny-cosy.rosy siny_ {liny losy)cosy _ctgyi--'
1 sin'y sinY cosY srnf {srnY-cosYr
11) cos'zd(cos'9s 1) + sint cr = -cosz .t(1 - cos2 c[) + sin2 s = cos2 o sin' d + sin" ft =
= sin' ct(1 cos' o) = sin: cr sint a = sin{ ct;
12) sin'd(sin' o + cos: c{) + cos' c{ = sin'9 s ' 1 + cos' d = 1;
t3r cosct-coso ig o cos.r{l ts? ct, "'i* aj.* = ""1r,r sinB - l- sino sin0 1-sinp+sinP 114) p - tclr
"".0 .,=0 *"p -"F
623. l) r 2cqll-cte,9-1 2ctsp cts ll- ","t
pt ","t
p="r,i"p'
2, sinzd cosr,rtts s rl+crg'd+1) "t" " """'1J,"-;"',") =
=sin2n+cos2s=1;
^. cosB(1- sinP) + cosP(l+ sin B)r' -- li+ sinBxl_"'nBJ2
sinf, Ein x(l si n r.)--.-_'' cos r. i I sin r cosr.(l - sin x)1+ sin, 1
sinr+sin':c+cos?:rcos r(1+ sin t)
cos r(1+ sinJr) cos r.
", "." p:rgrp:lr
-1414--9 n p) - cos'p- I 2sinp I sin'p
"' ( t - sin o)cos P 11 sin0lcoso
_ 2-2sin0 2(l-sinpr 2- (1
"lr' P)cos P - G sin P) cosB cos P '
39o . ii*: AJTrEEPA MepsrqKA. r. ra iH. aKaaeMi'{Hr4i piBetr i:.:ililillliili:j
7')
tg'q(1+clg'?0) _ te'a+1 - 1
(1+ tg" o)stg" c[ ctg'c, + 1 cos'9c[ '
I "'"cr) /- sincrl cosa+sina\ coso/ \ cosc/ coscr
1 sin': a
-=-=tg"cl;. sind + coscl (cos.x + sincr)sin s _cos q(sin o + coso)
= = tg(x,
8) cos'z d(cos'z d + sin': s) - cos, 09) sinz d + cos'zcr(sin? cr + cos, c.)10) tg c . cte & + sin? cr = -1 +
1624- 1t IInHn: adsa = .'2
SHaiLmu: sir. a; lg d.; cLg cr,
sin'/ ci = 1 -cos'? c; ",no =.,,[ -.odo, "'"t -r[l
"ino= $, rr"= +,;, tgc'=-!5. *eo=*o!,
a6osino 6: ,rt=f,!, rscr=.,6r "igc=f.2J AaHo: sino 0.6' tr. o.n.SH,aLmu: cos ct; lg s; ctg s,
"o"o=t.,[ "irfo; "o"o=-',/i-O,6" , octrinbrr]r c, - Ryr II qBepri; cos tr= 0,8;
0-6 3 4 rtso : cts(l - - 1--"0-84'33
cosF cos 0 sin 0 + cos 0 + cos F sin F 2cosF
1 sin'z P cos'p
_ 1+1 2sinp _(1 - sin P) cos B
6)
cos a(1+ sina)
-. sin'z- (1+ cosa):' (1+ cos s)sind - 1 = cos, d . 1 - cos, Cr - I = 1:
=sin'9C[+cos'cl.1=1;sir' cr = -(1 - siD' cr) = cos'zd.
"6.3'
3') ,qaHo: te a =- SHanmu: si[ &;
3rr
2cos d; ctg.q.
lI"II"tao E, "o",o
r, tg'si cosc/ rr/l ,t,s,
ocftinr,&r cr Kyr III .rBepri; *""=-,F= *
./5 l)
$ noxo: ate..=-! i !4<a.:".
SHaiLmu: tg qi sin st cos a.
p,s 'raHHs:
t'o = !. t'o = q
'cta0'4
1+ ctg! o; sino=t
ocRi,'l6rair c[ &yr IV .rBepri.
:tiitttitl::i:lt: AnTEEPA Mep3nqKA. r. ra iH. AKaaeMi,rHr,rn piaexu .r:l!:
E
1
"itf " =
391
q
""so = uii:1-6py = 16 - s,a6 = ."f0, el = o, s.
12 n625.1\ AoHo: coscl=- i u < d < -.
S'ailmu: Ein e; tg 0; ctg cr.
"i,'o = t.,/illll'o; "i'o - ocRinbKn c. t(yr I .rBepri.
'12=5 ' .tno=12 =2.E,13 12 ' 5f 144 E{ s
srntr= Vr -=11*n=ra,,,6 zn
2) AaHo: si,ncr = i It < ct < t.SnaLmu: cos ct.; tg ct; ctg &.
"o"s = 1J]_ "ir,'cr; pess=-
I a r'iT Jr a Ja r ,[5) Ja "6,roscr t-*== t/,u - 4 : reo - -:l n l'ffi= rei
"/1t "6,J33
3t naHo: tlct !, !. ".r*SHai.Lmu: cte &i sin (}i cos c(.
.tgs=-l r cLEd=-3; 1, =1-ctg'oi sincr=-- tg q srn- cr
",'"= f t.'-, ocki,rlxx d - Kyr tv.IBepri\ I + (-3)'
L 1 ,,[osrnc = ., , "o"o = -.'fi *in o;\110 JIo 10
tr a 3u4o
!10 Jto 10
4) \aHo: ctsa= z i !<a <n.
SHaitmu: Ne $i sin ct; cos cr.
teo = -L, te" = 1= -1,c[g 0
"r"o = E. ocxinl,x,, c!l+7'
tittosina ,/_' =-L--'!1 | cosa=r'[r sin,c;!50 5;2 1O
f ,il | 2 7,[2coso .j1 -:'I lr .1! L rol !- loo ro
626, IIlo6 4onecrn roroniEicr6, Eeo6xiAno BnRollaru roro*cEi neperBopeHss olHieia6o ABox 'racrrjs rt oAepr{arr oAHarioBi B!rpa3r-r. Mon {a cKnacrv piafir.rqrc niBoi ratrpaBoi qacrfiH ii oAepxarn r0r.1) BIrItoHaeMo reperBopeHEs niBoi .racrlrEn:(cosd sir\(xxcos'cr + cosC[sina + sin'o) - (coso sinoxl + cos(lsind) _
l- sinocosd I -sinocosdy pesynr,rari Mlr oAep,Iianu piBHi Brrpa3rr.
2) cos'd+sin':s sin'7c+sir'zo!g a=I sin'rr{I-rg:o,,t- ftit" "#=
=1a19'q=-l;cos,o
sin'n ^ / I \3) ----.- sin'(}=sin'o
--ll
sin':c tg:c:cos-d \.oc'o l
-. "6 z"i,'o 1+2coss-' z-"o-r 2sinc+Js(.,6 -2sino)(JE + 2sins) - (1+ 2coscrx2coso - 1) _ g - 4sins 4cos, d + 1
@=e"*"_1)12"-;16=
l
I
i
:.:.;:.:.:.:.1i:lid
cos' a ctst a=
",";*.i""", clg d 'Lg'o t cLg'?ol ctsuc:
6)
7\
L=t+cts,q; sina = I
Ryr I1 'rBepri.
_ 4 - 4(sin'? o + cos'? ct) =
4 4 =n.12cosd lX2sin(l r Je) rZ"o"o l)(2sind + J3) "'
"( 1 \cos" 0l ;--- r l\sm-c );;t'- : l
\ cos'd/
5)
"tnt' "o"o sinocosc+sinc -- srnotcosd- lt.l sin il
I cosc cosd coso(l + coso). sirr' a
1 +.Lg' c( cos' a ::+- cos? u = I -.tg, n cos, c - sin2 c = "os, cclg, ct =
= cos' o|t I t ctg'd) = co", o .1 - "."r o.sin'.r
8) "i""a,f""":"__..","J "f_g. sin,o sin.c _srn,cL sin'cr / I cos, q(l - sin, d) cos, cr . cos? ry - ros. o
= tln a.
627. 1) sin'zlI cos'c((sin'ztl + cos, (r) = sir, c, cos, o|;
2r H#--"." "*,of t, - - 1 | = .os, q . c€^ a.\ qin'd )
,, 1"i.lo -"r",ol.Ie'g. sin'/otl cos'?d) cos"c"' lcos'c _ " sin'c _
"oa'o sin s";n.o =
_sin'?csin'o cos'a ,.cos- G srn' .I srn_ rl
llilli;::jilltiii ATTEEPA Mep3rqKA. r. ra iH. AKaaeMi,{Hur piBeHb llil 393392 iii: AJf |EEPA Mep3neK A, f. ra iH, AKaAeMi,{Hnt piBeHb ::l::::l:::::::i:l::::
i
624, 1)sin{cr(1 - sin' o) + cosa o(1 - cosz c[) = sin{ d cos2 Cl + cosl o sin2 o =+ sinr cr cose o(sin' o + cos2 c!) = sinz c cosz d;2) (sin'zd)3 + (cos: o)3 + 3 sin'?c(cosr q = (sin's + cos? dxsin{ c - sin2 o cos2 c! ++ cosi c[) + 3 sin! o cos2 C[ = sin! C[ - sin'? q cos'? q + coa{ c, + 3 sin': ct cos': ct == (sin1 Ct)' + 2 sin' c cos2 cr + (cos1 a)'z = (sin? cr + cosa a)'z = 1'?= 1.
629. 2(sin'? o + cos' sxsina c[ sin' o co€'? d + cosa (x) - 8(sin! o+cosa d)=2sin'rq- 2 sinz ocos2 cr + 2 cosa o 3 sinr d - 3 cos{ (t= sina d - 2 sinr Cr cos2 s - cosi o== -(sina Ct + 2 sin2 o cos2 ct + cosa q) = -(sin3 d + cos'? (r)' = -l! = -1.
630. CxoprcraiMocs ocHoBrrom BnacrrBicrro Apo6y: st qo qucer6HxR i BIraMeHHrIx
apo6y roairtrrr Ira oalre i re ca e qncno (a6o Blipa3), BiaMisse Eia Eynt, ro 3sa-qesrrs apo6y Ee 3MiBr.rTEcs.1) lloAirsMo ql,rcen6HfiR i aHaMeIrlIrrK sa coa ct:
cos -cosd_tsu-1 _( ,. -rl,(, * r) ___r, n __t.sind cosd tss-l \3 ,/ \3 ) 3 3 2
2) IIoAin{Mo q cenl,nnx i 3HaMeEslIx l{a sin2 cr:
2cos'n ?sin'o
"i"6 -
"itf.,zcte"a-7 _ 2-(-2)' 7 _a-7 - l= 0,,u.
3 .os: c . 4 sin a cos d 3cLg'zo'+4ctgo 3 (-2)'-4 ( 2f 12-8srn- o srn- ct
631. 1) noAin{Mo qnc€nr,HnK i aHaMeBHLtIr Ea cos s:
y IV qBepri: coE c > 0, ctg d < O, roMy cos o.ctg d < 0,
"..o*cosc.coscr sin2o+cos2<l 1
1 sin (r
2) floainnMo qncenLHr.rR i sEaMeEHrrR lra sin2 c[:
"tg1 =9,L iCl'l g,t, 9I 3,-7 -3 16- 12-r-sl-ctg's 4 \ \4') 4 L t6r 4 16 4.? 7 7
u"r.,,@= "t""' ". """ "
r" a. "t"t ". "t" " "." " = .[."' " t r"t" a """ ". "t"' " =
= r,6;" - "ir "f = bos o + sin al;q - xyr III .rBepri, roMy cos o < 0, sin (I < 0, cos cr + sin o < O.
P$xpr{BaeMo MoAynb: -(cos s + sin d) = cos q sin c[.
". v6*'" -*d"*f 0 '1[oJ"{l*."'P) VGs,c"-lp coscs:npl.
"' tcg.te" tep.tc" - tse"te" - tgp.tg"'cr - Hyr III qBepri, cos q < 0;0 - lcyr lI qBepri, sin P > 0; cos o sin ll < 0.Po3Kp{Ba€Mo Moaynb:
cos s sin p : (tgpctga) = -"o"o. "inp, !9{. !in d
= "in cco"F.
sin lJ cosd
r'"+" |]",Jr- tl "i,,o-.f,o *w,o -u"". "tno \i"in, o -cos'a = sind - \i, ,sin,o
= sln a - lcoso.ctg al;q - (yr III a6o IV .rBepri.y III.rBepri: cos ct< 0, ctg o> 0, roMy cos(r ctg d < 0.
394 ili:AITEEPA Mep3nrK A. r. ra iH. AxaaeMiqHrai piEeHb iiitailliii:::'t
634. l)sin d + cos d=D; sinzc + 2 sin dcos cr+ cos2d=12: "ino"*o = b,
2
2) sinr a + cosr a = (sind + cos axsin, C[ - sin Cr . cos o + cosz d) =.(, ^t'rl ,(s-b')
\ 2) 2
3) sin!c + cos. d=sina d + 2 sin2 c! cos2 o + cos{ Cr 2 sin2 q cos'o= (sinz d ++ cos'tr) - 2(sin cr cos ctt, = \-2.t-glJ- l-b1 2b'+\ -l+2b'-b4422
635. 1)tg cr + ctg d = b; tgz u.+ 2 tg ct ctg o. + ctg! s= b2t tg2 &+ ctEz (r= b2 z;2)-tg3 cr-+ ctg, o = (tg d + ctg dxtg, (t - tg o ctg ct + dg;a, == b. (tg, @ + ctg, ct _ 1\ = 6162 _ 2 _ 1) = 6o _ tr.
636. sin, d + 2 cos2 c[ = sin2 Ct + cos, d + cos? {x = 1 .t cos2 c,:-1 < cos d < 1; 0 s cos2 c[ < 1; 1 < I + cos, a < 2; 1 < sin, d + 2 aose o < 2.
637.3 sin, o - 2 cos2 d= b sinz 2 sin2 q - 2 cosl c, = b sin, 2(sin, o + cos? o.) == 5 sin'd - 2; 1<sin ct< 1;0 < sin3 d < 1; 0 < S sin, d< 5; 2 < 5 sin, a_ 2 < ij;-2s5sin?d 2s3.
638. 1) <DyHAqir craAae, sl{qo 6inbuoMy apryMerrry BiAroBiAs€ MeEIIIe sHaqesdsOyHIcqii.
-. 7 7nexax. r >I /(xr) r_,: f(x,) ,,_-5.CknaAeMo pi3Erqro 3EaqeHB OyHXt-tii:
7 _ 7 =1xt-35-7x, AB_ 7(\-x,t
,,+5 z,+5 (r, +5)(r, +5) (r,+bxr,+b)'I - r,.- 0i ,., + s > 0;.r, r b .0 npx;€ (-s: +-r;1r,1 _ L*,,. O.fla,\ < flx,1, orxe, gyE(qia cnaAae,
2) OyEKrtis 3pocra€, .EKrr{o 6inburoMy apFyMeEry BiaroliAa€ 6inLEe BHa.reHEsOyBnqii.Hexail x|- r,. l(xl)=6x, -x'zt fk,t 6t/-r:.Cxrs{eMo pisnnqrc ssavefi r 6ysrjrii:t6a, x:) - 16x, - xi t = ax, - t:-6x, xi =6(x,-rr) .G:- x:\=
= olIT rr) Ix. - xtl(J, + ir.) - (.r, xr)t6 (.r, - ,r,))..r:-.r, >0i -t, .r, < 6. rovy 6 - (i, , i,t ' o. '(,Y? - xrxb - (x? +:,)) . 0 npn.r € (--; 31.IQ,l - I(x,l ' 0i t'ta,t . lr,), orxe, OyHKui' rpocrac.
="1t'2)=" =/ tl =1_r t'=\ 1000 i \125/
.!;; "': ( -9?5 I '= 4/roooo ro _,' 10000, v 625 s -
_ ^lD+DIgC 2 6
3tgd-7 " I
" -5,52
80 ,25 _555 55 11
t:.:.i!.:.i:.:{
:::li:li,i.iil
1l
I
*,,, [#J' =1i",,] *
= r"' nr'
= 126t = t25.
,,[#]' f+J' r"n,t'=.
i
iiliii:iijiiilii AnrEEpA Mep3reKA. r. ra iH. AxaAeMi,{Hhr piEeHb !it: g95
640. Hexan trepffs ApyKap&a ApyRv€ jl: cropilloR 3a roAnHy' a Apyra !l cropilror{56
3a roAtrEy. IlepIIIa Apy&apRa HaApynyBarla 56 cropilrox 3a roAr!I{' a Apyra -
"o 4
"os"t. rr"p*u rr'Irpar{'a Ha po6orv ,," I
!9 - !9 ] roan* MeHUJe' ro 3a vMo-g t a r)
solo AopiB'roc 2 ro.au'a'. nppure prBstHHt ""*"*,t'09 tl t
5Ilepllla Apy(apxa llaApyr{vBarra 5 cropiBox 3<r roAets' a Apvra - 4 croprEkr
4-ca ' roarn, 3a vMoBoro Bo{Ir Bxrpsfl'urti Ha 're oAHakoBufi cac'
54Apyre piBssHEa crcre*", ;= ,,4-P= z, ls, = +,,a x l_^ -^
1o a 199 4=z,z;l-= I v x
/sz n) 4n3l cos _+ =cos =0:\ a al R 2
4) cos cr cos (cc+ B) +sin Crsin(d + F)= cos(c (o + 0))= cos (s - (r- p)-= cos (-p) = cos p;
sjn53 cosT -ros53'sin?'-sin (53', ?') cos53"sin7"- slnOO"=4;2
sin ((cr + P) - (cr- P)) = sin(d + p a + 0)= sin 2F;sin' (d + p) + cos' (cr + 0)- 1;sin l2O" 5") sin15'cos {10' + 5") cos15'
cos cr eos B sin C[sin 0 +.2 sin ct sin 0 = cos (} cos p + sin d sin B = cos (o - B).
l) cos (6d 20) cos 80:I
sin (12" + 18") = sin 30' = ;r
sin 75'cos 15" - sin 15" *""rU" = "r"
uo' = @,
cos ((d + P) (o P)) = co6 (q + B o u B]= "o"
2p'cos t64" - 4') cos60'
= cts so. : @:sin (19".41'l sin60' - 3cosocos B+ sincrsin ll- 2 sin dsin F=cos cr cos B siD osin p=cos(o+ p).
11rsrfl_or= rsdr rep = 2 a i,l r tl 3.2 6
t-tga tgp r_1.1 8 L 8' 4 8 7
u = O.8.'2424,2A 2A =I;- -=t1
0,6x x
5)
6)7\
8)
9)
644.
2)
3)
4')
5)
6)
645.
2a 22.4 O.8 ^ 5,6-0,8rr ^ 15.6 o.8'r=o'0,8.r 0.8.r [x z u:
BiAnoqiAb:7i 5,6.
7. OopMynra AoAaaaHH9
5.6y=_: x=t..u=5.rt,0.8
641. 1) cos c, sos I - sin {, sin B + cos d cos [i + sin l:r sin 0 = 2 cos Cr cos l];
2) sinSO'cosd+cos30'sinCr (cos 60" cos c[ - sin 60" sin o) =
1J3 l./3i-"" - "r9"'" " - jcoso - f sin a'
"6sin a:
3) \E(sin Gcos45" - sin 45'cos o) I sin q + cosc[ =t; t.
JZ v'"ina € tscosc-s:n,r r'osc sind coso-sincr-coso 0:22
4, 2(cos60".oso r sin60"sina) J3"ino "o"o
=,t;
=r r...a : v""inc-J3sina-costr cosd sind'sinc-coso=022
642. 1) sin o cos B - cos t[ sin B (sin (1 cos P + ccs d sin p) =
=sin c,cos B cos osin P - sin c. cos B coscrsin P= -2 cos ct sin p;
2) sin 30" cos d - cos 30' sin cr + cos 60o cos c( + sin 60' sin o =r ,,6 t .,6.
sincr ' coscr- slnc=cosc;
-l n ft l3l J2tsinrcosd-cos^sindJ cosd -sind =
E-1r= lz v3coso-J2 -t'sinc coscr - sin..r -coso sinc cosc sinc=0i
22
643. 1) sin(d + 4(I) = sin 5cul
2t cosl17" + 43'l = cos60'= t:396 i::::: AInrEEPA Mep3ncK A, r. ra iH. AKaaeMi'{Hnf piBeHb ::ii:::::::i: :':i+'l
24646. rsra Br tga - tsp 3--l
= -3 = -1= -o-rzs.Iraotao I35 16 8
647, l) tE OA'+ 47", = tg60" = .,6;2) ts (1" - 46") = ts (-45o) = -ts 45o = 1'
B) I =--.1--=",nun"= 6,-' Le t27' 33') te60' '-'-' 3'
o tel$.ff.)=te$=tel=r.
64A. D Le @4" + 36) = te 60" = \6;2) tg tsd 30) tg 20.
649, lqo6 AoBecrr. roronisicrE,, roroltrHi neperBopeHH.s riBoi qacrnllnri orpuMacMo s[par. piaHr.rfi Bxpa3y. eKIrii croirb y trpaBiii qacrysi.
,, cosacosp sinasin0 rsinosinp cosdcos0 ,." "..
r "".0
*- r "*,p "* r "t"0 -
"."""."0 - "
2t sin d cosp - cos(}sinp + sindcosP -.osdsin 0 _ 2 sin ocos0 _ rsocrsB.srnacos0-cososin0-sinCtcosB-cososinF 2.osos'n0 -
;
". 1E ros a - 2rcos 4 s.cos d - Ein 4s. stn d) Jzcosc-z "jcosn+z 'fsincJt
-
"' 2tsin45"coso r sinocos4S") ,[2r;.""- ^ Ji ^ J, .2 -2aoscL- Z 2 sino Jzsind
- ,,8 "o"
o -.,8 "o"" - Jz "tn
a Jz"in"=
Jz "o"o , Jz
"in c Jz
"in o ,72 "o"o "sui
:ilitili*.:::Jtit AITEEpA Mep3neKA, r. ra iH. AKaAeMi,{Hri pieexu iiL: 392
I'
4\
5)
sinr{a - pl {a-plr _ sinlo +rd-0)=!in2o_tn2o,cos((d-pl rld-pll cos{dt0 c-p) cos2osin 45" cos cr + sin d cos 45" - (cos 45" cos o - sin45" sin 11)
"iffi-.1, "E Jt lE .
;cosa+sina;- ms(I+ o ",na JE"ins,12 J2 J2 J2 J2 cosa' .6c n rsind SrnC
sin s + 2(sin 60'cos d - cos 60" sin d) "i"o*z f*"o z l"n,,S *"o n 2. ]"1"o "6*"o
sin(I-\3cosC!-"jnfl \6"o"" 6-,--.6".*,. "," "' J3.*t "';
\rrtPu'
,("*€o' ;;;;ao' "- ") .f3 ".- -,
*"P = ;, sinB = 1ri;: cos' P,
sin ll =
t16 fs s--.." \t- 2b V2b 5
cos(n F0r=cos,rcos0-",,.ir"'"n 3f a) a
' 5' 5, 5
654. sino= ]f; "o" o = t.,ii -
"i,," o; cos,x=-
f , -Jsino=tJr-cos"g, "-p= !/r I ;l
105 192 297= 17.% 17.%= 4%'
9-6ss. sinP - : .osp Jr sin p: cosp =
I
l
I
I
I
:a.];.:l
::::::i:l.i!!r!
ri:,:J"11
1
-"0=1,
,[H
6)
12 12
25 25
ocninb:in ll - Iil"r IV qBepri;
, ocEi,lERu c[ &yr I qBepri.
6so. 1! " jn o "oggllg:qqp lt! 8t9. o
sin d.os U .os(1sinP ' srnPcosn
J2coso -2{si-45'.oso .os45'srns)2(sin60'cos d rcos60"sinor J3.oso
Ji...o z.*.o"o*z 9"i"o -z.f"o"o * z !;
"in o - .,.6
"o" o
sinctcos0=
"*""."S = ''
Jz"oss v2.oso' f sinc J2sino - ".J3 cosd + sinq ../3 cos(x sln d
^ 2sin ocosB - {srne.osll - s;nlJ.osdr - 2sin dcosP sinocosP - "rnpcosct"' costo 0, .os{o + F)
sin0cos0 rsin0.os0 sin(d{ 0) -= -
.g(d + 0r.cos(cr + lJ) cos(d + P.)
OSt. r) "o"o = r.',[ "in'or "o"a=
ocKini,Rn Cr - Kyr II qBepri.
9 ./2 i 40\sinrcr 4s")=srnc.os45" rcosl:lsin45' -2 I A)
B1\Ea2
652. cos cr = -o,o; "irts = rn/il "o"'cr; "itt o = .,/i:105f ,
"i"o = -u/i: o3o = -"6,0n = -0,s.cos(60" - ct) = cos 60" cos o + sin 60'sind =
l"o"o, V'"ino= ' t-O,Or !-o t-0,St 0.3-0.4J3.
es3. coscr = 9. "i,'o=tJt-*""o;5
sin 0 =
s,n,d-Br=q,nn.oqn-.^.^.r"n f t5) 7 ( 8l (-24 ------' t 17) zb \ t7) \ zb)
"E , s"E242
40,t8
^ t e Ee q ^ 34 3cosl -.Jl - .l : tslj'! 25 \25 5 - s5 4
. -'1 3
tgla - g; tgo 190^ 2 .l ^ 5 ,5 = 2.I-tgd{gP I I.J 4 8
24t2
656. rs{45"+at=-lg1)'-Lgd t 5,1 '-- 1-Lg45"Lga I 12 3 3
3
657. 1) sin 15" = sin(45o - 30o) = sin 45'cos30" cos45'sin30"=
="8 "E _"8 y_"6 _,8 _,16-Jt2 2 22 4 4 4
z) sinr05" sinr60. 4b"r cos60"sin45.. f 9 t ) " ^tt,3t crp -ro5" I I-=L te60'1s45" r-!6 I
€105" 1e(60'r45') rg60'+1945' Jf ' t
/r J:)(r Js)_r-?.@-B_4-2$ h,i' ,lltt' "at-
t-s -2
ocKi"{blttt cr - kyr III
, oclrirbrcn cr x]"r I .rBepri.
398 ii::: AIrEEPA Mep3rcK A. r. ra iH. AKaaeMi,{Hhr pieeBr liii:jlliilli::::i :lit:il:liltii:.rli AITEEPA Mep3neKA. r. ra iH. AKaaeMiqHnn piBeHb al:l 399
658. 1) cos?5" = cos(45o + 30") = cos45ocos30 - sin45'sin30'=
J, Js J, y-J6 'E2 22 4'2) sin75" = sin(45'+ 30") = sin45"cos30" - cos45'sin30" =
,E h "li r J6 ,'E2 2 22 4
659, npoBoazMo roro*cEi DeperBopeHss niBoi qacrrl ii orplrMaeMo Bspa3, skniaopiBllloe trpaBiii cacrrlri.
sind sin0 sinocosp cosdsinp sin{d-pl .1) tgo igp=-osd r -;=
""ir"*p - *o-"p'
cosa sinB cosocosB- sin0sinc costo 0)2r cls.r- rsL, -{
- ---:" sins coslJ sin(r.osl, sLnosrnp
cos rt cos0 coscsinp cosPsino sin{(r+lll660' ctgq -"iep=
"ino "
"i^0 =
"1"r"""P = sinc"inp
c,(Id(td0cos d cos r srn o cos o cos, o
661.1) z.-___J t z=___t - r=- cts _;I 0 I ct ..r _4
--"4 4 4
.'r cos cr oos2ct _ sin2dcoso co62dsina - sin(2cr-a) - -sind
_' sinn sin2a sindsin2ci sinosin2d sinosin2d
^. I 1 cos0cos2a cosdcos2ott ;, {gf,n ro = -",}*+q re''n d "l"ry = c"",rr' - d, =
"."4 =
' cosccos2c cosci cos2d
rr is1-:sg lci-lcP -2f,cL-' t-rsdrgF+r-Lgdrgp+2Ls,cL'tgd + tg0 iga - tgF1-tC"teB 1-te"teP
= 2 + 2ts2 ct = 2(1+ te' "l = Z. ]-= ]-.
cos- ct cost ct '
064. 1)cos(o+F)cos(s p)=(cosC[cosB sin s sin Bxcos q cos p+sincrsinB)=' cos' ct cos'? B - sin'2 ltr sin: p = cos' o(1 - sin'z B) sin'z P(1 cos? cr) == cos'?cr - cos'o sin'z0 sin? p + sin'B cos'?o = cos':o sin'?p;
2) is(cr + pxl - tc q tc p) (req+rep)=l+l++ 1-tgCltgp (req+teB)=I tgorgll r
rg0 te! tgd 1gP 0.
r -/t665. lr s:no Jacosa zlrsina 'i -s".J zrsi""*"60' cosqsin60')
= 2sin ({x 60");1 <sin(s-60")<1; 2<2sin(ci 60")<2.
Hdn6inbrueJna,reHnfl 2-
lt; 6 \2) sino. cosc Jz """ina-Y-"" - J2(sinocos45'+rosasin4s')=\2 2 )
= J2 sin(0 + 45");
-1 < sin(o + 45') < 1; -'E < .,8 sin(o + 45") < '6.Haii6i,rrue sga.regrlg - .,6.
(t" , \666. I I J3 cosd - sin cr = zl vrf cos" - ;"* d] = 2i.os30'cosn - sin30" sin dr =
= 2cos (30' + (x);
-1 < cos(30'+ cr) < 1; -2 < 2cos(30" + cr) < 2.HanMer ne sEa'reslls - -2.
2) rE sin o + '6cos
cr = rO[]"t.". f *""J =
= 2\E(cos 60" sin d + sin 60" cos o) = 2\Asin(o + 60');
1< sin(d + 60') s 1; -2nE s 2,t0, si]lL((t + 60'\ <2\8.
HanMen e sga.{egng - -2!6.
667. ItorfteH.IneE apr.OMer*r.rHoi rporyecii, rorrrEaroqn 3 apyroro, € cepeAHiM apso-MerII'rEr{M cyciAHix qnesiB.
t4x+5t-lx-+2t , -( Kia{eMo prBHsHHs: 2- - lx - L Z,
4x 5 x" -2=l4x- 2;x'?-10x+9=0;lx. rr"-10.I .r. =9;.r"= 1.r,+j2=91
1. r,=9;4 9+5=41; 7.g l=62tg' + 2=83,2. \=1t4 1+5=9; 7.I 1-6;7'+2=8.Bidno?iob: 41, 62, 83; 9, 6, 3.
i:iilitiitili_iati AITEEPA Mep3reKA. r. ra iI{. AKaAeMiqHlri piBeHb iiil 4Ol
1
sin 2cr '
cos 2.r sin2dcosc, slntt
sind
sin cr cos 2o - cos s sin 2o sinl.r 2dl sin( ([)cosrrsin.I cos ct sin cr
cos crsind coscr
cin 2d qin o662. 1l cos2d + =1 cos(]
cos 2ct cosC[ + sin 2 sin ct
sin 4.x cos 2cr2) cos4.I' 1 sin2csin( 20J sin 2dsin2& sinz(l
cos 4C[ sin 2c - sin 4cr cos 20
663. 1)(sinCrcos P+ cos &sin Bxsin ocos B cos osin B)== sin, ncos,0 cos, o sinr p=sin'c(1 - sin'z p)-sin'p(1 sin'zC[)=
= sinl cr - sin'zcr sin' 0 - sin' P + sin' p sin'? d = sin: o - sin'zP;
2) sin' c[ - 2sin q sin P + sin'z 0 + cos'z cr + 2cos cr cos I + cos' - 2 == (sin'cr+ cos'2d )+ 2(cos C[cos 0 silra sin p)+ (sin'll + cos'p) - 2== 2 + 2cos(ct + p) - 2 = 2cos(0 + B);
^ LEr(t ls29 (r'eo-tgoxtgo rtgp) rgo tgp tgo rtgp"' 1 r,e'aue'0 (l rgargBXI rl,gorgp) l rigctg0 r tectgp
= tc(o + P)tc(ct - B);
4oo ii:: AITEEPA MepsrrKA. r. ra ifl. aKaaeMi{Hrr pieexu fillllltlli!!::j
sin2c,
sin(2d 4d),sin2q
:
i
{
668. ItBaapar qreHa reoMerprqEoi nporpecii, roqlIsaloqlr 3 apyroro, € ao6vrlcoM aBoxcvciAEix qresiB.CxnaAaeMo piBEsHns: (r- 1X* + 7r=(t 2x\'; x2 +7)t r 7 =l- 4t+ 4r';i - 4tz+6x+ 4x-7 -l=Oi 3x,+ 10r-8=0; D=100 -4. (-3) . ( 8)-ai
"lD = z:
-10+2 8 4 -1O-2t- -2.' 2{3) 6 3 2l3'J
" a.!-t=!' r z4=-2.! z 25,-' s'3 ' 3' - 3 3'3 3'
,, = 2:2 - 1=lt 1 2'1=-3: 2 + 7 =9.- 1 5 25 - ^^utdno6tdb: .li al -. t:-t: v.
669. Hexan reprEa rpy6a Moxce EatroBHgrn 6aceiE 3a J' roA., a apyra - 3a I ro.r.
3a oagy roarHy nepna rpy6a EaroBHIoe 1 qacrrtrry oacen aa, a.qpyna rpvoa 1 "t"TY
rnny 6aceiua. ABi rpy6r HanoBslororb 6acenr ra ? roa. 12 xB. = z* = z ! *u.605.IlBi 1p)6 3a I loauHy HanoBHlo]orb
,'r = fi o"""ti"u.
5
c(rraaaeMo trepue piBrr'IrHs 'rcreMlr:
1.1 = :.x!36IlepIlra rpy6a nparloBara 8 + 4 = 12 roAlrrr i 1? 6ace;ara, a ,qpvra rpvoa
4xrpaqmBana 4 roAlrstl i rlarloBErna i 6aceiiEa. PasoM BoHa HanoBHnrb Becr,6aceirH
!c*nanaeMo apy.e piB'slr,,n clrcreMrl:
13 t ! = t.
I 5 |4 4 U'oI I |t-4t. I
lir r 36 ) r u e 9 a," re_
112 4 1124, rgl-+ =I: l-+-=l:I' c l* c11515113 | =-: u=12.18a 36 y 36 18 I36
BiAnosiAb: 18 !or..i 12 to4.
673. 1) tg 124" = ts(90" + 34') = cte 34";2) sin(-305') = -sin 305' = sin(270' + 35") = -(-cos 35') = cos 35';
- tr\ I n)3) .rs{-0.?n) = - cue0,?r cr,el 'l r '-l- -1 2 s) [ ''5, -"5'14r! I n)4l srn =srn fl--l=srn-.15 \ 15/ t5
674. l) .os225" = cos{180" , 45") cos45" '; .
t;2) sin 240' = sinr180" r60') -sin60"--;:
^ 5r ' snl n J2rjr cos; - cosfr 4 ) -cos 4' -Tl
f a,r) 4n / nl n t4) cos cosl rr+\ 3.r 3 I 3l 3 2
675. 1) tg21O'= ts(180'+ 3o') = ie30'= +;2) cts 315" = cts(360o 45o) = -ctg 45o = -r,
n3l cosi 150") .os I 50o = cos{ 180" 30") cos30' 'r;
4r sinl 5Jrl -"i.8= -.i"lzn ^l- I "i"nl .i,' n - J3.\ 3' 3 \ 3,r \ 3) 3 2
2) -ctg(x tgC[=-1;
4)
-=
1;
6) cos {:{ + cos & = 2cos ct.
2)-cosC,+cosC[=0;3) cos d - cos o + ctg cr c.tgq=0; 4) sin'c,+cos'?c[= 1.
678. 1) 3 ts(180" 45') - 2 . sin(180" - 30') + ts(360' ,60")
2srn(180"+60")=
3ts45"-2sin30'-is60"' 2sin60' 3 r 2 ;-Js++=t;, E
^. sin (360" - 45'.)cost360" 60', tg{360' 45") sin 45" cos600 - tg45ozr stn{ro. + 30"r.osr1S0" - 301 cos30'. (-cos3o',
r n' "'( ' nr) , rr3) sinIn. 4.]cosl'r-;l l-tclr 5]J"'*['' rJn r nr ir o "D r Gt Jo' 'ts cts l=
-'4 \ 6) -3 "3 2 \ 2J 4srn 20".os tO" - cos 20'sln 10" sinl20'r10') sin30"
sin 2l".oE 9'- ros 21" sin 9" sin(21' 9") sin30'
i:i:iii{iijiliii: alresPA Mep3neK A. r. ra iH. AKaaeMi.{Hlri piBeHb iii:r 403
676. 1)cos (t- cos (I=o;
3)-sind sind= sin'd;
5)cos'?lt+sin?ct=1;
677- 1\ cLg a- ctg d= 2cte si
L OopMyn]a 3BeAeHHg
670. 1) cos ct;
3) sin d;5) cos(182" - cr) = cos a;7) lg dr9) cos a.
671. 1) sin c;3) -cos C[;
5) sin Cr;
2) ctg d;4) cos (270" cr) = -sin q;6) cos q;8) -sin 0;
2) te si4) cte (270' - cr) = te d;6) cos q.
l@l'1.,\2)2 1.2s 4 s.- - ;- ----=-
- ;'
J3 | n3 l2l z)
672. 1) cos 123" = eos(90' + 33') = sin 33";2) sin 216'= sin(180" + 360) = -sin 36";3) cos(-218') = cos 218'= cos(180" + 38") = cos 38";
5n /n nl ,r4l cos =cosl -+ l=-srn-.' 0 \2 181 1a
402 iii: ATTEEPA MepenrrA. f. ra ir. AKaaeMi.rHr4i piBer" liilitlil:l:i::ii
d
., cos66"cos6"+sin6'sin66" cos(66' 6") cos60""'
"""65'-."5"-l,tr5'"1r65" =
""qAt'-S"l = cos60" ''
679. 1) 4cos(180'+ 45") - 6cos(90'+ 30") + 3cte(360" 60") + tec80. + 60.) =
=-4cos45"r6cos30" 3cr.s60.+ tg60.. -4 f 'u I t 4-.n== z"E+z-"ls+"8=a-z"E;
6111 .,66cos'60"ctg30" 12)cos30" J3i
082, 1) ctg 55'; ctg 65" ctg 75'; ctg 85" saMiEnMo raEreHcoM sa ibopMynorc.rg (r tg(90' a).oAeprRrMo: ctg 5' . ctg 15" . ctg 25' ctg 35' cte 45' ' tg 35' tg 25' tg 15' . tg 5".C$opncralmrcE OopMynoro tg cr ctg s = 1, orpr.rMa€Mo ctg 45'= 1.2) TaHrencr ryrrx KyriB saMiHro€Mo Ea raHreEc rocrpnx EyriB sa OopMynobtg (180" q) = tg (t.te 20" + tg 40'+ tg 60" + ... tg 60' tg 40' tg 20" + tg 180'= 0.3) CBopnc?a€Mocr lbopMyrrolo sin(360' d) = sin o.sin 359'= -sin 1"1
sir 0' + sir 1' + sin 2' + ... sin 2' Bin 1' + Ein 360" = O.
683. 1) ts 10" ts 20" ts 30" . ... . cts 30' cts 20" cts 10" = 1;2) ctg 15'+ ctg 30" + ... + ctg 90" + ... ctg 30" ctg 15" = 0.
oea.rrlLeln'Il "rs"l ,loel z' 'l "ig"l -,\'.4)")\"|41.)
| "is I - "ts"J * l"rsI -.is"J = {1 + ctgct'? - 11 - cr,gcrJ'? =
= 1+ 2ctgd + crg's + 1- 2ctgcr + ctg'cr = -f - # = #t,l ft i+(I
,, '"' t " '-"i,.1r..,1."1,,[r -1"-"t] =
,( " (" )l 13 ' -t2 '6 r/.tq'l d I"\2 r6 1)
l:t I "ln l /n I- : l srn-L +nl ctg- +{11=.ln I 13 I -\3 )
6cos'?(180'+ 60")ctg(l80" + 3o')2'-sir(270'+ 30") (-1)'
ar "i"fzn -
r'J-"1' - n l,'l n,nl".nl\ 4) \ 3./ \ 3/ -\tr'6.] =-srn4 l-'os3.]te3 cte6
Jzlt\ n e ali2 \ 2) 4
4')cos64'cos4' sin4"sin640 cos(64o-4') cos68' _ cos68" _ _l
cos71"cos41' sin41'sin71" cos(41'+ 71") cos112" -cos68"
680. t, -"ino "o"o--= "]no "oto --"o"o'-tgd (-cosd) sln0 cosqcoso I
sin F sin p - cos B. (-cos P) = sin, B + cos, p = 1;
. ( sina coscrlcoscrsrndrrgc ' crg0)= cosd srn dl- "o
* ",rolsin?a+cosra
= coscsin d
-=1;
cosc,sinc,
at -sint"-atslnl " al. sin'rn-atsin2ln+at cos'?rn '"r."*'llI-"I=2 \2 ) \2 )= -cosocosd sin2 nsin'n - cosz crsin'cr = -cos'd sint s sin'ocos'c == - cos' c( - sin'g o(sin' n + cos' c() = - cos' o - sin'z c{ = - (cos' .[ + sin': q) = 1;5\ sit" t + tg' r. clg', + cos r cos, = sin2 r + cos' r + tg,.r. ctg, n = 1 + 1 = 2;6) (cos t + sin.r)'+ ( sin., + cos r)2 = cos': r + 2 cos r sinr+ sin', + cosz.x -- 2 cos r sin r + sin'9 r = 1 + 1 = 2:
". tga ( cosx) ,.
' cosr {-igr) -'
^ cos' .r sin'.r sin'r sin rdt -
+ " .:_+-t_ _ sin..jr rcos"-r I.ctg'x tg'.r I sin'r I cos'"r
681. t) stn qigla = -!!!a . sina
coss;teo ( sin0) 1 cosd2) sin r.sin jr + cos r. (-cos r) = sin2 r cos2 r = -(sin, r + cos, r) = -1;^. -tgd (-cGd)ctes tgd cosd crgd"'
"."a (- rgox cteol =
"o"o lgc cugc 'l
4r sinq crso-coso-"'"* -"'it "11",
I cosq+ sino=' cos9 I sinq I sinq = si g'cts cr (-sinel cosd
ctgd ( cosq)sin d ctsd(t) -
- -Lga=Lgo- l ted l.- cos ct ctg ct
4o4 l{t AITEEPA Mep3rrKA. r. ra iH. A(a,qeMieHrr piEeHr iillt::i:itiii:l
""",1r ' ") ".",f' ' "l .i",f" , "lL3
1 "(n ) lsin' + cr L\3 l
=.i",1 I *"1 **",1 1* "l = r,\.3 / t3 )
2\
3)
\3 )
\3 )
sint ct - sin' o(l t cos': o; sint o sin'? o sin'? o cos' a
-sin'zcr(l- sin'?Cr) - sin'crcos's - sin' c[ cos' cr - sin2 o cos' oI cos'za I ". _ ctg.11.
2sin'ocos'd 2 sin'0 2
.ln lrn\685- eos"' ' .""'-'
' "".'l " - " l* """' '- -
=8 lt \2 a) !2 11,/
cos'", slnt " r cos' '" - sin'? "'\ = 1 - t = 2.8 8 11
3)sin. crl;;5,g I = ;r;: G;;.d) =
"t".t-1-."", crxl +;tcr) =
11
::iltlliillltji:ia AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hri piBeHb t::::: 4o5
t.
l. l.\6a6. t.y cos'1" rol rsin' 'l l'l "l r( sjnsr.coss.iso\4 t \2 \4 t)
.(n ) . "ln ) sinscoscr sinq -=cos'lz+dj+sin'la-".1- I """"=r-srn'd=cos'c:
2) sin':lgo-- t20" - d)) clg (90" (q , tu ,rctg {8u cr)
srn'f/u- + 0)
- sin:170" Fd' +cLs{so.-rr}cls(8o"-crr=r-crs'r8o'-.rr= ---Lsin {70'+ d, sin (80" 0)1
= ;JGo% cr)
BnpaBx arc noBTopeHHs
6g7,1) ! lo zs; t' 'o-8.0, -rr 3r Io -o
txt.r'- 3:c - 10 = 0; \= 5, 12= -2.SaMiEro€Mo EepiBdicfi, piBHocr.nr,Horo cncreMoro:
lrx-5rrr+2r>o. x(x- 5Xx- 2)=0: r,=0: x,= 5t xx= 2.r.r0;BilnosiAb: | 2; 0) u t5; +-).
2l* -:- 6..0 r'+r--6-0:x rx tii 0ir.r=-J: rr=2.' r-2 t-2 v-2SaMiHroeMo HepiBHicrb piBllocrrrbHoro crcreMoro:
)\x + 3\x - 2)tx - 2t. 0. Irr-3xx -2r' - 0.
lir 2,0r i 2/ol(.r 3X-r 2)' 0r x, 3i.r2 2.BianBiAb: | 3; 2) w (2t +-).3) r:- 3r- 4 = O, tt= 4i x2= -1.2x' - x - 3 = O: D = 1 + 4' 2' B = 25'
1+5 3 1 5
BaMiFlo€Mo HepiBHicrr, piBEocun6Hoo clcreMoro: 1
689.
3!(x + 12)
r' + 12r. - 45 = O, t, = -I5 se sa,qoBo,rLHs€ yMoBy sa.qaqi; r, = 3.Orrrie, nBrrAKicrb nnora 3 nM/roA.BiAnoeiAb: 3 t<M/roa.
g. OopMynra noABiiHoro apryMeHry
t
flrir ?
tra 5 ro,q. 2 xs. =
= s| ".r. oi"'**.a 20 xM
tIoB€H sa 12 nMhoa. 6in6ua ? 20 RM
Hexafi rnBsArcicrE nnora - r I{M/roA., roAi BrAllicrr,.roBHa (n + 12) nM/ro,q.,n
I]nir noAonas 20 xM ra ; roA., a soscH oa '"r2 'o4rH. n,Iir 6yB y nopo3i
t20 20 \ -1 16
", L _ I t2J roa. b'nhlxe. Do 3a yMoBoro aoprBH$c b roa, -,o4.
20 20 t6 5 5 4(-xnaAa.Mo piBEflEHfl: ; - ,- n- :t .4i , , , .12 3i15r. + la} l't - 4r' - 48j.
= 0, I 4'' 4sx + 18o = 0l: (-4),
l3.r(r+12)*0;
34tlr,* ou*. rxr ;xr-r,.0. 2r,r-ar(r-;Jr'-rr'so.
l
1,, !u' " , o,
L.. i,",'Bianosidb: (!: 4 .
12 -l
B) cos, a sin, d sin2 d = cosr d: 41 ?!1l25""o"25' "tn
rr",2aos25"
, cos" 22'- sin" 22'a sin'z22" cos' 22'"' "n.'zz7-;*22
- ''
- cos'c sintc tcos(}-sinaxcoss rsino)t,t
-
-=cosa-stnc(;
cos0 srno coso - srnd
7)
8)
22 sin c, cos cr
;?s. "jts =
I cos0
2sinccosct 2'
6ss.rr vr-J2 |t-2.12-l.,l2l =Vr-J2 i/(r-J2) =t/r ' Jz.{lr Jzl
= {r -Tz lTj r(.n - t)(o r) = tD l = Vi = r'
zt :,lr . z.z.1s. (v:r' .,,/zl dtz v:)' ..,/z V: u{z - Jr .
"/z - Jr -
= lz - 'axz - "a) =.ln-s=ur=r.
406 r:i::: AnrEEPA MepsneK A. f. ra iH. AKaAeMi.{Hni piBeHb iil:i:li:i!!ii!:i:ll:
sindcosd ,2.
'r 2-*i**
5, 2.t"1, 11"""1,-1),\ 12) \ 12)
5)
6)
+)/-T-V -V-
690. 1r cos'? 9 sin'9:222) 2 sin 1,5{:! cos1,5q;
2ts !ar --:{,1-tA':'4) cos'4o sin'z4cq
^. 2 ts3.50trl-.1- te' 3,5q
6e2. 1y ?!i19!9!9 = 2"o"o,
691 . 1) 2sin 5cr cos 50;.r-B n-B21 2qin .m :22
- "a "q3) cos'; - srn'-i
n, "".,1,{ -, o.l -",",|.1-rn.),\.4 I t4 )2t91,5d.
1 ts'1,5q '2tg6s
1-i8 6d'
sin2ctz) '-"- = tgza;
i:iliiiiillllll: UTeSPA Mep3reKA. r. ra iH. AKaaeMiqHri pieexu il:i IOZ
14)
693.
2)3)4)5)6)
7\
10) sin'? I - zsin e cos Q + cos'? Q + 2sin I cos q = sin'? Q + cos' Q = 1;
r .o ,")rr) sjn" a .os'7= l.os" 4 -srn'41 cost:
2sindcosc sin2s 1. ^|2t
-
t-p za.i' 2 cos2o. 2cos2a 2 -
r:lr I .os' I ft
- c I - "in' I n olll*"'1" or-"i"'1" oll ='"' ["--14 -) -"'\4 ,rl r4 t '4
= cosl; - 2dJ t=sin2nr
sint n + 2sindcoscr + cosz ([ 2sincrcosctsin'rr+cos's+2sin'n
sin: cr + cos'c( ,= -; = li
ar I "i" as" = €,24
5) ts330'= te(360" - 30') = -tcao" = -+;6, 2{r - tg, r s.y 1- z"tezo" zJz.2te15" te30'
. t,t695. 1) cos45" =;:
2) te150" -tg(180' 30') = tero'= €''T,^. 6fl 3n r nt n Jz;ll srn" " 8 " 4 " \" 4) - 4 2
n' -12"..'a-rl- -"..r - -G.\t2)62
oso. "o.o -,/l "in'o: .osc l-163y J0,64 0.8.oc!ri.r6&a o &yr IV.rB€pri.sin 2cr= 2 sinocos s = 2.(-0,6).0,8 = 0,96.
lst 2l.c(4-5' d) = !!er90" . 2cr . _].rezo;' 2(l-LE @5" + dj 2 2
16) 4sin o cos d(cos' o - sin'z o) = 2sin 20 cos 2d = sin 4ct.
1r 2sin40"cos 40" _ 2s.n40".cos40"
cos 11C[;
cos'2P - sin'2P + sin'20 = cos' 29;sin 40"icos 204;cos'z3c[ - sin': 3a + 2 sin'3cr = cos'z3Cr + sint 3q = 1;
cos'g35'- sin'35" _ (cos35'- sin35')(cos35" + sin35') = cosB5, sin35":
cos35" + sin35' cos35" + sin35'
OgZ. "in
cr = tr,6 - "o"'cr; "in cr =
d nyr II qBepri.
10) :sin2 cos20 =:l sln 4ct;1
2 42cin2dcos2d
11) (sin'o cos'? crXsint o cos'?rl)
1","f1 ,".] = r"."ro.
2sin 2.! cos 2.r=-=r<in2d.
coR 2.r .1
(cos'(p - a5")) sin'(B - a5")) = cos(28 - e0") = cos(e0'- 2B) = -sin 2B;
asin ! cos I Gcoscr) = 2 sin d.(- cos o) = sin 2d;
.-. 2sin l,scr.f, sin l,5a 2sin 1.5c. cos'1.5{r I sin'1.5stbl-:tl+-=-' "' cos I.Sa I cos' t.lc , .os 1.5cr cos' l,sa
= zsin 1,5<rcos r,5a = sin 3ct.
694. 1) sin 150" = sin(180' so') = sin aO" = j;L
zl co" 30. = #:3,
"o"1= J3,'62
4o8 i::l: AJITEEPA Mep3reKA. r. ra iH. A(aaeMi'{Hnr piBexr liiljiii}.i:.:::ili:,i
sin 2a = 2 sin c cos cr - 212.( 5\- t2o .r3 \ r3l 169
698. sin? o I cos qi sin'o , U' ;, cos 2s cos? o sin'z oi
i1l' 8 1 8 ?.coszcr = I -l3l I I I I
699.cos,cr= r -"i",4: c"s'c,=r l-r' I ri\ ;/ =1 16=16'
, 15 r l'1 15 I 14coszd cos- 0 .srn" c _
16 \ 4.r 16 16 16
7oo, Ls2ct - 2lgcr - 2 4- - I -8 ." l-Lg'd l-4' -15 15
,1 l4
I ll ,\2)
2";n9 "6=9 2 si198) ' '= '=ta-;
2"".'9 z"os9 z221+ sin 2ct
sin' cr + 2 sin cr cos cr + cos2 cre)
1+ sin 2q ,.1-.i. r" '
12,
13)
14)I
zot. tgn = -l; tgc'= j.
1\ 2 si.n' 2ai
I
702. Cnoprrcra€Mocfl abopMyraMn 1+ cos2o = 2cos" f,; 1- cosza = 2su."I
2) 2c'ltl 3) 2 sin'z 25';
4) cos'z d + 2 sin c{ co6 d + sin'z d = (cos d + sin o),.
lt:lt{tiiiliilr: MTEEPA Mep3re( A. r, ra iH. A(a,qeMirHrt piBexb tit 4o9
703. 1) 2\ 2 cos' 60. 3) 2 cos' 2o'l
o cr d r c/ 0l4l cos" Zsln cos r sln' = cos- - srn I4 2 2 4 ! 2 2J
3)
4\
6)
/.'a ""sa) rcos fl, cos'zdr'sincrcoso. sinzd - - =2i\ coso srn ct / cosd srnc
1+ tg 1 + tgs 2tlo ,-r-.{1 tsq,(1+tsa) 1 ts:d -"--'
- 4Lgotl lg':fl) - sina cos2d sin':d
/ I \" COS O cOS' C'
l"*61= 4 sin o . cos c[(cos2 {I sin' q) = 2 sin 2q cos 2q = sin 4d;
sin20sino l'sin2a sincl sin2(lsina sin 2d cos a - sin a cos 2C!
cos20coso Icos2o cosoJ .os2acoso cos20eosdsin2dsind cos2dcosCt
= srn zc[cos2dcosd sin(2c - (})
z.:"'!9,12
zo4. 1) Lg19s; - 1 coslox2.
t+"o"13.2'
1+ cos(8x + 20') .
2'
705,
2)
3)
4)
2)
3)
2'1 cos(4iu - 30').
2'
r'.ii::::iif.:il:i.l;:iiisi!:d.::i.fl
2 sin' 92
2sin'92
{sin'z a - cos'9 crXsin'? n + cos' a) sin? cr - cos'cr + cos' n 2sin' cr7)
a sin'geos: q= - - =2(os',rr.i"'9 2
2
2 sin' 92706. 1) 2sin'zo + cos':C[ - sin2 o = sin'o + cos2 cr = 1;
cos3d 2-in'?3a2l - --- 2 sin 3o.os 3c _ sin 6disin30 1
.. I {cos i:, sinr o) I cos'c + sin':c sin^ d + sin'o zsin':o "."'
"it " ' sin cr sin'q --
"itl" _
2 sin' 204\
-
= ts'2c1.2aos'2a
7O7. 1\ 1 cos(21o" 2.x) sin 2cI = 1 + sin 2C[ - sin 2cr = 1;
1 + cos' 4cl sin'2 4o cost 4cr + cost 4cr zcos" 4d sin2dcos2c[
', ,""(; il ;r)-"tl'!l ,",.11 ;r-.f 1,;t "''l; "l -."cos 6.I eos 2.l + sin 6.l sin 2cr cos(6cr 2([)
sin2c[ cos 2d2cos4cl 2.os4d.
711- 1)2 sin 2cr cos 2C[ sin 4c[
= 2ctg 4di2cos20 2coE2d 2cos2d sinacosd2l
-=
s)n Zoi.os c( srn d cos" a sin' 0 -t cos 2dsinq cosd sin scoss
3, t9a__- L€?c-,tga- lg'ct ,21g.! Lg2o:' (l+tgdxl-tga) l-€a
cos cr sincrcosfl rcose rsinocoso 2sinocoso 2coso 2sindcoso(1 sin0)(1 sin 0) I I sinT o
4sin d cos'?d=_=4srn(I;/cosa cos2c\ cosasin2d - sinacos205l I I srnzcr =\sind Ein2d, sindsin2d
I
_ sint2o o).fin2& _ sin0sin20 _ I.sir(rsin2(r sin(lsin2crcos'? c - sin^ c + I - cos' n 1 sin (I cos'o coso 16) =--=--ctgcr.' -siD2cl -2sinocoso zsinqcoso 2sino 2
zr2. t cos'( n, ln zoll -"'ln-ln*zoll "o""Ir-zc'I-"o" lr+zaI' \ \4 ,.1 \ t4 ') '4 ' \a t
""",1n zol ",,,]..^ -lt*r"rJ ="". l r - zo t - "r. , r - zo l =t4 , \2 ,4 ', 14 ' t4/- \
=.""1 1- arr I = "in acr,\2 )
;J::t{ilttii{i AITEEPA Mep3rrK A. r. ra iH. AKaaeMiqHrt piBeHb ::::i: 41 1
2sin4(tcos4c[ 2sin40cos4(x 2 sin 4c, cos 4c[
7O8, cos a =
709. sin d = -
"Ez,E
utJ,u,d2222
cl'5)
4
3'
sin2c[
*^ *4?,(;) #
24
sin30cos(r cos3d sin (I sin(3a-cr) _ sin 2cr
7
2sin d cosc ..71fJ.1'srn C[ cos c[ s1n g cos cr
2"i. d ... d
2) _=_ tsdi,,d ,d I -l ^dl 2eosd 2srn' 2l cos' sin" l2 2 2 2 \ 2 2)
41o lil: AI|EEPA Mep3rex A. r. ra iH. AKaaeMi,{Hnr piee+ru :i{lil{:iiii{!l*
TI
2) 1+ 2cos 2C[ + cos'z2o.- Ein'2.,=(1- siil'z2d) + 2cos 2s + coEz 2a== cos'z 2q + cos2 2a + 2cos 2c, = 2cos2 2c[ + 2cos 2ct = 2cos 2s.\1 + cos 20) =
= zcos 2a . 2cos' d = 4cos2 d cos 2cr;
2srn2 2d zcos'2d 2sin' 2q 2cos' 2(t"' I I I tg'2ct ctg'1 2ct
cos'2d sin' 20
2sin'92c[ cos'2q 2cos2 2d sin2 2d 2('os'20 sin? 2cr) = 2i1 sin'2c 1 cos" 2d
1 r sin2c-{cos'o sin ct) 2sin':a+2sins.osct 2sjno(sino-cosd)t'l*"in2ct*("*'o"in'o1=z"oJo-xino"*o2-"o"ot"ino*.o.ol
sin'? Cl - 4(1 sin'?ct) sin? 2cr - 4 cos'z ct 4sin2 o cos'? c - 4 cos? cr= z"in"z., g"into ' s"in'o-" o g"in',* =I Ssin'.[ cos'2cr + sin'za
-.- sin?5" ros?5' sin'/?5' cos/ 75" -2cost50. -cos150,cos?5' sin75' cos75'sin75" 2cos75"sin75' sin150"
= 2ts15o' = -2. ts(180' 30) = 2ts30" = 2J3.
1
716, cosd - sin o :, ni,aHeceMo o6rABi qa.rrHH 40 nBa4para::t
sin'za-2sindcosc ' "."' " = l,II -sinzo 1: sin2c=1-tr sin2o q
999
717. cosg-sino l, "o"'9-2"o"9"ind ' "in'a "1, l-"ina 1,
2 2 2 2 2 2 2 4 4'
"i,'o = r 1' "t.'o=9.44
218. tr 2sin r 2sinocosa _ 2"in{l*"o"q] = "ino,zcosa+l-1 2(coso rl)
2) cosl q 2sin'scos'?(t+ sinn d 4sin, crcos,o= (cost o sin, cr)! - sin, 2a == cos? 2cr - sine 2cr = cos 4cr;
714. !r1q * ig:lli =sin'? 15'+ cos' 15'
^. cos 2c cos 2dot ------ = t :cos cr 2 sin'z .r cos {x
=_=_=_=42 cos 15" sh 15' sin30" 0,5
cos 2d. sin 0cosq(1 2sin'zcr)
5)
, 4cos'!d(sin'0 1) _ 4cos'o'( coslcr) cos'c 1
2s1n'n 2 -Ssin'o(cos'z (} - 1) 8sin'ct (-sin'za)
/. \co.I : - 4d Icos2cr'" lr __ J'_- sin4ocos2d 2sin2dcos2dcos2d 4srnqcoscr
"' 2*"' "-%""'2,a acos'qco"'24 - 4cos'crcos'2c 4cos'?c
cos'4q cos' 4c cos' 4c" tg2a - crg2rr sin20 cos2a sinr 20 cos'?2q
cos 2s sin2c cos2qsin 2c
cos'4s 2cos2asjn2ct cos'4d sin40 2cos4ssin4d I -"--:-. '"'--:::r '- -:sinEo.1 2(cos'z 2d - sin'2d) 1 -2cos4ct -4 4
zr3. rr sin,lz+1" no I I - "in' I "
* { I - a") I "i"'[I +"1 - "i"'fI . a"l ='- ,- l',4 r, \ | '4 t \4
"j,,11 ln noll - "in,l tr +4al= cos,ll *aol "i,''f\*lol- 12 {a -') -'-'q ' \4 t t4
l= coslU + acJ = sinsa:
2) 1 - 2 cos 3s + cos'z 3cr - sin' 8ct = cos'? 3s + cost acr 2 cos 3cr =
= 2 cosz 3c[ - 2 cos 3(r = 2 cos 3s(cos 3C[ - 1) = 2 cos 3cl(1 cos 3c[) =
-2cosBq 2sin,4 = . +sin, Sgcosiro;22
2cos'2d 2cos'?2c cos^ ct sin? c:{l
-- cos0 sind 1 sindcos 0
"it- -
"." "2cos2dsin2a I22
2 sin d - 2sin acos 0 -- 2sin'9zsrnq(l cos d, , ,2u,"tr ot1-
"." t) =
,"-+ q ='ts t2
| ''n'2c \41 zsin4d ll-Le'2o)='"'no" l ' ^"-o"'ro'1+ tg' 2d. 1* "i": ?"
-. cos'2C[ - sin" 2a cos'z2o, sin'?2o 2sin4.r cos 40 .n.2 2a= zsrrr4d.
-^
^ = sin a.rcos'2c cos'2c cos'20 1
sin'2a+4sin{I][-sin'2d
sind 1
4 sinn C["' 4(1-sin'3d)-sin':q 4cos2c-4sin'ccos'a 4cos'a(l-4sin,d)-
4sini cr sini q.
zl cnq'z o nnc': ocos 2ct cos 20 coE20.
"i"11-2'lt2 )
6)
l
2 cosz 2Ct . sin cr cos dcos2c
719. 1)cos 2d
sin2 2a cosa o sin'?oI sm_ t[cos".r".".2d f".":d "i'1q I
\ sin- c cos" q/_ cos 2ct . 4 sin'2 c[ cos'9 s . (cos' s - sin' a)(cos' ct + sin' a) cos2ir 1 _ 1,
1 sin':scos2q 1 Acos2d - 4'
l:ifii:llitlil:il AnrEEPA Mep3rsK A. r. ra iH. AxaaeMi{Hri piBeBb i3l: 413
4)2 sin c, + 2 sin c[ coa a[
2 cosf 'r - dl "t",
f ' "l , """1' - "l "'.l." ")\4 / \4 I \4 ) l4 )(n \
""la - "J
cos20
4t2 it:: AITEEPA Mep3rrcKA. r. ra ifl. AKaaeMi'{H!,ri piBenb :i{L:{tii:i:;ii
a[*",] "'" ;)(*ui''"*']]sin o +sin o r"-'la! +.r" i 4"t" ;1"'"';-r)
sin'o 4.4sin ! a"r''!"""'! a[r .r"'!J a-"']1"r"'!-r)
.,;i (-s*il =.,"'i,",e,*",; [-*",]J *" I ' 2
5) 2Eir2a'"'"Il ")"""[! G.")]='"'[i-,"""(:-") =
"'[;-*) =
= '"'-- =::cte2o..2si.n2d 2 "
?20.1\
8 sin 3cr
721- 1\
2sin(30 d)
cos2d 1 ^
sin18'cos36'2cos18' 2sin36"cos36" sin72' cos18" 1
4.W - 4'18' 4cosf8" 4'2n 2n 4i - 4n 4fi 8,7
4 sin Z sln cos_ I I I _9_ I =_ e
=
--^ 3. I t4cosrr+.oszd-l 4(1 tcoso) {l "o"ro'
8"o"'o -2"in^c3+1 4cosd+cos2&-1 4(1 - cos ct) - (1 -
"o" 2") S"ir,,!_Z"tn,o
41t 4n 8nZsin sin_ 7 7_ 7_
,11 1t
1sin'3ccos" cr cos'? 3c sin': a
srn'.lcos- d(sin 3d cos c[ -" sq!]lg)c'" tryg! "l *g:qS!qg)
=
,T ,r 2fi 4nlisrn cos cos cos7777.n
7
4n 2n 4ft4sin
2)
7
4sint3s .arsinl3./ rat ,1q1@ !l1o 4sin2d 2sLn2scos2a=8cos2d;sin? 2(} sin'?2a sin 2ct
.cl "c^ cos r/ cosd 2 2
ct t ,u. aosin cos sln-2-222')d rq22
(n)sm n+- -sin|tt 7__1
.n7
.n7
1
22 1,$n u; "d "cL13..s' llsrn' .os"= 2 2 2=
,d - ,c .dasm- asrn- cos'222
"-.'sfr .r'sl2\ 2l
s.i"'s[ -.'sl= ' '=rt,s'. "d ,d '2
223, ,"o"'o, "=(sin'(r + cos'o)' sina c + 2sin: cr cosz cr + cost a - 1- 2sin'ncos'cr1"
= ... _ = --cts'ct....2 qin' d.os' a 2 "(sin'z u + cos: s) I 2sin'9 a cost cr
724- 1'(Va + al + ({/a b) z:la b '{a + b \:la+b-!a-b) .
2sir2.l2')
a)
qE-.tE.bite: ! lr b .
16- lf'+b '
(Va+a-Va-a) 3Ja b 1!o+b_ _,: a
lo t to+u \tla+b-.9!a+b)= lCn {'4.
2cos18'n2a4T>lsrn cos cos
-. q I I I1l
I.( nl zsrnl JI -l srn\ 9.r I ..
sinl sin ll99
2sin3dsin 24(x
.71 nsrn -99
3)2sin 3d cos 3c[ cos 6ct cos 12(I 2 sin6qcos6clcosl2c[ 2.sin12cl'cos 12ct
725.1\2x-a<O:2\2r+6>O;31 0x 2 <o;4\ r+2<O.
726, N 3srai6Ha kirLkicrr, DoAiii.N(.4) - IlinbKicrb EoAifi, sld Ba.AoBonbnsrorb t'MoBy A.N=40.1) -4 = {noMep KBaprnps, repEe qrc,'lo};N(1) = 20.
prat = I!l:! ",o,
= ?9 = !,N4022) B = lEoMep l(Bapfiipr .rrcro, IiparHe 5);
NrBr = 8, Pr-Br 8 l,405
3) C = iEoMep (Baprr,rpr Ma€ oaHaKoBi qv Oprli
NtCt = +: PrCr = -{ = a.40 lo
i:iifliiiii:ilif uresPA Mep3rcK A. r. ra iH. AKaaeMi.rHxt piBeHb i:;i: 415
I
2 2sir''s. 2.4 sin 3cx
2sin54"cos?2"cos54' sin108"cos72'2aos 54"
sin(180'- 72') cos 72" _2cos54'
2sill 72" cos72' sin144' sin(180" - 36'4cos54" 4cos54" 4cos(90'- 36'
ar q ;::* utrespa Mep3neK A. r. ra iH. AKa,qeMi,{Hnr pite"o liilllllliill
IE-.\E+b
2) cos 15" > 0, 15" nyr I qBepri.
728.27O' < zcr < 360', 2ct - lcvr IV'IBepri, cos 2 q > 0t..; ti ll 1
"o"zo,.,t-"'"'zo-J,-l Y| -J,-; i; ;,Izsin 0 > 0, C[ xyr II qBepri.
729. 18O' < cl< 27O', d rcvr III'rBepri, cos d < 0'- '... ;, 6\' l a 11
1l. vol L ocoso -!r Itr -!,a= {r- z.
.,I
^ sin; J, l, ,f2\ J, z Jzb .Lz) 2J2 2.-8
r*"."n 2 \ 2t 2 2_J2 12+J2)\2_Jz) 24
2tJ2 tt G ,- 2 -,'-''
732. o' < c, < 90'; o'< ;<45';
I ." - lJ - Ryr I qBepri.
",.[n'" - il ' o,
@" Z) *vrI.rBepri, "'(,r-|)'o'F - """(ro'- ", F -r."(ro" - "),, ! ,
vl-slng {l+sinqr.u[+ "l" o f r.,/i "l" r f
Jt v/i - "ir* f + "ir "
="1-"(;-91-r"*(;-91,n.,.o,
"o"ln-9J .,0, r<9<1. ","[l-tl .6.2 \4 2) 4 2 2 \4 2)
,[ J2.".1 l-e1- Jz "i"{
r- e]l= 21"i"r"."I 1 ql , -"^"*l ' q tl"\2 \4 2t 2 4 2') t 4 \4 2t 4 t4 2t)
= 2","[l - l - e] = 2"1"(l - e'l = 2"".e.\4 4 2J \4 2) 2
ii ili$illltil AITEEPA MepsrrK A. r. ra iH. A(aaeMiqHrir piBeHb {ll: 417
l4 yci rAB l0M,!. l
3r rs?b"= . sinlso. sinio. r.1, "61 r z 1.(r.,6)" I r.ost5o" t..os3n. 2 | 2t 2 2 J3 (2_J3l(2_J3)
=lj="*,0'4) cos 75" > 0, 75" * xyr I .rBepri.
"Ez , Jz tz lz\ , _ _Jz(z ' _lz\ = -rQ"."\ = .{, .r,=-;E-A=-6-1il6;til=- 4 '
'/t+"i"" t Ji-si"s 1--rffi-_--rffi=l+sincr-l+sin.r 2sin.r
Jz Jr sin'c r/2 cosa
"o"9.0.2 - Ryr II cBepri.
730. Lc'{T-ol=,u'1"-ll "11,, |;,",'lr=ryj- I
1+ cosl + za) J
2
sr Ls112.so.= _jA??q sin{r80o-4sot -sin45. .E f, VzlI cos225' I r cos(!80" . 45") 1- cos45' 2 '
- , r,' 8 ,tzn '
: 816 tcos'2c= I-l- 3J =n,rg'1 o -ol
,-, ,;=s's z
[ \3//
731. l)sin ls" 0. 15" - I{vr I qBepri.
416 lil MTEEPAMep3ntKA. r. ra iH. AKaaeMiql"r pi"err lliiillililllf::J
lr
1O. CyMa i pi3Hxr.lt cr,rHyciB (KocnHyciB)
733. 1) 2cos 35" cos 15';2) -2sin scr sin( cr) = 2sin 3c, sin (r;
B) 2"i,5P"""f-qll 2"i"5q-"8,2 \ 21 2 24) 2sin 1'cos i";
5n 5n ,'I5) 2cos cosl = Zcos cos"' ' "72'" \ 721 - '72" 72'- tx r(I) (r.-d) {r ts) tr -(r) ^6) 2sin --- cos , zsrn.rcosn:
_ {a 0t-(a+0, {o ll)-rd+0r ._2srnscos( F)= 2sinocos0:t t -zstn 2- cos
- 2
tz. -\l-lz. nl r:o-"J '[- ^le' :.i,f-- !l l !l"o" 6' 3' -22
zrr-n zo+L 2a-I +z< n
,"r,, -"--o--l 3"o,'* 6-1 3 z,in tr
"o"l z,y nl;
2 2 12 14)1",,1 ln-"r f^ "l "
\
er 2cos J rul ls-urcos,, " _!_"1 z"os1.oso= z.l.o"o-.o"o.2---232734. 1) 2sin(-10') sin 26" = 2sin 10" sin 26";
2) 2sin 20o .os 8':3) 2cos 4d cos(_Cr) = zcos 4d cos c[;
l) 2"n{s'0t-to-0r.osrs 0) r(d-p} 2sinp.qso:22l^.1*ln-*l lnrol 'T
\
5) 2"inl 3 * '-* "o"'3'" --Lol 2sinl"osa-2 f *"o= va,2-232
. (n , (n )
or z",n[r'"1-lr-i-1".1t "]'Lt-' r",,*.,"i=r.f"'"*== .,6 sir cr.
735. 11 2sin5acos3d
= "in5o = tnbo,2.os 5.rcos3.[ cos5cr
er 2sj n 44'sin 30" -tsJ0.= Jj' 2sin44'cos30' - 3
236. 1) 2cosSc'cos.} = ig!i!:
'2cosSqcos(-4cr) cos 4(x
2sin 2cr cos 302l
-
= cis3cr:2sin2.rsin3d
2sin6asinr 5al sin6a2l
-=
= tgoct:2sin50 cosOd cos6(l
2 cos 45" cos 13": _=cts4be=1.2sin 45'cos13"
lc737. lr sin20'+cos20"=sin20" Isin70"=2sin45'.osl-25') 2
; cos25'
= J: cos25';
zr "o"n -"o"8 = zsinn"inl-11 = , .
J' "'n
! - '8 "i' 1 ;a a 4 \ 8/ 2 a u
418 ItJ AITEEPA Mep3ncKa. r. ra iH. AxaaeMi.rHrfi piBess t:iil{ijti;i:i;:l
, "-1-o ono,o3) sind - cosd = sind - ",'l] - "J = z"r"--|--.--f
z"intr"."l c.-rl=2.@."..1 "-ll=./2"..1 .,. nr,
4\4)2\4,r\4,/4) sins sin(90" - d + 60:) = sind - sin(120'- cr) =
2snc-120'-dcoso I20" o = 2srn{d - 60"rcosG0" = 2 J"ir,o 66'1=222
= sin(cr - 60').
738. l, sin 2s" F sin 3s' - 2sin 30'cosr-s") = 2 ;cos5" = cos5":
2) cos 22" - cos 24'= -2sin(-1") sin 23'= zsin 1" sin 23";
3r srn.r, sinrgO' or 2 "in
o - 90' - o "os
o - 90" + d 2sin45"costa-4s"1221r-
= 2.=cos(cr 4S') = J2cos(o - 45o).
739. 11 2l | "o.ol zl "o"n-cosdt-2 2 "t,'
a ' o
"tr' 1---a =\2 ,] t 3 ) 2 2
t; - 1o 1"2t 2 Vr-"."a =zl "".
I * "". " I = a
"n" 6
"o.6\2 .r \ 6 ) 2 2
/n a) /,r crl=4.os -+-\,12 2) \12 2)
i) J2lJ'-sindJ =J2lsin;-si^ol=J2 2"i"[; ;1""1 ; ;]= z,E.:,(! sl"r,lr.,. sl.' \a 2) \8 2/
zm. rr:l 1-"i"al =rr .r"n "r.ol ."r"f ^ "1"."f. ".],\2 ,r \ 6 ) \.12 2) \t2 2)
,, rl,6 -"J zl """
tr - """
o I = r "i" I n -9l"i"l I+91'
'2 r 6 ' rI2 2' '12 2)
,, [email protected]=21 .""1 -""1 z zcosl trrol"o"t n ol
\ 2 / \ 4 ) \8 2/ \8 2lin al fn rr)
=4cosl +\R 2l la 2l
741' 1) (cos3d cos4d) - (cos5rl - cosorr) = 2sin9sin+ - 2si"*"i" i ='2222"l 7a ttol 0 9.r 11 9.r
= 2sin- sin sin 2\in 2sinl f.l.os -4sin .os.222
:a::ii{liiilrii:: A'lTEEPA Mep3rsKA. r. ra iH. AKaAeMieHri piBeHb illi
t4*
419
r2) sin 4q + sin 8(r + sin 12o = (sin 4(, + sin 12cr) + sin 8s =2sin 8o cos 4d + 2sin 4c[ cos 4{[ = 2cos 4d(sin 8c[ + sin 4ct) =2cos 4d . zsin 6s cos 2c[ = 4cos 2c[ cos 4s sin 60;
3) (cosd -cosp)(coscr+cosB) = 2sin9:!si"";0 2*" "; B-" o; B =
0 n B-d cr+B s+02sin ',____: cos L .2sin ' cos _______: = sin(o.p.)sin(p_d):
.. 2 sin 2cr cos o - 2 sin 6c[ cos e 2cosd(sin2{+sjn60) _'' 2cos 2d cos d - 2cos 60 cos s 2coso(cos2c + cos6c)
-. 2(sin2d + coszd) 2(sin2o . coe2d)Dt Gos;- cosSc,,)-(sino - sinss) =
2 ";n
2o "in
o-lllf,f a) cos 2c -2(sin 2C[ + cos 2d) _ 1
- 2sina(sin2s + cos2a) sincr'
z coJ l ', z *" 51 -" f r*": f""" : "o"
tj l r"o" 3j "* o' ,# i = 2coscr:-' cos cr - cos 2cr
u "." 3_
"o"'222
zr +"rn,9:-0"in, Lo '
n "i,',
9:! "o,
o '
0
222'2_asin.d-Pfsin,s'0n"o",*-0.l =l o B
2\2L)stnzlsin'd-2sindcoso rcos2s _ l+sin40 sin4a sin2d+1-1
' 2cos 3.r cos rI 2 cos 3q cos o2sin dcoE 3ct tp ar:2.os d cos 3.r
9)sin ncos 2.l - sin2d cos cr -2sin4a sin(-Bq) 2 sin(cr - 2ct).2 sin 40 sin 3cr
d-p d 0 q+p ct-p=z"o"L-0 z"in z - -2"".--.r- z 2"..d--q.2"i"9.""0=222222
fI 0 rl-R= 4sin cos rcos r.
2224) (sin o sin0)(sind - sin 0t = 2sin
a - 0 co" LLq. 2"inan0 "o"
o - I'2222= sin(o + B)sin(a B);
. (cosd- cos50) {cos2d-.os4d) 2cos30cos2cr 2cosgdcosa(sino"sin5a)-(sin2ct-sin4d) 2sin 30 cos20 - 2sin 3d cosd
2 cos 3d(cos2ct - cosdl2sin3ct(cos2d - cos o)
6) sin'z d + 2 sin o sin B + sin'? p + cos? c + 2 cos o cos B + cos' p =
= 1 + 1 + 2(co3 q cos B + sin C[ sin P) = 2 + 2 cos(d 0) = 2(1 + cos(d - PD =
= z.2.o"" " UF = q"o"" q
,F ;
-. sin 2d.os 4q 2cos:c I' ' ^i. 2o "-* 2 -.4**
= t'sin40cosd - cos4C,sind sind + cos30
2 sin4C[ cos2s _
2. sin3cx .2sin20 cos .x8)
... sin2s 2sin4d-sin6d {sjn2q tsin6Ct)-2sin4q' ' ' cos 2c - 2cos 4d + cos 6d (cos 2q cos 6c, - 2 cos 4a
_ 2sin 40 cos2d - 2sin40 _ 2sin 4d(co32d - 1) _ ls4fl.2 cos4q co6 2d - 2 cos 4d 2cos4o(cos2ct-1) _
742. 1 t 2sintts c@t 2si" r
;d "." ; = 2*"i ["'. t1" - "'" #J =
= z"o"f . zsnlcoso = l-"9"o"o. "i,'?;2) 2sin2dcos(r-2srnscoso 2cosplsin20 sinar zcosc 2sin]cos3f =
ft 3.r= 4 sin tcos0 costi
;rr:"i,9i-0"n"9 P | 2 "i,,
d - q
"o" g--q - zcosd-pf"i,,g-l-p '"ino
0t-r ;-
420 t::i: anrEEPA Mep3neK A. r. ra iH. aKaaeMi,{Hnr pieexu llilil*{l:Iri*i
sinAcrsinc[ 2 sin d cos c[ . sin 3(x sin o4 sin 2c! cos tt
= _ = 4cts.r.sin 2q sin c
74g. 1) It t cosqt . sin o = 2cos 9 - 2"ina "o"
I = 2"o"9[-"g..r" *l -' 2 2 2 2t 2 21
=z"o"9l *"9-"*l n -oll. z"o*9 z"o,;'; ;.".;-;.i =
- c fi ld nt J2 0 rc rl r.! r,4cos2cos4.os[
' 7t-e
' cos rcosl2 i)-2.r2cos2-"[t-;],
-. 1+.os4d - sin 4q zcos'2.r- 2sin2d.os2d 2cos2d(cos2cl'-sin2qll - cos40 sin4d 2sin' 2d - 2sin 20 cos2q 2sin2a(sin2d+cos20)
=_=cls2ct:sin 2d
s) "i"'(?-rd "") **(!-'"-r")= "*.(; - -)- *c(; *)=","(;.^)="',(:..) ",,(T--)== l"in I
tr rzqt. "ini9r
* zo I ll "i"l ft
, zol+.i,'1!I*:.'tl=r '8 r 18 t.)\ 18 I L8 ')
=,"*f-;)-"fl.,"l z"r"{i-z"l-"1-lJ "i^}"i"1}.a"J -
1 cos 4.r=-- cos4d = --.
:iilll:;:iti:i{i ATfEEPA MepsreK A. r. ra iH. AKaaeMiqHirr piBeHb !t! 421
sin 2C[ . cos 20 sin 4asin d I
i
I
=sin,f-1-2crl -"o",11 ,".] =\ 8 ,/ \8 )
-"*,ll-ll-r"ll=\2 \8 t)
= 4sin 30;
10) -2sin2d sin( o) . 2 sin 2d cos c[
zsinz 2a= 2sin 0 cos q = sin 2c;
744,l\ 1+ cos2d-zcosd = 2 cos'z c, - 2cosc[ = -2coscr(1- cosa) =
2cosa 2sin'9 = 4cosasin' 9:2 2'
2l {.1 - cosa) - sind = 2sin o - 2sin
o cos
a - z"ir' o l"ir' o
- "i"l I - S ll =2 2 2 2\ 2 t2 2))
=zsrng.zsrnr g I "..I=4
J2 .r"9"i.19- ar"l=2 \2 4) 4 2 2 \2 )
= z-8"i,9"i.[9 - +s"],' 2 \2 l
:r (-"il-:,1-*"t'; -t)["."tT *] -"rT.*t)-= -zsinf sin(-zcr) zcosf cos(-zcr) = sinlcr
z$. \ (u6ra,-r")'= t'-rf , s + 8x - r, = r, - 6x + st -2x, +-2x(r - 7\ = O; xr = 0 a6o r -'I = O; x,= 1.IepeBipria:
t. ' or ,,6.4 0 'd
o':, r 3, piBHicrh HenpaBx,rbHa.
2. r t, Js,8 7 -7' -7 -3i 4 - 4. prBsrcrb npagunbHa.Bidno6idb:7.
lr 3i x, 2.ITpppBipI{a:
r. ,,c = :; n[-3y - 1 3y,6 = itt. (':); ."6 = .,6, pinricrr npan,r"rrna.
z.t z: Jz z a Jzz: Ja v a. Btspa3r 3riBoro ra flparoro 6oKiBMarorb aMicry, 2 se € RopeseM piBE EEE.BiAno6i0b: -3.B) (.,e+6 .,6 ,r)'=(z 2x\'i @+6Xb-2')=4 8x+ 4x,;5r=2t, + BO -l2x=4- 8t + 4r2:' -612 + r + 26 =0 : (-1)i6x' - z - 26 = O; D = (-11' - 4. 6. (-26) = 1 + 624 = 625.
/n _ o<. -_1r25_26_13. __l 25_,' 2.6 12 6 2.6
fiepeBipr.a:
BiA'eMsoro sfia.reHHs, piBsicrE senpaBr,urEna,
2.x 21 ,[z-a uli.z nzl z z t-zttBiAnosiAb:2.
<,1 /a- r l'' =r"['*t J5,-2, r 31 2 3J(3,r r I r3ir - 2r:Jt' z
:,': :n6l r' :,rl ',r ,,6*' r* z: rx-lr'-.(J9,. -3r-2)':f +2r+1=9x'_3t- 2;8x'- 5r-3=0| D=( 5\' 4.8. ( 3)= 121;
5+ll 5-11 3JD TIi .X L X"2.4 ' 2A 8
422 '.:., AII|EEPA Mep3nrK A. r. ra iH. AKaAeMi'.rHr4i piBer" i:ii;ii:i:iiji::l:*
srn1a = sin4asrna = sin4a.22
14x - Ot
Brpas ia nparoro 6oky Ea6yBae
13
6 IIe € IcopeIIeM prB]rnr r.fi.
2.3-6;6=6.
IlepeBipna:
1.,r l; - rJ3 l-l=3,,i3 1+l;J3.1 1
.3B'pas He Ma€ sMicry, -; He e RopelreM piBEsHEs.
BiAnoqiAb: IF I;; t- r-
z+a. -s,[z -a,.,!z'.2 ap]' 2"1'' {2 s .s.E + s,E + eJ9 - 6:14 - 2\6 =v9 !4 \27 \2'.. z"Jz t a.lz - z{s t t""z - 2""6 = etE.
747. Hexaii ro.rarnoBa BlrAtiicrE BerocrtreAr-rcra craEoBnna r KMhoA. Ilicnn B6in6-IneHEs uBr.rARocri Ha 30 % Bo1la crasoBtlrL 130 %, rqo AopiBEIo€ 1,3n KM/roA.nicns sMeIImeEIIn rrB*r,ariocri Ea 20 % BoHa craEoBrrb 80 %, rlo AopiBHro€0,8 (1,3r) nM/roa. = 1,04r RMlroa. HoBa rrBraRicrE 6irblfle Bia noqarrcoBoi:da.1.O4x x = O,O4 r nM/roa., rqo craHoBnrB 4 % BiA ro.rarlroBoi flBnArlocri.BiAnogiAb: 4 Y..
I 1 . OopMynn neperBopeHHq Ao6yrKy rpnrououerirvxnx OyHkqifiy cyMy
1) ;(cos(15" 5") + cos(15" + 5')) - ;(cos10'+ cos20');
I2 ; hos(3d - 2c) - ros(3a r 2ci)) coso r cossar
z |tcos((cr
+ ts) (q P)) + cos((d + P)+ (o - 9))) = cos29 + cos2a;
t( ,n rr ',) 3,r 5'r 3n2 sinL --l-slnl -r- l-sin lsrn sitr
2( lr0 40.1 \10 40.,1 40 40 40 8
jt"t"tup - nol * "rnfup
+ ao))= ]lsinza + sinroal;
lrcosr48" ?4") cobr48'.?4"tr - 1cos26'-fcos122"=lcos26' lcosr8':22222z. jf"*fo - zol - *"(([ + 2o)) = cos cr cosSd'
2 ;(cos((60'+
d) (60'- d)) + cos((60'+ o) + (60'- cr)) =
6=6.
l
il
I
I
....1.:.:nL::.
l::::i::ll,ri*tf::::aa.!:{
iil:illiil:fq
iI
748.
2\
3)
4\
5)
6)
7\
8)
|"o"zo I "o"-tzo'=
lcos2o ' lcos60" = lcos2o ' l.22222
ron.r' l.rl"""l r nl,"o.l n,nll ""'l -
3n l - "."
1sI - "o"
33 * "o"
lq2 t '8 5'j '8 5') I 40' 40 40 40
z);cin(2s' 24') sin(28" + 24')) = lsin 4'+ l sin 52';
3) ; kos(5d - 3rr) cos(5o + 3a)) = j cos 2o - j """ ao,
::::;t:::gil{l!: AIrEEPA Mep3nqKA. f. ra iH. AkaAeMi.rHrn piBeHb t:i:! 423
I
750, 1) 2. ; (cos 20" + cos 60') - cos 20' = cos 2g' t ! - "o"
zo' = !;2) sino + zsinocosd = sl"a + z. jGint lx) + sin gc{) = sinc[ sinct + sinSq =
= sin 3c[;
3) 2 jtcoso + cosao) cos 3cr = cos cr + cos 3cr - cos 3d = cos d;
+l cosza + z f,rcoallr-+
30') (d - 3o')) - cos((q + 30") - (c[ - 3o'))) =
= cos2q + cos60o coszcr = "o"60'= ].
751.
2)
z sz. U f, coa za - f; co" ao * j "o"
ao - j "os
12cr = ] (cos 2a - cos 1 2o) =
]t-z) sin zo slnt-sdl = sin?c/ sin sdi
,, I [","11 r - ro I I o * zo I I - "i.
i I n * so I * I
* . zo I I | --'2f' ll4 ---t t4 rl ll4 t \4 ttlr[-"llr-*] ln-ooll "o.[ln*ol-l'l eolll =2[---l\a ''r'a r] L\4 ) t4 t)l
=11 "i,,so,"r.'l I+zol
"o" zo *
"o"ln - so ll =2f-----' \2 t t2 tt
I - - -l z "inno"osd = sin4s'osd..-
2 (sin ird - cos 7ct - cos /cl lsrnbdl
2
753. 1) ; (cossct + cos 9cr) - j (cos 3o + cos rrcrl =
= |{cosScr + "o"so cos 3cr + cos r ro) = }
(cos 9o cos11d) =
= ] t-z) "t,,{-o) "ln
roo = sincrsinlocr.
2) BnRo1raeMo roro)r(Ei reperBopellss niBoi i rpaBoi 'racrrs:
r. z"o"a I snlld+rs"l-ld rb"ll*"inll"-rs.l-lg rrlll=-2 2l--tt 4 ) t4 )t t'4 t 4 ,lr( a\ t d 0 d
= cos ;lsin30' sin ;J = tcos 2 rcostsin
2 t
424 ;.!* ArlfEEPAMep3rqK A. r. ra iH. AKaaeMiqHnfi piBeHb ititilliiil::::::
z. 1l"nlt+s", dl las' 33ll . "'"lr ar" * " J * I ar" 3"tll .-
2l Lr 4r | 4)t ,' '"
+'t)1 lf^^^dlt lotc crd= srnd+ 8rn 9U" | - sin(1 r-cos-= -cos Tsin cos..2 2 \ 2) 2 2 2 2 2 2 2
y peBynbrari oAepxyeMo piBEi Bnpa3r, B ,IlBii i rpaBii qacrrEax.
7sa. 1r sin d+1lco"lIn-ol I^, * tI * "..1
I r - "1 .l 3 -"1ll2l Lr3 ',13 'r r'3 "3 tl)
sin'o r I cosr 2.,, , 1"".4 = "i"'o * 1"."2o * 1l
"." *l -2 2 3 2 2\ 3l
t " I . 111 11r rlslr'(I l-cos'd--sr["c+ lcos" d lsin'.I1- -=---= :2 2 22 2 4 2 4 4
zt cos'o -cos'0-1rcos(cr-p)-td- p)t cost(o p) | (o -p))=
-- cos'o , cos'g -|rcos2p-cos2dr cos'o rcos'p j"." "-i"'"'U--]-" " - |"r"'o l*"'' j"i^'0 , I
"o"'o - 1"in'p =
= ]r"*' " + "i"' "t* ]1"o"'9
+ sin' py = 1 -r 1 = 1
3) cos'(45"+o)-cos'(S01-o)+;(cos(15' (75" 2q)) ' cos(15" + (?5. - 2d))) =
=coF'(45"+d) cos'(30" - d) +;cos(2cr - 60') - jcos(9o" 2o)=
- jtr --"rso'" ,"rl )t '.osr60' - 2cr) - | rr + cos(60" 2a)) Isjn2d=
= i-!"^^ -i -i"os(60" - 2cr) +]cos(60' -2cr) - 1sin2cr = -sir2q.
755. 1) ;G - cos2a) + ]0 - "osz0l + jtcosrta + P) - (d - p)) + cos(d + 0) + (e B))) =
I l"o"zo,l-1"."24*1-.20+rcos2n t:22 22 2 2
z; 16+coslso' 2s)) ;(1+cos(120"-
2c:D-lGiII(lb 2ct 78")+
+ sin(?s' - 2d + ?s')) = f,. f,"n2" -f,-!*s(eo" + s0" + 2d) -; sin( 2c)-
- | cost9o" - 60' - 2ct = l sin 2a - 1sint30' . 2ot r lsin 2c - 1cosr60'- 2at
= sin zc + ] cos(so' - (30' + 2a)) j cos(60" - 2o) =
= sin2o + ]cos(60' 2o) lcos(60'- 2cr) = sin2cr.
756. I ) r 6. /f, stn zo. stn no. sin ao" = a JI sin zo". I tcos+o. cos 120"r =
,"6flsinr-2o'r - sin60' l, I srnzo' ==aJ3lsin2o""osao. rsi.zo".r.] =, ,, J 2
= n"6l -1"i"20"-1.@.'"r"ro'l aJs. J3 s,\2 2 2 2 ) 4
liliiiiiiif:iil: ATTEEPA Mep3reK A, r. ra iH. AxaAeMi.rH].ri piaeHb tl, 425
" i["."(;..) -(; - "))J ["-[(;. ").[; - "))J = ;*"'* - ;"""; =
= !"o"zo - 1.24
f) Z. |{cosc -
cos3a) + cos3d = coso - cos3cr + cos 3cr = cosq;
1l r/., n1 ld fttl tIs 1tt to n,tlsind-2 ,fsinlt;-ul \; rzll'"i.ll , u)*t r' ,r)t)=
.tn\ n I$n a - s,nl
6.] - s,n CI = sln
6 = t .
iI
j
I
I
,i't,,J
:::::::ii!::::i::&
#fl:ii:::u
II
i
i
r
zsz. I.a"i,'91 "inllso..
ol-lao' "ll,"i"lloo' 1l l:o'-llll'- 2 - 2\- iL 2r L 2') t' 2t ' 2tt)
= z"i,'9("i,'ao" + sin(so'-,r)) = zsin! j + z"n]*"o =
,r 1r r.l I rcr ) a 0 3d 3(r=sin r2 sinl - o srnL rcr l=b'4 sln +sln
2 2t t2 ) t2 )) 2 2 2 z
2nn4nn6nn.ns sin r .os srn + cos
758. l, 7 7 7 7 7 7
, rrr 3n 3nr 5r f 5r)s,nl 7J-sin I "'"l\ z.l +s'n 7 ,s,nl
7 l+s,nn
2sinI7
-sin1+sinn2'
7
sin 10" sin 5' + sin 20" sin 5' + ... + sin 50'sin 5'2)
sin5"cos5" cos15" + cos15" cos25'+... + cos45' cos55"
lepeBipKa:
f. r=O;.',4*nO d =0-1; 1= -1, piBgicrL rretrpaB!'Irbga.
z.r :; n/i-l:-a- -3 li 2-2'BiAno6i0b:3.
3) (J(3r 4x2r sr] r2x- lr : 6x'z- 15x ax 20 4x' 4x t li2x'-rlx 21 OiD tzt 4-2-t-21)= 121 r168 289i
vr'l?: .r. ll-17 7' *"=t' 't' 3.
22 ' 2.2 2IlepeBip(a:
t. , = z; "|s.7
a. J2.7 a =2.7 +li 5.8 = 15; 1b = lb.^
-
, i,,. ,-- i,r/'i il , r/, l-il-'=,1 ;1,r. BMpa3HeMa,3Micrv.
Bidno6idb: 7.
,,Gr:**r*a 5+,r r-4t , =-; vtr r 3 s''; l{'-r^ =r*z;J5 r ,r J5 '.r
'ic+t2=x'+4r+4;a=4.nepeBipra: x q;Jq- 9=Vt.4:2 t 3i3 3.
J5+4Bidnosidb:4.
761, J]iHinEa SyrKrlis 3aAaHa oopMynolo y = k, + b.
CKnaAaeMo c[creMy piBEsflr, i3 ABoMa 3MiHnIIMni
l-to* + t' = z.J I top+a=-2., I 3b=O;5h=l.h O,2.L5k+6=1r '2 ll0k+2b=2i
OyHnrris 3aAaEa OopMynotu y = O,2t.
762. Hyni OyE(rrii sHa.reHH.E sMiEIIoi 1:, npv $]/"llv ssaqelrHs oyHllqii AopiBdlo€
t 2 r -6 .r'-6=0. ll" Jnll",./e t=o-'' - o: '' --0: I 1- '-"- = Jti: ,r^ =-Jti.3 .r 3x L3jr,0: x'0;12. fapMoHi,{Hi Kon}rEaHHs
763.1)A=2,6;h=3u 2)'t=+; P=!3
764,1\A=O,6t h=2n; 2) A=Ai k = 7.
765.1) A = 2t k= 2'
2) Ssin10'sin50"sin70' =
4 cos 80" cos 40" sin 40' ,sin20'
8 cos 80' cos 40' cos 20" sin 20'sin20'
2cos80"sin80" , sin 160" = I1?!l = r_
sin20' sin20" sin20'
cosS' cos55"2sin5"2sin5'
sin 25'2sin5' 2sin5'
2sin n cosf, +2sin tr "o"3n*2",n
n "o"Sn-...*2"i'
n ."o"r-7-n75-o.
---- 19 l9 l9 =
' 2sina19
2n 4n 2^ 6JI 4n 18r l8nsin rsin -sin srn 1... L sln srfl,-"'re " le -:ls - le ""ls' ""'ls =:::-!-q " le =I7r-i2zsrn zsrn19 19
760. 1)' - 3 = \,/;=; (r - sl' = (.vG L)' ; f - 6t = s = x - 1; f - 7' + to = 0;
Lr,x, = 16t
IlepeBipnai
1. x=Etb 3=u[-r; s=s.2. r=2i 2 3=nli-1 -1= 1, piBEicrb HerpaBrn6Ha,2 He € ]{opeEeM piBnsHEs.BiAnoqiAb:5.
21 ,!t 4x-x =r l: (JI F4,r-"r ) (jr ll':: l-4r .x'z x^ 2r-ri-2t:'z + 6r =q -2r(r 3l=01r=0a6o.n 3=0;.T=3
426 !it: AITEEPA Mep3neK A. r. ra iH. AKaaeMi.rHnr pieeau iiilillii:i:i:*
7e;7. a=J2' 1" Jhi u lsl 2-"i"e"-**"a'l; "o.,p
2; "ine L' lJ5 J5 / '/5 J5
y = 16 sin(S.,' - 9) &yrlttIris rapMogiqrlor t'=J5; h=s.
5xl2jr)5t2768. .1 - Jb - 12 = J16e 13: e I3l r;sin; - i;-";1, "os+ ,"*: sino ii:,=tr"*(;-*] ibyE(rris rapMoHi.rsoro Ko,'Barr's.,{ = ls; ft=1.
i:iialiilililii AnTEEPA Mep3reK A. r. ra iH. AKaaeMienr,li piBelrh i:.:.N 427
2sin25"sin( 30")
2sina19
766.1)A=3ik=ni
2) A= 1,5; h = 5.
2, A=:; h=7.
769. 1) a = !rE- + 2i D(d =tli +-); E(y) = (2; +-).fIoMiHs€Mo apr.yMeHr r i BnaqeHEs ibynKqii uicqaun: * = i[ L + 2.
Brpa3rMo y.rep$ r: l,Ej = n z:y l=(a-z)st!-(r 2)i + 1 trpu r € [2; +-).2)v=@+3)r 3; D(y) = R; E(v) = R.
' - (y + 3)5 3; (y + 3)5 =, + 3; y + 3 = {,6 + a; c - 1,8 + 3 - S,
3) v={l!. D@)=(--;0)u (0; +-}; r(y)-( -; 1) u (1; +6).
t = !!J; xg=y+r;ty-a=l,aG- tt=1: y=-A npr' .r e {-€: 1) u (1i +*).
q ! =1,1; 2t ,(y) = t2; +-); E(y) = to; +*).
"=1,6 z; v-2='a !=ra +2Dp"€[0; +-).
77o.' ,5-o ' vt--"; * tt .[ br (-r t1): jr 5:Jrs 1
t'z 23x + 121 - x + 5 =O. r'1- 23,. + 126 =OiD = 2A'- 4'1 126=529-5O4=25i
J o = s. r. =4ij =a.,^ =4-1 =s.'2',2Ilepeaip&a:
t.r=ta; ,ft I s- ,6 -1; I l-,/14 5
2. r=9: J9-5----:- =tr I = L PiBHicrh HetrpaBr"bEa.../9 - 5
BidnosiAb:14.
zl liGTa+s=i{r+3t. saruisa: {.r+3 =t.It -t t
t, 4t-5=oi ]:' _' .l r,=-t:r,=i.Itt t'z= -b
O6epBeEa BaMilla:
1.9t+3= 1; r+3= 1;r=-4;Z. i,6+r =S; a + B - 125i x = 122.II€peEipna:
t. x - t; a.lJt+e,s i[ay.o1 .lr's: t-r.z. x = t22i 4.{t22+3 t s . ",[-tzz" -e .nz, s; zt =zs.BiAnoeiAb: 4i 122,
771. Hexafi Bapricrb roBapy - r rpn. nicn.s ii niABzqeHrs Ea 30 % BoHa craHoBrrb130 %, a6o 1,3r rpE. Eicnr 3nn*cenHr Baprocri IIa 30 % BoHa craHosarr ?0 %,a6o 0,7 .(1,3r) = 0,91r ryn. Bapricrr, roBapy BMeHlnunacr Ha (r 0,91r) rpa., qocreHoBsrb 0,09 .pH., s6o Ha I %.
95. TPl,lTOHOMETP]|qHt PtBHgHH9 I HEPTBHOCTI
1. PiaHrHHr cosr=b
772. ll cosr l,* t"r""o"l .2Tn,nezi x=!f, r2nn,neZ:223EI;
"""'=#, '=="'**Y -2ftn.nF zi x -\-2nn.nez.
::i:::AnrEEPA Mep3rrK A. f. ra iH. Ar<aaer.,ri..Hui piaexs i::i:ii:-::i:i:.:itii:ii
+2nn,neZl
x = tln -:l+2nn, n ez;
r = t!! + 2nr, n eZ;
.. I4l cosxa 5: -r, Jsrccos;-+2nn,r? eZ:
ct cosr = di - = 1,04: piBHflHHs xopprriB He Ma.i
-. n (n \ -b) cosr=; u
<ft r = i arccos : r 2\n. n L t.
zzs. tl cos x = f ; t = x arccos * + zm, n e Z.; r = ):!.+ 2nn, n e Z;
2) cosr= -|;l', = * ***(-1). znn. n e z; x = t(n - ^,"",.f,) t z^n.,, z;( ntx=1Ln
tJ .21tn,ncZi x -;,2fln,nczl
.l; t t;\t, *"'=-)Lr'r r=ra."cosl -1?Jt znn.nezt x = -(n - l)_ zn,, n . z,3rrx=! +zfin.n€zi
nt *o'= f [f = t,r' piB's's' ,.ope',iB re Mae;
-- 4 at) cosx = .-i r=tarcaos:-2nn.neZ.
7z4. tt cosr,*= -f,; B" = t ^,..o,(-r) * 2nn,,.zl
tr = *(n - """"o"
1) * znn, n e z; sx = x(n - !) + znn, n e z;
ax=+T+2nn.nez: ' = x2{ t!,,.2:
zl *.*r=*; !' = .t""""o"@ * 2n n, n ez; !x=+I+2nn,nez;n 12anx=x-+-,nezib5
3) cos 6r = l;6r=2nn,n.2, '=!!,neZ;al co"?=o; U=!tzn,,o.z,
" =1*T, n.r,s) cossr = -|; s,=t*"."(-!)*zn,o.z;n, ='(" - *** l) . 2,,.,. z:, = t([ - ! u"*"!) * znn,,. z,
iiii::'...x:i:ifi::: ATrEEPA Mep3nrK A. f. ra iH- AraAeMi{Hrf piBeHb::.::::i
2t
42a 429
t, ", ,/:r ' Js x
"6fil .nsl -- +Z1tn.n -li\ 3,' 3 3 3 3 3
r=t3arccos@+6nn-neZ.3
775. 1) cos 2x = f,; 2r = t arccos! + 2nn, n e Z; 2x = !! + 2nn, n e Z;
)T_x=!6+^n'neLi
' -E ' f JA)2) cos" ,": f =-arccosl '- )t2nn.nczi- ( ,5\1= rfr a'c.o. "j] + znn n -z: i ln i J+znr' n.z:
L=xl1+zn,nez; x = +ff +:rlnn, n ez;
B) *"?= t; !=n+2nn,nez, '=!*!,".2.776. rl cos\n-t) t, ' ';-.,*-"* 2rn.n. zi ,-I==I ^.,.,.
,=ti [+2""."e2;zr "osln rl -J3, "o"1,
n' 6, *- n ==u.".o"6 2nn,nczi\A I 2 \ 4) 2 4 2
' - 1=.1 '2nn,n-zi' ' )-!-znn-n-z,46643f *"[;-rJ =-r x 2 n 2nn.ncz: t=n z 2nn.ncz:
x 6,1+12-12nn,n-7,
ar zcosl n rxl+r=o: zcoslar "l -', -"1a" "l I'----\8 ) \ 8' 2
n lr - s' n :l^-".""""f] ,z^n.n.tiJn--=larccosl 2)-21n.n.zt a \ 2)
,,-l='[^ I) ,,^.,-,, *-l=.? 2nn.n.z:
2an2nfiz^n,r -j - 8-zfin.ncz:
t -g,2q+ S.n-L.
zzz.u.""([ *) =', *"[*-3) =L; 4x !=2nn,nez;
qx !,2nn,ncz;,=!-,"!,^ - t;9362. 1(t Jz)z lz*"li-sj= r: cosl; ,J =-r :a. " ,,
" ,=..*""", '') 'r*^.^,t, l"=-ln u,""o"fi1-::tznn,n-z;2 \ 2) 2 \ 2l| *3h -t-2nn.n.zi t +3^ o-4nn,ncz.
43o iti: AITEEPA Mep3nsKA. r. ra iH. AKaaeMi.{Hrr piaer" :lilliilllii:l:liii
77a.rt cos( x-nl=1, r n + arccost ,znn.n.z't 6,i 2 6 2
n'un ox. ',' I, *^=!-!=^.366362[D'r,r =-t ,. -n n zn I3n., =I-I-n=-I-366"362
,tHa/oubruun Br{ cMHr.rx KoprHb - 6 .
t; I 1;\779. cosl f; 1=rar.cosl -1! *2nn,n.t;
4 2 4 \ 2)
{=.1 n-u.""o"V2 I znn,n-z:' .-3J! 'znn.n-zi x--:,ntBnn.n-1.4 \ 2) 4 4
fipr n = O rt= -31ta 12- 3n.BiAno'iAb: 3n-
' = x! +[+ 2"", " ez.
t; 1;7ao. eos3,r Y, ar . -"--"Y -2nn, n. /t22
n zftn+ .n./18 3
Ioru =o x. = -4, r =4,la ' ra
2\ ,:,b
,n2nllnn2nlsr.DDX n l.r I - -: Ja^ = +'r8318'r8318
4a'oMr rpoMi'$Ay Hane*ar6 '.opeEi
piBEEriH" -+' #,*'#.BiAno6iAb: .{orrptr.
781. "."1*+rl =-!, ,- " . -..""."l. t) 2o,.,-2,\ 12l 2 12 \2)l n2nr. '_=- ,( - arccos - t a znn. n lt xt ! 2nn.nc7:12 \ 2) t2 3
2n n 2nn+ he/31232nngn2nfr7nllDr n = ll i 3 12 t2' '"' 3 12 t22n n 15n 5JI 2n ft 31trltnu r I I
-trr=-- t2n
312 124'3t2 t22n n 39,r 13r 2n n 55nLIoJ1n:2 x t4fi
-t x-=_- -4n312 124',312 t2
n7nn5nn3larl3tr_\-?4n: --<. <4'I: - _ _4n: \ <4'I.6126461264
ab cLb
al
iilriiitlii::ji A'TEEPA Mep3neK A. r. ra iH. AKaAeMi.rnr4i piaexu il.l,| a3r
^n2nn;tx=1: + .ne/,-63
I
il
I
I
r"..t, {1lo'..... ^.3', r:x+2=o;D=24 4.3.z=rt JD=1; ,,=fi=r,
l3r'-5x+2>oi3) sin 5r = 1;5r=!+2nn,neZ; "=L+2-!!,r.7,+y
"t"1 a'y=f,, sinsr=-J; r"=r tr"**r( ?),n,,.2;
{-11'1 2ir
-arcstn o
L 7r[r'cz.
,"r. r, "rn"* = S, 2.r ( 1," arcsin !, nn. n, z. 2x = t-tti
ft nn. n c z.
, = r-.' x' "1' , .2,
2t sin{=01 \ nn,ntz: x Tnn.nczi
s) "t-?=,+j ? = c'r"-*'[-.4) + nn. n ez)
?! = glyu L a no,,1az; x=(,11*14a!!!,n.y.
tae. ri "t"(,-fi) =!, . [= ctr ^,csin@ +nn,n ez;
t = (-11" ! a! 1 ,n, n.7t
2r sinll-xl' 6, .i.l ,-nl JaL8 r 2'---!'' 8/ 2'1=1-1fi!1!1no.o67..38
s) "i'(;+r= 1, i*t= -X*znn,,ez; != -!-1a2nn,,.t,',= -! a+en ,,ez; .-
, ",(#-,, =#, ",(*-#) = -9,a*-lr, = r
"""'".1"(-.f) , \n.nczi sx=(-1\"^f,- lr, r,.^cz:
x=t. tf 'a*-I +ftn . n =7,.12363
zos. ry "i"[s'- ') =t; ex-{;=-!a2n ,o.z; s'=-!*#+21tn,n€z;
8x= -9! +znn, n ez; ,= i"ni,".z:,r "'(; -.) = -1, f -+ = crr. **i,(- !) * *,,,. z;
t - n - ctr" i * "", ". z; ! = t-tt,,' f, * a, + nn, n e zi
r = (-r\"'t ! + 20 + lnn, n e z.
:!lt!tjittt;i1: AITEEPA MepsreK A. r. ra iH, AKaaeMieHnt piBeHb :-t{ 43g
r^=9--L=lt &r t)l r-:l>0.' 2.3 3 \ 3/
Po3B'sryFMo sepiBEicrE veroaoM iErepBa"riB:Tr\
Bianosidb: D(y) =lu i lu (tr + -t.L n)
2t 1" ^ "'13-xl(3 | xl>oixz-21[-r+2+0;
(3 - r)(3 + r) = 0; ,1 = 3; t, = -3.BiAnoeiAb: D(s) = | 3; 2) u (2i 31.
lr'z+5:-1+>0.3\ I -rz+5x- 14=0:lx' 64 * o:
lx, x,= 14:
----T\ /z:\/.-=--l<:<RK403 l'
2
(x+7\{, 2\>Oik- 8)(af 8)*0; t+8tt+ 8-BiAnosiAb: D(y, = (--; -8) u ( 8; 7l !, [2; 8) !.](8; +-).
n, {a -2f," o' zJi < r; 4.r< l6i x<4i } > o.L-r > o:
BiAnosiqb: D(gt = loi 41.
2. P|BHTHHq sinx- b
784. 1) sinr ft; "=t-ll'a,csin fi tnn.n.z, x 't-r't^f,'nn.ncz:
2) sin.r=-+: ' (-rr"*"h[ J;).^,.,.r, t. t.|'][-nn,nez:
sr "in* - l, r =(-1t'arcsinl +nn, n eZ;
4t sinr = J2 {Jz - t.n:r.n ' rlr piBE'EEr Kopegis I'e Ma€.
zas. r) sinr=|; r=( 1)"arcsin|+nn,nez; t=(-t\"1+nn,nez;E(t-.r
zr "in*=-121,
.=r rr,*"r'l-f.J 'rn,ncz: x=( lt^")-nn.nezt
sl si",=f ; x=( rY ansir !! + rv.,nez;
4) sin r = 1,5; piBEaIIIIs riopeHiB Ee Ma€.
z8o. r) snf = ]' f =co"**t( L)*nn.o.z' l= t-r\"'l+,o, n.z;r. = (-1\6n + 6nn, n.Z;
,) "in
4J f: 4rr = ,-u' "'"",'
Jt +nn.nezt a{ -etri*n^.,,2t
'=61y!+4!,,e2;432 t :::An|EEPA Mep3reKa. r. ra iH. AKaaeMiqgr4fi piaegb iti:jtlttlit::iii
n I -Al-r-t={-1rarcsinl - )+ fin. n ezi
'/ J:)7e0. sin{r+ll "i, '.i=,-rf arcsin( ::J ,nn.nc?:
t = 1 ty" ! -! ', nn, n.7.
rp n=o jr=( ,,: x=-:-x=-3,npr n= r -!=(-1)!1 it"= #r"=#p16,oui6o. !!!.
12
rn'. "''("-,!) = ,, * ir=-X.r",.^.2, z,=-I- ls*z^^.,<2,*=_4!+znn,nez,,
" = _ff *2{, n.z,
ttDnr=o.r -13n, rro,,=t '=.13n,2" lll'9090390
3i6noui6o -1J1.90
-lrzsz. rt Ja.in'*"o"' z1,z: Jr!.",n'* r -"' 1,
",nr'.o"I rcos' s'n1=t: "t"lr, "l ,, x.!=\.nn.ncz:6 6 ' 6' 6 2
x =I f,+nn, nez: x =! + nn,n ez:
z) .Esinr .Ecos.,c=11:2; ' , * *", *=;t
"i,,,"."1 *","r"1=i' "',(., I)=i,,-i=,1).arcsin!+nn,nez;x = ClY ! +! + nn, n <Zi
'.' rtrvE3) ssin'-+ J3cos; 3i:2J3: 'r"-stn, r icos, .i;n x n Je ,, ^, .Itsrn2cos6 rcosrs'nd=; I srn|\2,6J= -2 I
./r' - '; Fi ,rcs1n re .' n,?. 2 6 2, i= r t [- i- "^. ^ ,2,
x = (-1\'2J! ,! + 2nn, n eZ.
ze3. r) sinr-16cos"-r ,r, j"r,-f *",=|, "i^,*"1--","*3 =;,
"'nf" ;l l, , i=r-r, "-"r"] nn.atzi x=t-tt'n,lrnn.ncz.
2) sin-y+cosr ='El,'Et | "i", -L"o"r I: sj n r cos I , cos x sn lr l,' Jz- J:---- ' -' "---4 ""-" 4 Jt'
434 ii:: AIfEEPA Mep3Iex A. f. ra iH. AKaaeMiqH]an piBeHb :::::::;i::::::::ii::i::
"*[,. ;.) = *,," i = c,r.***f +,h. n ezi
'- ( D" X -X* "", ". z.
^o. "'"['-;) =], ,-I=( u.a,."ini+nn.,ez;
npsn=ox=1+I=1.6 3 2'
,+f,=t tt,\*tn, nez:
t=gty!+!+nn,nez;
nplr n = Lr.{ t} I r:. r='ll;
npr n = 2 r= r-lt'?I+1*Zr= I-,6 3,_,._2
_ Hp BxoAurb y npoMirnoki
npun -t ! =r-rr | -". lr= tu
"p,n= 2: "=(-r).;-; ,"=_+ _ ,,e BxoaHrL y npoMr*ox.
-^ 5\ ft 7^626
7es. sin3x =f , ",
, rf u.."in:2 , tin,n-zi ax= t-tf \,nn.nez:
,=1ry$*!!,".2;nprr=0.r={ 1f 1=a,
12 12
npun t.r I rr'. 'I.+t=31 =n.12 3 t2 4'np n=-l;=1-11 "1-4= -8.' 12 ?i 12-
.pvn= 2 r r-1r..!-':=-!1,,=-3,x, { l)J " -,,-l!1,t2 3 t2 - t2 ' 12,n=- 4.x=t tl' n -1n-- I5T.
t2 3 t2',n 2n gn
ti_.t = tZ He BxonHrr, y npoMi)KoH.
Biano6i0b: rtic\h.
zgo. rr 9=@=2.,E.J33zr rq_ 15.V5 _15if _.,r.' v2b \y'5" i6 5 -'v".. Bo ao Jo goV6 -.-"' m-F G= i =ovor
ot -- 12- l2('4? J5) Lz(Jrz - v;) r,Jti ,5 ("rrz r"6lt,rz-us) - rz-s =vi/-v5:
ri:ri::::iiii::i: A,lfE6pA Mep3nrx A. f. ra iH. AKaAeMieHri piBexb ;i:::
I
435
r-. 16 16((f)' {?.r)'' itt - = (vz,.J@f Vr;il
=
= zltg zlF zj
", 2t zr (.,,6 * 'E)-'
{/r5 - Vio - {a - (Vs, -,6 .8 , r/2,)(Vr , Vz)
a2
I
ro(Vns -,F * 1) - ro(Jas - {,4 * 1)
(J7)' * r' 8
- u({:r*u{t) =
"a1 u n r;,12.
lx.gxmors0.'197- lt u=l" [4x x', *rqo r > 0.y = t, rpaoi& rp€Ma, sria trpoxoarIrb qepe3
roqrcn (0; 0); ( 2j 2);y = -tu + 4r, ryaoil( trapa6ona s BepmrEom
,,",,, -=_L. ^=___L=2,' 2a 2(1)n--22+4.2=4;(2,4r.To.rlir r€pertrEy s Biccro Ot:-t2 + 4z - ot -r(x - 4) = oi tt = oi t, = 4.Toqrcl,l repertrEy - (0; 0); (4; 0).
Ia| ,axutox<-2,t.r
2) y=l ir,rlcqo-2s-rs0.lV.x.sxnox'0.
1. IIprt< 2 y=-4, rpa6ix - rinepoo.na.
2. llpt -2 3 z 3 O y = -t, rpa(bilr - rpdMa,'afta poxoarrrb qepe3 ro.rKr (-2; 2); (0; 0).
3. flp{ r > 0 y = {,6, rpa4irc uo6y,cyeMo Ba aotroMororo ra6nn4i.
3. PiBHTHHq tgx= b i clgx= b
798. 1) tg.r =."6; r=arctg^'E+nn,neZ; 26=!+rn,nez;
zr te' vj, ' -*cl.-vJ]--, ncZ: x=-!+nn.n=Z;
4) tex = 5; t=aJ€tg'+Tn,nezlE
r1 "tgr- vJ, tg=v6; r=*"tg1,6-nn.neZ: x-l .nn,nez,
6) ctgr = -1; lg r = -li n = srclg( l) + nn, n e Zt " = -! + n", " e Z:
h t J:) - rzt ctg.r=-u6: U*=-f, *=arcwl i, I nn,nFzi r - -'d-",,,.2,
436 ltl AIrEEPA Mep3reKA. r. ra iH. AxaseMiqrrlrfi piaert l{;{ilii::ritltl
q c4x =."F; t",=*, ,=**"*+nn,nez,9) ctg:c = 0; t=!+nn,neZ.
799, 1) tgr=1; x=arctg]'+nn,neZ: ,=!+nn,neZl
zt rc, =f: *=-"te@*n,,,. z: x=n t nn,ncZ:
s) ter--a6; t = "utg( h\+"","e2; t=-!+nn,neZ;4\ tgx-2:. x=aralg2
^n,nczi5) ctgr=u[; tg Jj-,
"=***f -ftn.nezi ,=[*^^,n.2,
u, **r= f, Wr= nE; " = u."te (-nE) + n,,, o ez; r=-L+nn,nez;7, tex = O; x=nn,nEZ.
8OO. l) tg2r= l: 2I=arcrgl-nn.n eZ: 2x \-nn.neZ; ,neZ;
') te; =;; !=*.tet,rn,n.z; x =sarcts*+vnn,nez:
3) t"[ a4)='6, t"f=-"E, !=a,.tg(-Ji)+nn,,ez;7x tt - 41 4fin-:=- - tTn,ncL: ,.. :_= ,nez;432774l cLg-=Oi 2 2-nn.ncZi x=fi-2ftn.neZl
16nnx = - arcig +;-,neZi.
I;B6) c!s(-gr) =
uj, "tss"=-uj, tgsx=-/3; Sx=a."ug(-Jr) | nn. n czi
sr = -! + nn, n ez;, = -ff *!,,.2.
8O1,11 tg9a = 6; ?r=nn,neZ; r=4!.neZ;t; .- I t;,
2t cLs' '6: tgl=-w. ;=*",c[-v3{] .-. ne z: }=-!+nn,na7,
x=-L+2nn,neZ;
B) ctc;r=b; tu|, =It X'=*"el+nn,nez; '-|u"tsL*,n,o.7.- G .Js n n802. 1) rcf3.r-;;J f,*-i! arctsrs+nn,rez: ax=')t',. -nn.ncz:
^ 11 _ llltn|Jx= 4-nn.neZ: x= t2' Br.nczi
i:i:lifjii:illit: AITE6PA Mep3rrKA. r. ra iH. Axa,qeMi.rHri piBeHb :.{i 437
8 -4v 0,5 1 2
1 16
u 1
/ tr\8o3. 1' telr+iJ ti ! + ;- arctsl + nn' n ' zi
-7t2x = - 6 t nn, n - Li t = -- + :2. n. 7i
npu n=o x=-12i-fin7fi
'12212
"p",.-2,=--o.-^ 1::
Fe Bxoa,{rb y trpoM,){oKi'12 12,rrJI5JInDlIr=l r= +-=-.'12212
npun 2x. .'^'n=9 - He Bxoa'rr6 y rpoMixoK;'12 12
12\r2)12t24Bidnosidb: n
.4
Bo7. E ! = Ji; | = a,.ts.ls + nn, n e z: ! = I + nn, n e z: x = 2! + znn, n e z:
2nnpnr, 0I a:2n 4finpl...n=-t x 3 z\ 3:2T lotrnp, n=-2 x- 3 4tr
3 - HF sxoAxrby npoMirltor:
,'o"n=1,=?!*2n=9!,- 2n 14finpqn=Z x=-+4n- .r He Bxorurr, y npoMilxok:
2n ( 4n\ aft 6ft+ l+ = =2n.3 ! 3/ 3 3BiAnoeiAb: 2it.
8o8. {x + d)(Lg.r - J3) or r o . 0: .r = -a a6o ugr J: or
,r arcte.,6-nn.n cz. x ntnn,nel.-3
PiBHsHHs ig-r J: 0 "" npori*,"r /- n
[u: ] Ma€ oal'n xoprnb - -.
Ulo6 aa"e piennnsa Ma,1o onrH xopiHb. norpi6eo. ilroO -a=Ir a IBidnolidb: Eopt o=-n,o. ft o'g.
809. (r a)(te r + 1) = 0;
r o=0:r=aa6otgx'l O; 1g.r '1; t=-!-nn.n.2.
PiBET,,E' ts ' + 1 = o "" "n"*,**" [- ], o)
piBH.EEHs Mano oAr-rE nopilr6, trorpi6Ho, qo6
Bionoliab: rrp*t "= !;"< !;">0.
2) te(3 - 2'\ = 2i tg(zt 3\=-2r2x 3 = srcLe e2\ + nn' n e z:2r = arctg (-2) + 3 + nn, .Z;: = I arcte(-2) + 1, 5 + !,,. z; * = - f;^r"tc
2 + !'5 + T, n e z.
i) Jscre(s,-{J re -o: nels,'iJ Jr: uslrx'li= f'*.
3 = *""(-f) - n,,, e z; rx = -f, -i + nn' n e z; 5x = -L + nn, n e z;
+-.naL..10 5
, "'-[: -;) = +, *(; :) = -,6, !-i= **s(-15\ *,,.,.2;L--!*X*nn,n.z; ,=-n+!*znn,oez; r= f,+ snn, n ez.
fir!x= --+\n,nELa
2) ctea-3x\=2; is(4-3r)=;; E@' .4:) = -;t sx-a= arctg!+nn,ne
s, = - a,.teI+ E+ nn, ".2. ' = -+*&e;*tt!, ".2,3) 3te(3' + 1) -.,6 = o; tg(arc+r1=f; 3"+t=atc4:$+nn,nez;
Bx - ! - t + nn, n ez.' = ft- !.!, ". z.
804. te 4.,. = li 4, = arctg 1 + nn, n e Z,
."rr=O r=3,' 16nnEt
f,nu n=l x= +-= i'16416
nnvn=2 r=-+ = :'1621ti
'I 3,r 13nnnrn=:J x= + =-_' 16 4 t6
+-,neLi16 4
n l7nnp{n 4x--: '^ ;;t - He Bxor!,rb y opovi)xoH.
Bidro6idb. .rorxpx HopeHi.
.i;aos. ctsf= uJ, ,*; --Jt, i--."*( Jr)--., ELi t= n'ynn-n-Li
npvn=0r fi- He BxoA rb y npoMi)*ox:npttn=1t= n+3n=2fi:Rpvn-2x= tr I6'I=5,I He BxoA[rB y EpoMi]HoR.
BiAnosiAb: 0qrd]l.
806. crg2:r=-./!; tsz'=-f ; ,"=^,.@( @)*no,n.z,
'lt ^4t=-+nn-neLi'4
Ma€ oar-{E Rop1ts6 --. t[ob,4axe4
n4
438 i::J AIIEEPA MepsnqK A. r. ra iH. AKaaeMiq{lir piBeHb i:i:::r:li:it{lillj ATTEEPA Mep3rrK a. r. ra iH. AKaaeMi.{HrF piBeHh t:i:l 439
'l
A1O. trIo6 rpaoi& OyHriaii 6l'8 ctrMerpr.rqElri siaHocEo oci &oopaltlrar' OvlrHqin no
BI{HIIA 6YTII trAPHOIO.
q-x' " 4-l x)' 4-x'I I /(r) cost: rl ir' = cos(2 ( .rJJ cos2.r'OyE&qis trapsa, ryaabirc cr.IMerplrqHri BiAHocBo oci Oy.
sin r sin(-.r) sin.t2J l{})-, i ll-x)=:=' l-cos.r I lcG(-.r) l-cos.r<DyrIKrIrs Eeraptra, ryaoirc Ee cvMerpn'rE ii Bianocso oci Oy.
st t@) = dr- + d2 + t; tt-'> = E-t-"l + lz + t i = \Ei + tE - ".(DyHFirIis rapEa, rpaoiK caMerplrqHr'ri BiAEocEo oci Oy.4) f(x) = x' \E x' f( x) = (-t)' ts(-x\ = -x' te r.(Dys&qis EenapEa, rpaoil{ He csMerpt{qHsfi BiAHocEo oqi Oy.
811.1\f(t)=f + 3i t e IOt +4i t = g' + 4; a" = * 4' u=$ a trprre [4; +-);
2\flxl- 'z-1;t€(-;Olit=A' 1;U'=x+1t A= Jx+1, t€[ 1;+-);s\ f(r')={V; re( -;ol; a="\Ft u= vF, re l0; +-).
4. Oyxxr{ii y = arccos x; y= arcsin x' y = arctg x; y = arcctg x
-, . (n ^ trl 3r nt " Ji/l srllt -+2, -sm_=sintn_ -cih_=-\4 4) 4 \ 4/ 4 2
81s. 1) tg 0 = 0;
2r "i.1=@,32/ _\3r cosl 2.1 l= .".1 = o,
I 4,] 2
ar "tn[z
t'l = cts4 = o:-\ 4,r -25) ts(2'i) = b;
6r cosl n-11+lll="".r= r,\ 3 3,/
812. 1) Hi;
4) rarc;
?) si;
lO) 9a+1=r. rar:4413) arcts(-1) = -:, si;
813. 1) I{e icEye, si;4) raK;
7) arccosO = I. si:2
10) ralc;
13) ri;
tr !!."-! ="!L . "i t2l43 \2
14) rax;
2, Iz$i5) ran;
8) arccos 1 = 0' Hii
11) raIi;1t n 5r,ra);+6=-.ra1c;
3) raK;
"/n\ti) - l -- l= --. Ilr:'3\3,r I9) ra&;
arccts0=I.si:'2r .3r _.13n -r3 4 t2'""
3) ra(;6) ran;
9) se icEye, si;
12) arctg Q = 0, IIi;
15) rax.
2\ ait
5) Ei;
8) raft;
rr+-+ fi- |3 t 6)
4 \ 3)
34'
n-+2
n4.
15)
6636n+3n-3fi+ 4n-r 14n 7n
12 12A
814. 1) cic; = L
,) -"[,;J =ot
" *"(;9=+'
619. 11 -I..s14-,1=I'6 46 4
zt zln-!1. s.1*n.l-I)=2.sft sft 4\ 10,I-lon-l2n-'-1" 6J -3'\.2t-'e e-T= a-=-2"A2O. l\ I < t - 2 < 1; 1 < r < 3; D(y) = [1i 3l;
2t -1<,'- 10<1; 9<',<11; B<:l<."{J; lfvl = l-Jii; - s] u [s; "/i1];rr t'f sr, -2s1<2t r< -j'u.'= |,og1=y*r-Lp1f,, a,4\ -1< Ji <t; 0 < r < 1; ,(y) = [0; 1];5t D(y) = Ri6) x / 5: D(y) = (--: -5) u ( 5i -)i7lx 2>0ix>-2:D(gl L2t *)l
[-'' .1.,S) I--x-" ir> l;D(?)=[1; +-).
lr-1>o;A21, Ir -1 < x + 2 < lj -g < r < -1; D(y) = t 3; -11;
z) rs:<L -:= 1. :, Dtvt=(-,-:),'l:.'-J,3x2x2r3) -1s J.! < 1; 0 <, < 1; D(y) = t0; 1l;4, x 3>0; t>3: D(y) = [3; +-);
::i*iir::itttil: A'TEEPA Mep3ncKA. r. ra ifl. AKaAeMiqHr,rfi piBeHb li.l 44.1
a) cre(2 (n-a"ccteJtf)="*lt ("-f lJ ="1"101 =".,un ""[r^ ])=.11 Jt
= _ crge = _;:
rr "i.ls.I-1ll = "r"r nr=-r,' | \ 3/./I / nl n) I r\' !56) telz L--l I
6.J - tcl-6I - t:
440 l$: AITEEPA Mep3nrKa. r. ra iE. AKaaeMi'{Hr'rr pieens llillilif.il{!:l
zr "o"lr.n,l" ".""."111 -"o"1,,,, n' I 7t 'r I
\ r \ 2,) , r-51=coslz'I s.] =*"5=z'
eto. rl "o"],u.""o"
1l. lr 2ta: 3t tr: 4t I\ 3,/ 3 4 2
817. 1)
818. 1)
zr!2
4* 4:: 4) n.
3n+6rt+2rt+6fi-n 16?! 8'r
fl
D(v\ = R;x+7+O;t+ 7;D(V)=(-; -7)u( 7i +-)i
I' x-1-r. lo-1=r.,,r, to,,r.lx>0i l.r>o:
ezz. r) -]<u."si,'' <!; o < ",.'i"t +! <'I; v.,^ = 0; v^,., = 7.;
2) 0. arccosr. n:2sarccos.r+ 2<n t 2iy... 2i 9,,," fi- 2i
g) -1<u.""i,'r<;; n<2 arcsinrsn; "-I<z**r' 3=n-3t4nn2fi4n2n--i.zu'."int t's,s", -T: ,"^ = a,
1114t 0 arccos x'n,
ur."o"r t n, Y- = n.
823. 1)0sarccosJ.<rx; n < erccos r. + t! < 2n; g, ',=
n; y,,^,= 2n;
z\ -! < u'""in'<X; -L z < u'csin" <! z; s-,, = |-zt o-,"=X, ",
3) 0 < arccos, < 7t; 0 < 3 arccos ,. < 3fi;rr fi 19r
; : 3 arccos ,r r 6
i 3 'r 6i 9"." 6. C",. 6
a24.1) J;>o; o<arccos,4<|; z<arccosG+z<]+ 2; v,",= 2:
- .E; ,E;zt ')',*'t,*: ir 0t Jarcsirx:ll' : u.,, =0i v,' ="r"
82s. 1) \t>0; o<u.""i,''4<l; 4 < a.csin G + 4 < j + 4; v",'= 4:
21 0 - arccos,r ' o, O sl6.cco"r: Jn.
sr6. r) *"[***;)= pe.1% E''1J15
zr tel**nJ) =
",,. ', "*(***]) = F;G;r = lIH( t2\2) cts arccos- ="t t3)
A2a. 1) 16 3r3 - 10 = 0. SaMiHa: ts = t. t2 - 3t 20 = 0; t1= 5i t,= 2-
O6eptr€lra 3aMiga: f =5a6ox3= 2; x,=lli; ,"=<l Z=-:12'
Bdno1idh: !2i \6.
442 i::l: AITEEPA Mep3neK A. r- ra iH. AxaaeMi'{Hhr pieenr lil:iiii::iili:iiii
5)6)
7'
2t l:lxttl -3V,rr4 =28. Sar,aiHa: (G+a t.t?tBt .28 Ot!t=.7.t2.4.O6epEeHa saMiEa: {rtS=-l - &opeIIiB HeMae; \li+4=4; x+ 4=286tr = 252.BiAno6iAb:252.
T 4'r .4. L=5. 3r,i,u. ?I I ,_x 2x+7
[r' -si ++=0, ]l = r, r, =a.
lr+0, lt*0.o6ep'e'a seMiHa: 4j] =t; z'+1=rr"= yt2"'1 =4,tx2x + 1= 4xt 2t= 1;x=O,5.Bidno6idb: It O,5.
4) r'+x-2 {x' t-2=8 z.gr-1"", G' *-z = t. t, - t - 6 = o: t1 = -2; t, = z-
O6epEeEe 3aMina: r[S *t-Z=-Z; ftopeuiB HeMa€; .,8 *t-Z=Z; x2+r-Z=g;,,+ ,-11=o;D=1 4.(-1.1r=45: Jo =a,,E: ,,= t-:n,
""= tr:.lt
- 1-3.6 t+3.622
829. /(-5)=( 5,16 0:g(21=2" Oigtl)=l:g( t) 1.Bidno6idb: et I ): E{l ti /(2)r /{ 5,,
830. CrnaB Macob 36 rr uicrrrr 45 % Miai, rqo craHoB'rb 36 . 0,45 = 16,2 Kr. flIc4oAo Irboro crnaBy AoAars r Kr MiAi, ro iroro Maca cranoBmb (36 + r) !tr, a MiAi B nr,o,My 60 %, qo craRoBnrb 0,6(36 + ,) Ir.. CKna{a€Mo piBHnEEs:0,6(36 + r:l=16,2+ t;21,6 +0,6t=16,2+ tcr 0,6 t - r=16,2 21,6i-0,4x = 5,4: r = 13,5.Btdtlo6,ab: 13,5 llr MiAi.
5. TplroHoMerplr.+ri piexiurr, r<i aaoAirbcr Ao anre6pai'qHl4x
831. 1) SaMiHa: sin r = t, ztz + t - I = Oi D = 1 - 4. 2 ( l\ = 9:
JD s; r,=-l-q r, r"= 13 |
2.2 2.2 2'O6epHeHa 3aMiEa: siri r = -1;
n1x,-'t t2nk-htz:: "i"' j, "=r-rr,X ", ,"t.BiAnoliAb: C1)'! + nn, n eZ; -! + 2nh, k eZ.
2) SaMiHa: cos a = t. 2t, - 5t 3 = O;
D 25-4.2.( 3t 25 F 24=49: JD t, t,=5rtl a, r,=!r.l )O6€pIIeIIa saMiEa: cos a = 3, (opeHiB EeMa€;
"o""=-.1, r -fr r,..." t.l ., 2nn.n-zt x. !2n t2nn.n 7..2 \ 2) 3
Bidnoaidt: 14 +2nn. n eZ.3
3) SaNriEai sin , = t. t, + 2t 3 = O: tt= 3; t,= L
O6epHeHa 3aMina: sin 3r = 3, KopeHiB H€Ma€j sin 3, = 1:
iiiiii{lilllii: UresPA Mep3rrx A. r. ra iH. AKaaeMi.rnri piBeHb ,:t 44s
,*1-s=0, {j*=0,
,, =\+2.
,, =L+4.
fi zftn3x=:+zfin,n(Zi x= 6. 3:,ncZ.Bi.lnoaial6: :+-.nez.
4) SaMiHaftgr=r. t' - 2t - 3 = 0', t1= 3i t2= -1.O6epneEa saMiHai tg r = 3; t = arctg 3 + fln, n e Z; tg x = 1;
r = arctg (-1) + 'rt, he Zi t=-I+nk,heZ.
Bi()nosidb: arct! 3 + fini fr + flh, n, h'2.-45) 3a{ina: ctg 2t= r. 3t' + t - 4 = Oi
D = t - 4.3. (-4): 4e; uO =tt t,=-j| = -!tO6epEeHa 3aMiBa:
433-cte2x = -;i tgzx=-=i 2x = - arcLg i t nn, n c Zi
cLg 2x = li lg 2x = li 2t = arctg 1 + |th, h e Zl7fi,th fi nh -x= +-,h€L, a= a+r,REa.
l3rrztrft[Bidnosidb: - ;arcLc;+ ;t ;-
:-; , n, h e z-
6) SaMiEa: cos I = l. }t'z + 5t - 2 = Oi4
D =2i - 4.s.{-i)=4s: 1o =t, t,=fi . -z;
O6eDAeHa 3aMilta: cosl = _ 2, xopesie uemae;'4
-"f=|, i = t**osl+znn, nez; r = +4zrctoe!+ am, n ez.
Bianoaiaa: !4 arccoaf, + 8nn, n ez.
832. r) 2 sin't - 3 sin t + 1= 0.3aMiEa: sin, = t.2t'z'3t + 1=Oi
D = s - 4. 2. t = 1; ln =1; r, =f;j =t r,=T: =io6ep*esa 3aMiaa: sint=l; x=!+2nn,n.rt "tr t =f,,
Biatuolilb ;+ 2nni F1)' [ + nk, n, k e z.
2) BardiBa: cos 2.x = t. 2t''t | =O;
D-1 4 2 (-t)=9: JD=3; 1,=L1!=1; ,,=;;= ;O6epEesA 3aMiEa: cos 21 = lt 2t = zfin, n e Zi x = fin, n e Zi
"""2' = -tt 2r=rarccos( 1)-z*.*.2, 2x=x?+znk,nez;
r = tL + nh. heZ.3
Bianosilb: nn !;+ ftk, n, h eZ.
444 l:::l MTEEPA Mep3rr|( A. r. ra iH. AKaAeMi,{H'i piBeHb ii:i!#idlllii
3) SaMiHa: tg r = r. 4t, - t - g = O,
D=1-4.4-(-r)=as; JE =7; \O6epEer€ rar.iEa: tg r = 1i
1-7 3\= tt = -i'
z=!+nn,neZ; tgr = -9; r = -arct "l*
nu, u r t.Bidnolnb:
X+ nn; -*cttl+ ah, n, k ez.
4) Sauina: ctg{=1. Bt, - t - 2 = Ot D = 1 - 4 . A . (-2, = Zb;
JD=s; t,. l-l!=1. ,, =r-5 , ?' 2.3 ' 2.3 3.O6epEena saMiria: ctEl = t, 1=O*nn,neZ; r=4+Bnn,neZ;
"*i = -?' ts; = -;; ; = -*"t sf, + n*. * e z: r = -t *cLcf, + ''-h.
k e z.
Bi}noarlo: 4 + Snni -Barctg! + Bnh, n, h eZ.
833. Aerlri rrir piBBrsE - oAEopiABi. glclqo IlptrIryc"rrr, qo cos , = O, ro sin , = O,oAFoqacEo rli ABi piBHocTi se Morri]"r,r, BrrxoEyBarrrcs, ocrcirbrin cog2 , + sins , = I,ToMy cos .r * 0.
834. 1)sior- cosr=0l: cos r; tg.r 1=O;tgr=l; r=!+nn,neZ;
2) Jfein++cos.r=ol:cos:; Jttg"r+r=0, tc"=-;br x = _!+nn,nez;
3) 3 sin r= 2cos.rl: coatiatgt=2; tet=!; t=*.tef,+xn,nez;4) Acos2x-sin2r= 0i:cos2.t; 4 tg2x=OrtE2r=4:2.=a:(jts4+ftn,nez; l.= I*ctea+T, n ez;
5) sin;+5cos;=01:cosf; tef +r=o; tei= ^s; i=-*"teb+nn,nez;t=-3arclg5+1i.n,neZ;6) sin'?.r - 5sin.t cos r + 4cos? r = 0 | : cos2.ri tg2 r - 5tg, + 4 = O.SaMisa: tg.r t.t,-it t 4=Oi fr , l:r,=4. -O6epEeEa BaMiEa:
tg r = li r = srctg I + nn, n e Z: t = I+ nn, n eZ;tg z = 4; x = arclg 4 + ith, k e Z.
Bilnoaidt !nn: arctg 4 + Itk, n, h e Z,
?) sin, ; - ssin;cos ! * z*." i = o;l** i, E ; _ s E ; + 2 = o.
Saruira: tgf, = r. *-Bt+2=Oit1=2it,=t.O6epEeHa BaMiEa:
Le i = tt i = ^r.tc t t nn, n e Z; | = ! + n71, n e Z; x = ! + 2nn, n e z;
j:i:lttilJii::ti: ATTEEPA MepsrrKA. r. ra iH. AKaAe&ti.{Hri piBerb rt:j 445
-l +7
lsfln^.cts-+-.neLi2 -4 2
-5+7 1
1+72.4 -'
E;=2t t= arcrez+ nk, k ezi t = zarctg 2 + 2nh' k e z'
Bi(Jnosdb: ;+2\nt 2arcts 2 | 2flk' n' h - z'
8) 3 sin'.2 216 sin r cos, + cos2 ' = 0 : cos" x; \te' x - z^13 Lg t + 1 = O'
BaNriHai ts,=t. 3f zJat+1'=oi o=( zJa)" -t a-t=o;
ts'=f; r=*""tsf +nn' nez, x =I+ nn,n ez
834. 1) sin, + cos.I = 0 : cos r; tg, + 1 = 0; tg' = -1; t ='! + nn' n eZ;
2) sinr.- J3 cos"r 0:cosx: ter-J3 '0: tsx J3: ' i' "^''-z'3) 2 sin ir + cos, = 0l: cos t;2tg Jr + 1= 0;
r1lgx=-.i x= arctg +nn,neLi
4) cos 4jr 3sin 4' = 0 | : cos 4r; 1 9Lg 4' = Oi
I1-tlnntgar i: 4x=arctgl- nn.n-Zi x
Aarctg B1 4'nFLi5) sin':r - 5si.n r cosJ. + 6cos'r=01: cos',; tg2 ,. 5 tg' + 6=0'SaMiHa: tg, = t. t2 5t+6=Oitr=2"\=3.O6epHeHa 3aMiHa:
te t = 2t t = arctg 2 + nn, n e Z;
lg r = 3:.r-ar.tg 3 - nh- k - Z.
BiAnosiOb: ^rcte
2 + nn, n e 4 ^rctl 3 + nh' k e Z"
6) 4sin'::s- 3 sin .r cos :c - cosr :r = 0 | : cost4tg'2t-3tgt 1=O'Sevinai 1g x = l. 4i' - 3i -l 0r
D - (-3)', 4. 4. (-\) = 25i,1O = S; t, =?E = t;
O6epEeHa aaMiHa:
tgx=7; t =\+ nn, n ez;
11tgx= : .r = -arctei+ nR. n e L.
.1Bidnostdb: " -F arcLc;- nh. n' k - Z
835. 1) 6 cos't + 5sj.nx-7 =O;6(1 sin'zjl:) + 5 sin t - ?= 0;
6 - 6 sin't + 5 sin jr ?= 0; -6 sin'n + 5 sin '=0
Sauinar sin;c=t. -6t'1+5t- 1=0J: (-1); 6t' - 5t + 1 = 0; D = 5' - 4 6 1=1:
- 5+1 r 5 I IJD.l: il- z.t Z, t ZG t'
O6epllena saMiHa:
.r." = 1, r=r tt'L+nn,n.z;2ti11
'inx i: .t (-Irlarcsin nk AFl'
'!t I t n*-n-k-7Bidnfiidb: /-7l 6',T,?: l-1) arcsLn
J
446 li* AnrE6PA Mep3neKA. f. ia iH. AKaAeMi{H,r pieexr i:::iliii:ii::l:i:ili
2\ 2(l -cos'r)+ 7 cos t + 2=O;2 2 cosz r + 7 cos r + 2 =0;-2cos'zr+Tcosir+4=0.SaMina: cos , = t. 2t, + 7t + 4 = O I I C1\; 2t, - 7t - 4 = O;
D=t-lt:-4 2.{-4,=8lr vD 9: / t^'.n *' ,. t.+=-122 2.2 2
O6epHeHa saMiHa: cos r = 4; ftopeEiB neMa€;
t, * .( ^ ***'l ,^,., z,,= ?!-2nn.n,r.2 \ 2) 3
Bidnosidi: !2n t 2nn- n - / -3
3) 2cos' jf- 1- 1 - 4 cos r = 0; 2 cos' r - 4 cos x 2=O.SaMiHa: cosr= t.2t, - 4t - 2=O .2; t, 2t 1=Ot D,={ 1f - 2.(-t\=2:t; t;.. ,, t;-. , t;
O6epEeHa saMina:
cos rc = 1+.8; nopesiB HeMae (r +.8 t r);
cosr = 1 nD; x=x.arccos(t-nE)+znn,nez.
Bionosidb: ! arccos(l Jz)tznn., -2.4) 2cosr (2cos'zn- 1) cos,r=0; 2 cos, 2cos,.r+ 1-coszr=0;-3cos'zr+2cosr+1=O.SaMiHa: cos r= t. 3t'+2t+1=01:( 1);3t, 2t-1=O;D=t tl 4.3.r tr 4 rt2 t6i VD 4i i 2rtl t ,
O6FpHpHa 3aviua: cos x lr .:r htn. n - Zl
!, ,-,( , a.ccosl'l +:n*.ecz.3 \ 3)
Btdnosdb: 2nn, -r^ "...."1.l 21*, n, h * L.\ 3l5) (1 2sin' jr)+sinr=0; 2sin,r.+sinr+ 1=0.SaMiHa: sin ir= t. 2t'+ t ).1=01i( \)t 2t, - t - 1=0; D = 1 - 4.2. ( l)=9;,6=:, t.=1-3-t' ,^ r-3 -1.' 2.2 ' 22 2O6epEeHa BaMiHa:
n,stnx= li x= +zfin,n€Li
.inr= l, a=t 1tt't!+nk-kF7.26Bidnoaioa: L+2nn: t-It"'\ - nk.n.k.L.26er z.o"'{-r-r"n"1-2=0. BrMiE': "."1=1- 21:- 5i,3=61'333
D-l5F 4 2-\3).49:.JD 7: t 5'7 "
, 5 7 I
" 22'"' 22 t'ooepHeHa 3aMiHa: cos{ = 3r xop.r:le '"'o,;
1, " -l " ,--"tl',',., ez, x -2^ znn.o-2.3 2 3 \ 2) 3 3
r=!2n+6nn-neZ-RiAnoqiAb: X2fin + 6fin, L e Z.
i;i:::::ilLiilti: AITEEPA Mep3rel(A. r. ra ifl. AKaAeMi{Hr.ri piBel/.b;i,:.:i 447
2h "E- 23 3
- 3 5 _!" 2.4- 4
7) 1 2sin x {l-sin'rl-J2sin'r=0r l-2srn-'r-l'sin/x \Esinir=0:
- sin' :r: - rE sin r = 0.
SaMiEs: sin.t= r, ',t'-\f2t=oj t(l+.€)=o; tl=oa6o t,=-Jt
O6epEeEa saMilra:sitrl',=O:t=nn,neZisinr = .E; rcopeEiB EeMae.
BiA o6iAb: nn. n e Z.?--\
ar -"j ' [z*"'j - LJ = o, z*"'i - -"i -r = o.
3auisa: cos{=r, 2t2 +t 1=O;2
- r-3 l'3 ID=l -4.2 f-I).9i VD 3i \= 2 2 = t. t,- 2.2' 2.O6epH€ra 3aaliEa:
"o"{=.1: r-=n t2ftn,nFZ; x=2n -Ann,ncZi
222.".;" i, ;= -l-zn*'*.2, x a+ t ank.hez.
BiAno\idb: i++ 4rki 2n+Ann.nez.
1fik9) ter-- J-2i !t-.
\gx
saMisa:te,=1. t+!+z=0; t'+?t+1 -0. I:':;'.t='' (,r1)z=0; r= 1.
O6epdeHa 3aMiEa: tg t = 1i x=-:+fin,neZ.
16, g.1---j919{,41t cos,6x)-5=0r 4cos,6jr -4 cos6.r'3 0.2
SaMiEa: cos 6.' = t. 4tt + 4t - 3 = Oj
D - 4, - 4.4. (-3)= 64;,!o = a; t, --j:3 = -?'2.4 2'-4+8"' 2-4
O6epEeEa satrfiEa:
*"6t = -;; &opesin Her'{ae;
cos 6r = ! t 6, = ! arc.orf, + zn, o. z; 6x = xI + 2nn, n e Z;
ftnnt=+-+--neL.183
Bilnoeiaa: !{j+!, nez.
Irt 4tesx+-9 '7=0t 5x*T.ncz, * 'ff.r'ztsbx 2
a 4t-7t'3 - l4!" n+a o,3aMiHa: tg5,r= t,4t +=-7 O,- ,- uilr*0,
D r7l, 4.4.s-l:.lD=t, t, =.7r+r1 =rr ,"=?; i448 !!{j AITEEPA Mep3ntK A. r. ra iH. AxaaeMi'rHlli piBeHb iillia:.:tiilllN
O6epEena BaMiHa:
rg5x l:5x=Inn, n-Z: x ft.-Y.nEZ:
rs5r=9: sr ante3 , nh.kczt ' ru"rn!-!!.p.r.
- 4 "4 5 '4 i-finnl 3 nhEidnoaidb: _+: . afcle -|_,n,k€z.
20 5 5 -4 s
12, 7 + ctg'z t = cte t + 3t ctg, a ctgr-2=0.SaMiEa: cte r = r, t, - t - 2 = Ot t1 = 2, t,= -1.O6epHeFra saMisaiclg x = 2i t,= arcctg 2 + nn, n e Zi
ctgjr -li *=-!+nh.*-t.
Bilnoailb: arcclg 2 + nn; -! + nh, n, k e Z.
rr1 2"i1': . Acos, x -7 o; 2-llcos'rtcos- J co-+4cos-x /=0'
aaMiss: cos,.r = t.?-2t,tr z=g.2-2t-tl-zt =o. [er" srtz=o't t li*o:
D ( st .4.4.2=4si lo z, r,=Lz.l ,, ,,=\+=lO6epEeHa BaMisa:
cosz r = 2: .osr = -!f2 a6o cosx =.Et kopesis HeMac:
"os'x= l,
"o"*=-1.'oo "o"'=1, ' *2!,2,,,.,--- '- 4' "" 2 --' --'^ 2' ^
a6o t=rI+2nh,heZ.
Ilicnn o6'eAHaEHs ABox cepi:fr ftop€HiB oAep[ryemo t\ + nn, n eZ.
Bidnosidb: t') t nn. n c z.
14) 2 cos' r - 1 - 4/icosr + 4 = 0; 2coe' x - 4rE cos x + 3 = 0,
SaMiHa:cos'=r. 2t'- EJ2t+B=o; o = (t,lz)' - +. z . a = a; J-o =znE;
, aJr-2J2 BJ2 aJ2 2,2 .tE
"= zz z"'= 2.2 =T'O6epEena BaMiHa:
s.[2 la,6 -)cos.r= 2 i kopenrs neMac | 2
>]J:
t;-.osr = - ;: x-,".2nn.ncz.
Bi'noiiAb: r! + 2fin, n eZ.
836. 1) 4sin,Jc + 8cos r + 1= 0;4(1 -cos,r)+8cosr+ 1= 0;4 4cos,r+ 8cos r + 1=0; -4 cos, r + 8 cos, + 5= 0;4cos'z,q 8cosr-5=0.SaMina: cosr= t. 4t, 8t - 5=0i
ii1:itii:::lillil: ATTEEPA Mep3nrKA. f. ra iH. AKaAeMi{Hran piaeau !il:l5 yci rtq r0 u., !. I
449
T'
D=r-8) 4 .4 b t44i Jo tz, r, a-.12-2.s, , =";Y= L
06epseEa saMiEa:cos r = 2,5; KopeHiB HeMae;
| / l\ -n.2, ' =4 znn.r-2.cos -r ' - t; jf +| n - arccos
2.J I 2",
s
Bianoaidb: !4 +2ILn. n €2.3
2) 2(1 sin'j9) 1 sinr=0; 2-2sir\2x- 1 sint=0;-2 sin'? r - sin , + 1 = 0 I : ( 1);2sin'9t+sint 1=0SaMiHa: sin r = t. 2t'z + t - I = Ot
D=r, 4 2.{-1) 9i Jb.s: t.= )-r"=-t, ,,'}.trt I06epnesa saMiHai
srnr= 1: -r= \+2nn,neZ:
26Bidnoeiot: n,21t 1 ll' \ -2nh, n,k'-Z-
263) 1- zsin'.T + 8sin n 3 =0; 2siD't + 8sin t-2=Olt( 2);
sin'zr-4sinr+1=0.SaMina: sin, = t. t' - 4t + 1 = O;
a ?fi z*h, t.=z $D = 16 4 = 12: .lD 2J3t t, -2
O6epqeHa raMiHa:
sin:r=2+16; ..ope'iB EeMae (z *.6 t r);
sinr =2-.,6; r = ( r)"arcsin(z-16\ + nn, n ez.
Bianoliab: etl. arcEi"(z - nE) + "", "
.2.a) (2cos'9, 1)+(1 cos' x) - cos t = 0; 2co]' x - I + 1-cos2?-cost=0jcos'r cos r= 0; cos t(cos t - 1) =0;
cos r = 0, a6o cos t - 1= o; r =! +nn, neZ ' a6o x = 2Th, he z'
Bidnosiab: \+n 2nki n.heZ.2
5r SsinI l, -"ll ' 2 0; 5sin 1- 2sin'1- 2 o.- """6 \' ---31 6 6
sawisa: sin{ = t. 2t'z+5t +2=Ol6
D=5, 4.2 2 st,[D s; t,= 5.-r3 = z, t.=-f,tr3 ='t.O6epHetla BaMiEa:
"in I = z: xooesls rreMae:6
.t"* -1. ' r rf 'L nn,nez; x=( 1)' n.6nn.nrz-6266
Bi0no6iAb: Gl\"'tn+ 6nn, n eZ.
450 lii: AIrEEPA Mep3reKA. f. ra iH. AKaAeMi'{Hlafi piBeHb :::a:::::i:::::i:i$:i
6) 1 - 2sln' ; + sin; = 0; -2sin' ;+ sin; + 1 = 0; 2sin'; - sin; - 1 = 0.
3ar',rina: sinl=t. 2t'z t 1=Oi
D=r 4.2.( 1)=e; 5=e: t,=!j=ttr=i:= +
O6epEesa 3aMiEa:
"t"|= t: |=!t2"", n.zt '=n+4nn,nez;
'^ ; = - t, | = t-tl' f, t nn, n. z, r - (-:rrhi ! + 2nh, k e z.
Bidnoiidb: n - ann: t-:.f 'i|- 2'th- n, k , 7.
7) 2cosz 4' e.1*?"4'*r=o;2cos'4t 3 Scos 4ir + 1 = 0; 2cos'4r Scos 4a 2 = 0.3aMiH€: cos 4r '. t,2t: 3t 2 0|
D=(-st, 4.2.2=25,5=s; t,=f;j=zt ,=#= ;.O6epseEa sarilla;ros 4.r = 2i HoppniB HeMac:
cos4.r },.- -f^ n)tzon.nez: 4x -2n 2nn.neLt
x=+!+\.nez.63Bianoaioa: tl+!, n ez.
a) ter+-L a=0.
SaMirla: tg jr = 1.
2 t'!-3t+2 ll gt2=o.i, 3 0: l, 0F ), l.=2il-=1.t t Ltlo:
O6epHena BaMiEaitg x = 2;, = arctg 2 + nn, n e Z;
tax=l: x=L+nk,keZ.
Bidnoaidb: arcls 2 ' nn. ft nk,n,hFL."4
9) \6tg'+3=3(1+ts"x); \lite" r '6ter=0.saMisa: ts ' = t. 3l - rf3t = 0i .far(J-:t-r)=o; r-ouooO6epHeHa saMiHa:lgr=Oix=nn,n.Z;
1n
tgx = !9; x=1+n&,keZ.
Bianoliab: nnt [ + n*, n, * e z.
ljll::li::tlii*: AITEEPA Mep3re( A. r. ra iH. AKaaeMi,{Hrr piBeHb ili: 451
l5*
l
i
,=+=@J33
ror n"in'' * g{ -1- - rl -u=0,\ $n-.r )
4 sina t + 9 - 9sin', - 6 sin'? t=o-
4/--15r'9 - l4l'-15i 9=0'3aMiHa: sin, .r = t.
-- -
u o lt * O,
r5-9 15-9D 15,.4.4.9 8l:JD=9i,,':.n =u, t,=- -
O6epEeEa sanriEa:sin'z , = 3; IcopeEiB lreMa€;
"3!5"6sinz j=:: sinx= 2-.aoo srnx, tl
,. r-1-"! +nk.k.Z.a6o x=l tl -L-nn.ncz.-:li,
nicns o6'€ana$ss lsox cepifi HopeHiB orpxM*'o - l-* ^', ' c z'
Bidnoei t: !!+nn,neZ.3
837. 1)sin't+ 0,5 2 sin tcos r - 2 cos';=0]|cos2 r; lg2 x+\gx-Balfil:ai Lg t - t. t' + t - 2 = 0i \ = 1" t2= -2'O6epseEa 3aMiIIa:
lgx=Ii x= +nn.neLi
tgx= 2ix= arcLe2 -rtk' hF Z.
Bianoaida: L t nn: -arctq 2. nk, n, h' Z.4
2\ 7 sin' 5t - 4' 2sin 5.' cos 5: + cos' 5r = 0 | : cos'z, 5r;7tg'1 5x 8l,g 5r + 1 = 0.SaMisa: tg 5x = t. 1t'z - 8t - I = 0i
- i+6 8-GD=(-8)? 4 ? l=36; JD=6i tr = -r.:=lt t,= Z.Z=O6epEelta 3aMilta:
tfr!.nezttg 5.'r li 5r '"-fin.nczi *=m t111111k-
tgSr ;: 5.r = arctg ; + nh' k c Zt r=tarctgi+ 5,he''nnnllnk
BiAno1idh: i'n+:b' i ;^tctc; - i' . n, k ez.
3) cos':, + 2sintcost + sir'zJc+ 1=1 2cos%c;1+ sin 2t 1+cos 2'=0:sin 2-r- cos 2.r=0 1 : cos 2-r: tg 2n - I =0: tg 2t -li
2x _! + nn, n.zt x=-;+;,ncz:
41 3sin'z.t- Tsinxcosr- l4cos'x 2(cos'? r + sinT r) = 0;
sin!x - ?sin.r cosr I l2cosz r=0l: cos, xl tg'zx - Tlgx 12=O.
SaMisa: tg , = t, t' - 7t + 12 = Di t'= 3t t2= 4.
O6epEeEa BsMirra:
Lg, = 3i x = ^rcfg
3 + nn, n e Zitg x = 4t t = arcl,g 4 + |Ek, h e Z.
Bilnosi'b: stclg A + TLni arctg 4 + rht n, h a Z'5) 5cos'zt - 3sin'zt - 2sin.:c cos t - 2(sin'r + cos'zt) = 0i
-5sinz.r - 2sin r cos.r + Scos'x = 0l i (-cos'zrrt \te'E + 2te r- 3=o'Sauiua: tg x = t.'t'z+21-3- 0i
452 lll; anrEEPA Mep3rqKA. r. ra iH. AKaAeMiqHri piBet" llllii:ill:l;ili:1
D=2, 4.b.( 3)-64: Ja=6; 1,=-?:!=-l: r. -l+-q=q2.5 ' 2.5 5
O6epHeEa BaMiEe:
ts x = -1i 1= -Lana. a 12.-4
tgx =::i x = arctg:- + ftk, k €2.
Bidnosidh: -L + ttn: arcte 3 t nk. n. & e l.4 '5
6) Ssin'.' + sin.I cos r + 4cos? r - 3(sin, r + cos, r) - 0;sin r cos. + cos2 r = 0j cos r(sin r + cos x) = 0;
coat-o: x=!+nn.nez:2
a6o sin x + cos , = 0 : cos r; tg r + 1 = 0; tg r = -1;
BiOnosiab: ! + nn: -! + nh. n. h ez.247) &in, cos r + cos? r - (sin'?, + cos' r) = 0;3sinrcosr-sin2r=0; -sill r(sin r - 3cos r) = 0;sir']c=Oix=rol,neZ:a6osinr-- 3 cosr=0 : cosx; tgr 3=0; tgt=3; t=atctgB+fik,hE Z.Bidnoaidb: ftni arcLg 3 - fih. n.he Z.
gt 2cosr + sin x _ 1.Tstnx - cosx 2
OA3: ?sin r cos r * 0 ] : cos r; |tg t - f + O; tgz+f,:2(2cos r + sin,')= Tsin i. cost; -bsin r + 5cosr=01:
n_tgx=ri.x= +tt4n€L.
838. 1) sin'z, - 2 . 2sin t co_s r + 3 cos' x - 0 | i cos2 $ Ng2 t - 4trg t + 3 = O.
BaMiE&: tg r = t. t, - 4t + A = Oi t1= 1t t2- 3,O6epEesa BaMiEa:
tsy=l; y=!qnn.rg74
tg t = 3; r = arctg 3 + nk, h € Z.
Bidnoiidb: !-fin, arcta3a n*. n,n h- 2.4-2) 5sin'? r - Ssin r cos r + 2cos, r - (sint r + cos, r) = 0;4sin'zr... 5sin, cosr +cos3r=0 | cos, t;41g, t- Stgr+ 1=0.SaMina: tg r= r. 4t'-5t +l=O; D = (-S), 4.4.1=9t,6 r, ,. 5*1=r, r =!--q=!.' 2.4 ', 2.4 4
O6epEeEa saMiEa;1t_1gx=ri x= +ftn.neLl
5n, = !.. , = *.1n!*np.1r.7.- 4 '4
Bidnoeidu: \ +rn: arcteL - rik. n. k.:2.4 -4
ilililli_tl:j:.tt A'lTEEPA Mep3rrKA. r. ra iB. AKaAeMi,{Hri piBeHb l:it
x=-!+nh.keZ.4
2=0.
x*ar*ef,+nn,nez;(-5cosr);tgr-1=0;
l
453
3)6sin2r 2 2sinrcost l4cos?r. 3(sinz 'r 'cosr.rl=0:Bsin,.r+4sin 0l:co'.r:3tg x-4tex -1=0.SaMiHa: tg r. l. 31': ' 4/ . I 0i
- 4-2 I -4-2D 4, - 4 . 3 . 1 = 4t ,l D = 2: t,=-2.3 =-Ji rr= zB=
r.
O6epEeEa saMiEa:rl
tg.x = -Fi .{=-arcigg+\n,neL:
tsr= 1: r= \+nk.hez.'41JI
Bidnosidb: -arctg;r \ni -;- rk'n.k -7.
4) 2cosz t + zsin r cos ir 2(sin' t + cos': t) = 0i 2sin'?t+ 2sin T cos.I=0;2sin n(sin x - cos .T) = 0;
sinr=0: r=rz, ne Z, a6o siLt lc cost=0 : cos]'; tg, 1= 0i tgt=1;
r =! +nk- h eZ.4
Bianolilb: nn ! + nh, n. h eZ.4
5) 3sin'.r 2."6 sin:r: cos t + 5 cos'z t 2(sin'z r + cos'? t) = 0;
sin'x-2J3sinx.os-r, 3eos'x 0l:cos'r: !e r 2'6rer'3=o:
{re'-Jr]' 0: rer \6=0r ugx=J3r x--f, tnn n't'
6) 2 slan ig!1 l; o.[3: rsin x 4cos.r' 0 : cos'i srs.r 4 /0:5 sin.r - 4cosx 3
x+acctel-nn,ncZ:3(2$n r cos x) ssin t- 4cos x: 6sin x Scos r- ssin x I 4'os x - Oi
sinr .os r. o:cosxilg.t,l 0:tsx -r., -It nn,n -Z'
839. (1 - cos't) + cos, + 1= 0; cose, + cos jr + 2 =0; cosz t - cbs t + 2 =0'Sa]IiEa: cos t = t. t2 t - 2 = O: t.= 2" t,= -1.O6epseta 3aMiHa:cos t = 2; (opesiB HeMae; cos x = 1; x=-It+fin,nEZ'flpu n = O: z = r - Hafi6i"tbrrt{i BiA'eMsnft lropiH6.BiAnMiA': -n.
84O. sin'zir + 0,5 2sin n cos, - (sin'z.' + cos'zr) = 0; sin.!cos n- cost r = 0;
cos t(sin t - cos ,) = 0;
cosr=O: r=I+nn,neZ'2
a6o sin r - cos x = 0 I : cos t; tgt-1=0;tgt=1; x=\+nk'keZ'
'= t, "=\ n=-?!.tr
- uan6i,rsmrs Bi,q cM$Hii KopiH6.2
Brdnoaidt: -L.2
454 li:i: AITEEPA Mep3rqKa. r. ra iH. aKaAeMiqflr,ti piBet" iliillli:i;i;iiiil:
a41,61 c9s2{ +2(1 cos:2.r)=5;3 8cos2r+2 2cos'u 5=o;
-2cos'x - Scos 2,. = 0; -cos 2r(2cos.r + 3) = 0;
cos 2t = o; 2:r=Z+nn,nez; x=f,+!,nez:
a6o 2cos jr 3 0r *"' - - t: KopFHiB HeMac.
npun=o:,=x.
Bilnoai}t: !.,4
842. cos t(sin jr + cos ,) = 0;
cosx=o) x=L+nn,neZ;
a6o sin iu + cos r = O : cos r; tg x + 1 = 0; tg r = -1; x=-!+nh,keZ.
npvn-o x=i, net4k=o x=-|., opx*=r r.= -X.^=+Bidnociab: !.
2
a4s. r) 2sin2.r :::;-ff;, x .nlt zsinzx=":"J,";";*,
2,in2, = -L. ,in' 2, = 11sin 2x
sin2.r=-1: 2x= !tnn,neZ:, n rnn,n-z:242a6osin2x l: 2x n ,nh.keZ: t n rnk.k.2.242Bidnoaida: ! +9- n e7..42
2) 3 cos,r . '"t- o, oflt, cos,r*0i,rF n -an,ncz:
3..s'? x + 2sin r 0; 3(l sin:.r) 2sin -r 0; 3sin'z-r l2sinx r3 0;
a"in'.lo"i.in , r o.BaMisa: sinr=r.3t, 2t 3=OtDt=( 1)? 3.( 3)=10;
,,;'i;.lE ="To. r.=l '/ru. r^=r vro.
O6epEeHa aaMiHal
. 1+ J1o nopeErB HeMac:
r-.,/io 1 ,R _n,,,.2.gnr= e l ir={-r) ar$rn !
Btd,oetabi (-r)" arcsi nt f; *no,n.z.
::li:al:il:ilil:l AITEEPA Mep3rrK A. r. ra iH. AKaaeMiqHrn piBeHb :ii::; 455
4tg +;;
4cost 2t 4cos 2x - 3 = O.
SaMiEa: cos 2t = t. 4t' - 4t - 3 = O)
D = (-4r, - 4. 4. (-s) = 64; JD = s;
er g. l - cos2x -4r1 cos'2.r) rScoszx-5=oi
t - tcoe 2i + I - 4cos' 2t + Scos 2x 5 = Oi 4cos2 2r + 4cos 2t + 3 = 0 L : (-1);
4-A 1
' 2.4 2
O6epseEa 3arriEa:
"n"2r = 9: Kopenin seMae;2'r ( r) 2ft -
"o.Z'=-i, 2r-+f tr - arccos;J |21tn,n'Zi 2x'Ia-znn.ncLi
- 'i,"^.".2.Bianosiab: !;+ nn, n ez.
4) 3 + scos t = -(cos' .t - sin' .'xcos'z t + sin',); 3 + Scos .' = -(2cos': r - 1);
2cos"+5coB.r+2-0.gaMisa: cos, = t. 2t' + 5t + 2 = Oi
- -5.3 -5t3 ID=b,-4.2.2=9..ID-3t \= ;.2 -4: I, z-2 =-t.O6epnesa BaMiEa:
cos r = 4! RopeEiB seMa€;
e loo (o l;6 )"o"'='S ixopeEiBHeMa€ l. 'r"". -',].
aidnoaiab: xarccos@ 2 + 2nn- n e7..
5
2) 4(t - cos'2x) -7 co.2' -2.r-':"2' 6l'24 - 4coE'2x + 7cos 2x - 1+ cos 2.rc 6 = 0; 4cos,2l + Scos 2r - 3 = 0;4cos' 2r Scos 2r + 3 = 0.3anIiIIa: cos 2, = t. 4t' 8t + 3 = 0i
D.t at' 4 4 3 r6i ,to +; t,- l!=3;: t,=2.4 2 'O6epHeHa saMiEa:
3 l: 2t=L!+2nn.nL7.:.oszr = 'i xopeHrs ncva€i co32.r ' 2 3
t=!!+nn,neZ.
Bk)nosiAb: lL + nn. n e7..6
s) 7+2sin2.r-r,5rgl--':""1 - o; oaa: t, n!,n ez;\cos.r srn -rl 2
?+2sr2r+l'5{sin'zr' cos'r) 2 =ot z v 2sin2r r 3- =0,cos.r sin.r 2 sin2x
zsin'z2x+7s\n2x+3
"i =0t 2sin:2r' + Tsin 2t -3=0'
SaMiHai sin 2, = t. 2t' + 7t + 3 = 0i D ='I' - 4. 2. 3 = 25:
Jo 5,,. _7_5 g, 1"__!:J=_!.' 2.2 ' 2.2 2O6epEena BaMiHa:sin 2, = -3; (opeHiB seMae;
sin2x - 12t 2x 1 lfrarcsin I I nn,ne\i 2x = t-l\"| ! + nn, n c Z:
a = 1-11"t !: a\!. r 62.122Bionoaiat Gr)"' $+ !, n e z.
ar sin.x=lcos,r-st".if".",-, "i",r), "i".,=.*,. r,\22J\22)(1 - cos'zr) cos r=0; cos?r- cosr + 1=0i cos'!r + cos r - 1= 0.EaMina: cos r = l. t' + t - I = O', D = l'z - 4 1 . (-1) = 5;
-E=s, ,.= 1 6, r --r+n6-'2'2O6epEeFa 3aMirra:
-r-.,6 (.r Js -lcosir 2 i ropeHrs seMac | 2 <-r.]:
cosx . Vbj-I. r = larccos\J - 2nn, n cz.
BiDnoai\u: t arccoe@| + 2nn, tu e z.
ilillliii:ltlll AnTEEPA Mep3rrx A. r. ra ir. AKa.qeMi{Hratr piBeHb lil:
4+8 3
8-4 I2.4 2
$sdll:liI
ffil
1 I 1\cosx -t; r =-Lln-arccos;J+2rn' r ezi
2nBidnoqidb: t-+zftn,neL
I - cos.r5) 2cos'.r-1 gcosx+6=4 -.- i
r=!?+zrn,nez.
7 -5 |.,42
ne Z-
2cos2 t - ! - gcos t + 6 - 2 + 2cos t = Ot 2coB2 x - Tcos t + 3 = 0'SaMina: cos :r= t. 2tt 7t+3-O:
D=(-7\,--4.2.s=25: JD -5; t,=1!-s;O6epEeEa 3aMilra: cos , = 3; &opesiB EeMae;
s6gy=\; t = +!+ 2nn,n ez.
BiAnosiab: t:I+ 2nn, n eZ.
844. 1) lPa-ssin'=0; o,43: sin'+oir+nn,
4cosx-ssin'/n-0. n:gSlj!L-g:14 o: 5cos,.r - 4.osx s=0.cin r srn,f,
SaMisa: cos t = t. \t'z + 4t - 5 - Ol
D\=2, s. (-b, = 2s; Jo = Jm; O=-'*u@ ,
O6epaeua saruina:
-Dt,l2s fi 2.znn,nrz,cosx = - ;-; jr = larccos--
456 ii{: arrEEPA Mep3rex A. r. ra iH. aKaaeMiqHrlr piBexu fflJliii:iirif$
-2 Jn
457
b\ 2 (2cos' 21 1)-2.1119q?1-scos2x-0'
4cos'2x 2-l cos 2t - Scos 2x = O; 4cost 2t 4cos 2x 3=O'
BaMiIla: cos 2, = r. 4t, - 4t 3=OtD=(-4), 4.4. ( 3)=64; Jr=S;4+8 3 4 8 1t,= z.a=ir t,= 2.4=-t'
06epEeHa saMisa:
"o"zr = ]; ,,on""ru *"-.";
"."r-- l, * -("-;) ,2,.n.n-Li 2,= t2[ +znn'n-2.
r=+L+nn.neZ-3
Bilno'iab: !:+ nn, t eZ.
845. CtoprcraeMoce roroxisocrsMlr: "in" = z"n1.o"!r; co"' = "oJ f, - "in'I" l- rl ".*'r-, "t,,'t'l = o:trazsinlmsi-slcos';-stn'?;, \ 2 z.)
6"i";cos; - s"oJ ; + I sin" ; - s cos" ; - ssi^" ; = 0;
ssin' f,
+ osinlcos j - 11cos'z { = 0 t cos' }; s tc" ! + awf, - n = o.
3,amisa: tg! = t. 5t' + 6t 11=OtD=6'z-4 5'(-11)=256;
. -6 t6 ll -6t16 -J, 16: i. 2.5 5 , i, 2.5 ,
O6epEeEa saMisa:
t*;= T,r=-""(--'Jl ,^n.n-zi x= zar"tslt tnn.n-7:
LgI r. {= | tnh.k.z.. ,=!,zn*,*,2--2 2 4 2
Bionoaidt: -2arc4! nn., cz; |-zn*.n.t,zt .x ,ir' .r 'l ^2t 2zsin;aos;s[.os't sin;J tl."."', sin tJ u:
4,n;."";- 8""{ ;+ bsi.';- 3co{;-ss,\";= o'
-scoJ j+asi"]*"{ + z"in" ! = ol.z"os" X: te"}+ztc} a'=o-
3ar'dua: tgI=6. t'+2t-4=o;Dt=1' l'(-41=5; t' =-1-G; 4=-1+J5O6epEe:ra 3alttilla:
tei--t Js, i= *.tc(t nE)+nn'nez; x = 2arctg( t-'fi)+2nn,nez;
w | = t +,li; !, = *.tg( t t Ji\ + nk, n e z; z = 2 arcts(-1 + Ji) + nh, h e z'
Bionoliab: 2arc].1g(-l n[E) + znn, , ez.
458 iriaAIIEEPA Mep3rrx a. r. ra iH. AKaaeMieHrar pieenu llill{f:i:ilf:ii
846. lt 3 2sinxcosr,sl-"'* .i"''), sl-. {,"; {J =o,2l \ 2 2)
6"i"1"o"{ 15 "o"'{ - 5sin'3 + 3 cos'{ + 3sin'{ = 0:2222222sin'x , Gsrnrcosr rscos'r 0l:f 2"."'Il, tn'{-:rL'x-a o.2 2 2 2 ! 2l '2 '2
SaMiHa: LC; - t. t2 3t 4 Oi tt 4i t, l.
O6epEeHa BaMiHa:
ugl=4; {=u."t*o- ftn.n.li r 2arcle4 | 2\n, n .Z;'2 2
rn{= .1, I=-I1nh-k,-Z: x.-n +2nh.keZ.'2 2 4 2
Bidno'idh: 2arere4 r 2nnt n t2nh,n,hcl.-22r sJa 2sinlcos{-sl-"'.'-"r"'*l z["."'' "r"'') o,2 2 I 2 2' \ 2 2'
. ,x _ ,tt)\/J srn cos 5.os--I5srn---/cos' - lsrn- tl:222222-2":. r+0,,6"i"i"*i-t2""*i ot,( z*' l); te'|.a,E"sf,+a-o.
samina: rg{=i. i'-e,fit+o=0, D (3J3)' a.6 27 2a=31 uln =,f5.2-t; t; ^t; t;r ovo vo l;-. ovo-vd o/o
'2-2O6epIIeEa 3aMiIIa:
1s I = u/3, {=Iann,ntz: x=zn,2nn,nezi"2 2 3 3
t* t = ""Et | = arcte 2rE + nk. k e z: x = 2 arcte 2Jz + 2nk, k e z.
Bionoeidd: "l' - 2an; 2ar.cte2\E | 2\h, n, h t Z.3"
447-l)l 2sit]''r+ sin r= (1 sin,r)=0; I - 2sin, r + sin r 1+ sin?r=0;sin':, + sin r=0; sin r(sin r - 1)=0;
sin.r=0:x=nn.nc Z: a6osin x I 0isin ,-1, *=!-2np,k.2.Ilpr.rn=0:r=0; npun=1x=n; npBn=-1 .r=-7r:npx k=O x=*: e= 1:
r 3r ixo*: npxk=t *=l-zn.5] "-. "*ou,'"
x= 2-2fi - 2 se BxoArl,rr, ] Dpov 2 2y rpoMidioK.Bidno6idb: 4 KopFHi.
448. 1) 2(1 cos'a) + Tcos.r + 2 = Ot2-2coE':t+Icosr+2=Oi-zcos: r + Tcos r + 4 = O I : ( r).SaMiHa: cos .r = i. 2t" 7t 4 OiD ( 7), 4 2 e1f,=81;,lD gi
, 7+9 ,. , 7 I 1
' 2.2 2.2 2
O6epEeEa 3aMiHa:cos r = 4; rcopeHiB EeMae;
:iiiiiiitiii:i* AITEEPA Mep3rrKA. r. ra iH. AKaaeMi{Hhr piBeHb l:::t' 459
I
I
12n +2nn-nEZ.
-2T-2^2nIlpr a 0 x =-:-e6o r , ,-? t" Bxoal'rrb y npoMixcoft);
nvttn=t ,=-!+2,=! ,e" r=f *z*=$ t"".xoa,'rr, y rpoMixox);
2ft 4n
33Bi.Ano6iAb: 2n.
849.2(1 - sin't)=sin x; -2 sin'jr sin;r + 2 =01: ( 1);2sii'zt + sin t - 2 =0gaMina: sin , = ,. 2t' + t - 2 = Oi D = 1 4'2 (-2)= 17i
t -,hz- I'Jlz u[7 tvr'vrii rr=-4 : t,= Z.Z 4 .
O6epFeHa saMiHa:
r Jrz (-ttJtt .)sinr.= 4 i xopeHr! Eex,ra€ I a-.-t.],
"r,',='r;-t, :q = Gr)" *"sin@l +M,nezili;.,
urlr n = 0 r = arcsin gil < jr
rrpr n = 1 lr = - arcsi n[', t * n.
^ ,47-r4
aso. z"i"l*"i**"'r "i''i--"'i "i"'i -0,
-2"i""!+zs'"t."'i=o;
"i"|= o; |= nn, n ezi r-2nn,nez,
aoo sin j -cosf, = o l, "o"|; tef, -t = o;
452. 1) cos" cos r + a - .r2 =.O.3aMirra: cos r - t. t' t + a(1 a\ = 0,
[t.+t-=1.3a reoppMoro Bi.ra I tt ai tz I a.
li, .i. = o0 _ a):
PiBssHHs MarnMe KopeHi, sKqo -1 < a < 1 a6o -1<l - a<1; -2 <-a<0; O< a<2-BiAnoqiAb:-1sa<2.
2) Eijn'r- 2aEiI r+ 2a2 4a + 4- O.gal'riEa: sin r = ,. t' 2at + 2a' 4a + 4 = 0tD,=( a)' (2a, 4a+4)= a'+4a 4= (a' 4o+4)= (a 2),,PiBIIsErifi Ma€ &opin6, snqo ,r > 0,
BiAnoqiAb:
851. 1) sin'z .is (34 - 3) sin , + a(24 - 3) = 0SaMiEa: sin r = t. t' - (3a - Aft + 4(2a - A') = O.
li +r.=r,3a reopeMoo Bj€ra I ' ' l,= a - 3i t" a.' 1, t'=a(r-a):PiBEsgns MarrM€ Kopelri, triDro -1 < 2a - 3 < 1 a6o -1 < a < 1| 2 < 2a < 4i 1 < a < 2.
BiAnosiAb: 1 < a < 2.2) cos" + 2 cos r + o'z - 6a+ 10 =0SaMiEa: cos r = ,. t2 + 2a + az 60 + 10 = 0;D,= l a" + 6a - 10 - -la' - 6a + 9\ = -la - 3)''PiBHfisBs Ma€ Hopilrr', axqo ,r > 0.
-(a-3)z>0trpra=3.fipna=3t'+ 2t + l=0;(t + 1)'9= 0; ,= 1, pinng:rHs Ma€ xopiHl'.BiAnosiAb: a = 3.
460 i:::i: ufespl Mep3nrk A. r. ra iH. AKaaeMiqHul pisexu :i:li:ii'i:ili:i'.;i::
:(a-2r'>-0IJp]'a=2.S\{\o a = 2, t' - 4t + 4 = Ot (t - 2r' = 0; t = 2, npore sin r = f, roAi sin, = 2. PiB'IIsnIIs nopeHiB Ee Ma€.BiAno'iAb: aalrorc BE '{eIIEs a IIe icHy€.
ss3.r) rVZ t'{tz; '{n,,{Ez, *o*v iF ''V77;2) Jz i ,V33r 'F i ,Vra, ,V42.'V33,
'o..v Jz. t,fra:st fr# i i6rr 9225,a!t2s, 'ouy Vts 'vs,al {F i {6; '{tr ''iF, ,o*v iEr ' i6.
854. r)6r(1 2\(x ' 2\ o:,r = 0 a6o r 2=0; xz=2 a6o x + 2=O; rx=-2,BiA MiAb: -2i q 2.
2) x,(x - 5, + e(x - 5) = 0; (' - 5)(,, + e) = 0;,r 5-0; ,r- 5a6o.r'z I I - 0; KopeHiB HeMa..BiAnosidb:5-
3\ ta(E + 2\ + 8(r + 2) - 0; (r + 2)(r' + 8) = 0;xt2 0',x 2a6o.r{ t8 0l xopeniB Hevac.BidnoBidh: -2.
4\ (it3 - 1\ - (2x'z - 2t) = 0; (r - lX/ + r + 1) - 2r(r - 1) = 0;(r-lxr'?+r+1-2,')=Oi.r - I =0:.r = 1 a6o.r' - x + 1 = 0i KopeHis H"Mac.BiAnosiAb: L
855. Kirrbrlicrb % Itinbriicrf, EiliefloI 6Dvxr 5 0,05x rII 6Dvxr 40 0,4u rCwiItr 140 r 30 42i
Hexafi .f, r 6pyxry I BrAy, y r 6pyxry II BnAy. BMicr Hircenro B rrx - 0,05r r ra0,4v r Bi,qtroBi,qEo.vcboro 6p]'xry aBox Br{aig trorpi6so Bs.Err (, + y) r, a6o 140 r.I piBnEEHs cncreMn: r + u = 140.ycLoro Hi&enb B 6pyxri ABox ErIAiB (0,05r + 0,4y) r, a6o 41 r.II piBEflEEn cscreMr.r: 0,O5t + 0,4v = 42,
l,+y=1as. ]r-o.al J-0. ax - o. ae = -ro.)o.Os' . o.ay +zr lo.ob-r I 0,4y 42t
0,35' = -14: t: = 10i r + u = l{Oi a = 1OO-
BiAnoaiAb: 40 a i 100 r.
illiftllttiilL AIrEEPA Mep3re(A. r. ra iH. AKaaeMi'{Hrfi pigexu iii:j l6t
rl x rlzsrn lsrn- - cos2\ 2 2) =0;
i
|=f,r "*, *.2; x=L+2rh,kez.
L2
6. Po3a'g3yBaHHq rplroHoMerptqHtx piaHtHb MeroAoM po3KnaaaHHtHA MHOXH}IK}I
856, 1) 2cos 2, cos ,. = 0;
cos 2, = 0; 2x=!+nn,neZ: ,=\+T, r.z;
a6o cos , - o; x=!+2nk,heZ.
Btdnoeioa: I r "i, i-n*.,.a-2.2) 2sin 2.r.os 31 0.
sin 2r = 0; ht=nn, ne Z; r =Y, n eZ;
a6ocos3"r=o: 3x l+ nk. h-z:' -I-# r',Bianoaida: Y: L +4. n. * ez.2633) sin ,(2cos 2t - 1, + (zcos 2, 1) = 0; (2cos 2t - lxsin ,r + 1) = 0;
2rosr I 0i cos2x=!r 2x t\+2nn.n.Z: ,='[ "".".2,a6osinr.,l =0: sin,r t,x= 1 2n*.kcz.
Bilnoaisa: x[+ nn: :+ znk, n, k.z.
ay z sin r (tg r + ,6) - (te, n J3) = o; (tg"+.,6)(2"i""-r)=o;
ig'+16=o; tgx. = -',8; x=-\+nn,nez;
a6o2sinx r=o: "lnr lr x=t :':'in' nk,kLz.
Bidnoeiat: -!+ nn; (-:ohI+ nh, n, h 62.
857. I ) 2sin 4r cos 3,r = 0;
sin 4r = 0; 4r=nr, neZ; x=!, n eZ;
a6o.ros ax 0i 3x=!tnh.kt7: "=i *!,*.2
^finfifikBlonoanb: -i
2) -2sin 4t sin 5.t = 0;
si:n4;,=O)4x=nn,neZ: x =Y, neZ;
a6o sin br = 0; 5' = nk, k e Z; , = ! , n . Z.
Bidnoeidt: !: 4. n. k ez.453) is''(is' + 1) 2(te'+1)=0; (te' z - 2r(te t + tl = ol
(te' -.8)(te"..,D)rtsir + 1) = o;
rgr-\E=o; tgt=J5; x = ardg\E + nn, n ez)
462 ii!: AnTEEPA Mep3neKA. r. ra iH. AKaAeMi.rHr4i piBet" iililililiii:iii
A60 te;t+,tE =o; ts,=-Jt; r=-arctglE+nk,keZ;s6otgt+1=0; tg t = -1; , = -!+ n*, ^ eZ.
BiAnosiAb: l:^rclg\E + nn; !+nm,n,meZ,
a) .E cosr(cte,. - 3) + (ctsx - 3) = o; lctgr-:1(.ifcosr+r)=o;cNg t 3=Oictg t= 3j r=arcctg 3 +nn, ne Zi
a6o .Ecos:r + 1= 0; "o"=-f, '=t(^.X)*",u,o.t,t -3n . 2o*, a. 1.
Bianosidb: arcts 3 + nn: t! + 2nk, n, h ez.
a5a. 1) 2coslcosr= t: z @cosr=I; "o"r=$, x=!X+2nn,nez;
2) 2sinrcosl=1; z f sin.:c=1; '6sinr=1; "*,=;t "t",=f,ir { f}'arcsin Ji , nn, n -2.
*-l'-.,,1 ,, *(" . n"l3lsinb-r sinl; r'l o;zsin 3 cos---=o:
z"r.f 9" - ll "..1 l * ll = o.\2 4) \.2 4)
. /9-" r) - 9x n - 9r n n 2nnsrnl2-AJ =u; ---=nn,n.L: 2 4- nn.ncLi x 18 -,ncLia6o cosl
*,nl o,'.I=!.nk.h.Z: !=L-! -np.1112\2 4) 2 4 2 2 2 4
! = \ + n*. * ez: :c = ! + 2nh. k eZ.242-n2nnn'ttronostob: 1g+ Ii +zltl?,n,heL,
ar "mro, "i"[] z") =o; z"in
,"'"(.,-;) "."(,,.' ;) =.,
(nIz2
t"""tor+11 2al\2 )
2=0;
. (^ n) ^ ^ rr - - ^s'nf o.r-4.J =u: ox- 4 nn-n. Li rrx 4) nn,n-L: x=-+-,n.(/i
aoo cosf+r ,n) o, a,tno=\,nu.o.t, a*=|-! anp-a.71
4.r " tnk.kcTi x " t"".k=2.4 16 4
- nnnnnkBi.Jno6idb:
-+-r :-: -n.k.Z.246164
ljillii:.i{ilf;:;; mreSPA Mep3reK A. r. ra iH. AkaAeMi.rHr4i piBeHb iii: 463
10, -
459. rrzs,"fcos(, ff)-', , ]*"('-iJ='' -"('-#)=''x f;= znn, oez; t=!:+2nn,nez:
:r "r^l
1-s*l rsini.r 0: z"i.,lr-'l"o"ln r'l .0,' \2 ) \4 .r \4 l
"-(l l=0,"''('-l) =0, x n.nn.ncz: *=ltnn.n-z:
.u" *"(; ,,) =0, *"(*-l) ='' rz !-!+nk,hez;
4x =4 + nk, k e z:, =#-*, u.t.
aidnoaida: ! + nn: ff'I!,,,*.2.860. 1) 2sin, cos r + 2sin r - (cos t + 1) = 0; 2sin r(cos t + 1) - (cos, + 1) = 0;
(2sinx-lxcost+1)=0;2sinx-1=o; "i""=]' '=CU"fi +nn, €zi
a6o cos r + 1 = 0j cos t = ti r = fi + 2rtk, h e Z-
Bianosiab: el\"X+ nnt it+2nh,hez.
2\ 2cos' 4x - cos 4t = 0; cos 4t(2cos 4t - 1) = 0;
, cos 4x = 0i 4t=L+nn,neZ; r=!a!!,neZ;
a6o 2cos4' r=o' "o"ar=
j, 4x=t:+2nk,hez; "=xft*!,n.2.Bidnoaida: \"+Y: tL tI!,n.eez.3) 2cos r cos r + cos 2t = O' c$ 2t(2.os x + l, = Ol
cos 2.r =o; 2t = \ + nn, n ez;, = f, +\, n ez;
a6o 2cos r + 1- o, -", = - j' * = t(" - ;) * r^0. *. z; x = x2] + 2nk. k e z.
aio,o.ia,, lt!; x! + znn, n, * ez.
4) 2sil:. 2x - zsin r sir 2, = 0; 2sin 2r(1 - sin .jr) = 0i
si.' 2x = oi zt = nn, ne z; r=!, nezl
a6o 1 - sin r = O; sin, = 1; a = L a 2nP, P.7.
BianosiAb: T, n EZ.
5) 2sin 2r sin(-r) + sin t = 0; sin r(2sin 2, + 1) = 0;si'rx=Oit=nn,neZia6ozsin2t+1=0;
"i"2, = -f,t 2r=( \r.]+nh,hez; x=ttl'fi+!,nez.Biotuoliab: nnt (-1rr ++5, n, ne z.
464 iial AITEEPA Mep3nrx a. r. ra iH. aKaaeMi.rHr4t piBenb tllli:tlJJlii$
61 2sin2xcos2x+21+cos2x-l -0i 2sin 2-r cos 2x I I cos2x- 1=oi2
.os 2-r(2sin 2r I l) 0i
cos 2* = o; 2r = ! + nn, n ez: x = L +I!, n €2,
a6o2sin2x+1=0;
sin2x=-1: 2x = l-|t'-t ! - nk. k c z. x=t-lt''t n tnh.k.2.2 6 12 2'Bidnoeido: ! r $r 1 ry' ' ! r!, o, u. z.42 1227) -2sin 2t Ein(-r) = Ssine t; sin t cos .t sin .t - 3sin'2.f, = 0;sin': .r(4cos .r - 3) = 0:sittr=Oix=nn,neZla6o4cos.r-3=0:
"o"* = 9, *=tu'""osB + nh. k eZ.44Bidnosidb: nni 1*""o"1 , fih.n.heL.
48) (sin r + sin 3r) + (sin 2r + sin 4r) = 0; zsir. 2t cos x + 2sir 3r cos r = 0;
2cos x(sin 2.ir - sin 3r) = 0: zcosr.zsinfco"{ = o:
cos -r _o: -r ' n +nn.nezl
"0. "ln 1I = o, 5{ - op. a. r, , -2nh2 2 < 'R'Li
a6o cos;=o; f,=!+n*,^ez; r.=n+2nm,n. z.
Bidnoaida: \ t nn: 4; n + 2rtln, n, h, m e z.259) (cos 7r - cos 3r) + (sin 8r + sin 2r) = 0; 2sin 2r sin 5re + 2sin 5r cos 3n = 0;2sin 5r(cos 3r sin 2r) = 0;
z"i"s'l"i"l n-a*l-","2;l -o: 2sinsx 2sinl n 5*l"o"l n 'J=o,\ 12 t4 2t \4 2l
sin 5t = O) 5x=nn, ne Z: x =!!, n eZ;
.6. "i"l!r-rl =0, E!-!=n*.xcz, !!=!-np.1,.y,\2 4) 2 4 2 4
fl2fik--+ .keLi105-lxnl- xnn-x3n
aoo cosft-aJ=u; 2-a= i+tin, ncL, t= -+n^. ^.zt3nx=-+nmtnez,
n 2nh 3nBidno6'db: ;'i;o---'t -;' - nm, n. h, n -2.
10) Jfsin2.r-2sin?'sin(-2r)-O; Jf sin2,r+ 2sin7rsin2.r = 0;
sin 2r ('6 + 2 sin 7:c) = o;
si\ 2t; Ot 2x = nn, n e Z; x=Y,n eZ:
:i!f!i.:iilli:i:il:.:: uresPA Mep3rrKA, r. ra iH. AKaAeMieHrli piBeHb f.i:J 465
L
a6o 2sin?i+ J3 =0t sin?x= -;; 7x = (-lt'i ! + nh, k eZ',
x=( 1t*\L+!!.h€2.21 7
Bidnoaida: "": r It' " "".n.kcZ.221 7
861- 1) 2sin r cos, + 2sin r= 0; 2sin r(cos a + 1) = 0;sint=O;x=nn,n.Zia6ocosr+ 1 =0; cosr= li t = n+ 2nk, k e z.BiAnoqiAb:nn,neZ.2) 2sinrcos, cos,-(2sinr- 1)=0; cos r(2sin.r - 1)-(2sin:, 1)=0;(2sin r 1)(co3r 1)=0;
2sinx I o; ";,'r- 1; r=1-l;"\+nn,ncz;26
a6o cos x - 1 = 0; cos r = l; r = znk, h e Z.
Bidnosidb: l-1l L + nn. 2nk. n. k . Z.ti
3) 2sin':4r sin 4jr = 0; sin 4r(2sin, 1) - 0;
sin4r o; 4r nn,n z;x f,!,n.t;4
a6o 2sin,y I 0: sin,r .1: r=t-1f !+nk.hcZ.26
Bianoair Y. t-ltt \ + lth. n. h € 7..464) 2sin 3jr cos r + cos r = O; cos jr(2sin 3r + 1) = 0;
cosx O:,r fr tnn.ncz:2
a6o 2sin 3x I 0i
sin3r -': 3r -r-ll'r'' -nh-n-kc7- i=t-lr' t:-+':!.k-7-26183
Bidnoeido: !-nn t l)^'l "'1.a.F=Z
21835) sin x + sin 3r + sir 2r = 0; 2sin 2r cos, + sir 2r = 0;sin2r(2cosr+1)=0;
sin 2x = 0,2x = nn, n. Z; x=!,n -Z:2
a6o2cos,r r 1 0: cosx l. t -2n ,2nh.hcL.23R'an^Aiah !!!. +!!+2nh n he7
6) 2sin 8-r sin.r 2sin2.rsinx 0: 2sin.r(sin 8r - sin 2"r)=0:2sin , . 2sin 5r. cos 3a = 0;sinr=Oir=nn,neZ;a6o sin 5x 0; 5x nh, k eZ, t n!
, o, ,,5
a6ocos3x 0: 3x fr -nm.ncz: t"n-nt.^.2.263Bidnosidb: fini !' t !' , !" . n. P. rn.2.563
466 !i::i A'TEEPA Mep3riK A. r. ra iH. AKaAeMi.{Hrr piee}ts
'tiil:iiiii:lii:i:i
7) (sin r + sin 5r) + (sin 8jr sin 2js); 2sin 3:r cos 2r + 2sin 3r cos 5r = 0;
2sin 3x(cos 2, + cos 5 rl = o; 2 ein3z. 2 cos! cos! = o;
s in 3.r 0:3,r,rn-nIZ: I=!,ncz;ll
a6o cosTr o: 7x n I nh.h.z: ,=!+?!!.k,222277-.3l^3xn-n2\maoo cos 2 ui 2 2 "^,.-Lt x.- 3t 3 .ntL.
-finfiznkn2nmBidno6ia)b: :i :- : + .n,k,mF7.
s) .E cos5.r + 2sin(-2)cos5.r = 0; cossa(.rE 2srr 2x) = o:
2105t.
J2 2sin2r.. o; ,,"r-=+. 2x=t)f X+nk,k.z: x t t: ftk.h.z.
. ,.,n nhBidnoqidb: | ; ( ir; ;-n-h,7.
862. l) sin,r.sin,3t t, l-'osxrl 'os3}-1.22221 cos ]' + 1 cos 3ir= 2;2 - (cost + cos 3r.) = 2i 2cos 2xcosr=0;
coe2r = O,
cos r = 0i
lz* =! * n,,, cZ, x=n +rn , n. L,242_lx=" -ak.hcl: lx " n*.*-2.
!+Y.oez. L+nk.kez.4222r cosj.r -.osz 2.r + cos'a. t.5, 1+-"2' "osF , I "i"6'= r.l,1 + cos 2x + 1 + cos 4r + 1 + cos 6r = 3; (cos 2ir + cos 6r) + cos 4r = 0;
2 cos 4,r cos 2x I cos 4x 0i cos 4,r(zcos 2r. , 1) = 0; [:'"41= 0-
2cos2x+1=0i
l. n I n nn - I ^ nnl4x= ?tnn,ncz. x Bt 4.nez, lr s.-,n<L.I I r n' I
l"o.z' '": u=Lln-!l-rnu.u,t, l, -i,*.a.2.Bidnoeida:
ft ft!.a-7, 1L-nP,Ps7.8433) cos 2r - cos 8r + cos 6r = 1; 2sin 5r sin 3r - (1 - cos 6r) = 0;2sin 5r sin 3r - 2sin'z 3r = 0; 2sin 3r.(sin 5, - sin 3r) = 0;2sin 3a. 2sin.r cos 4iu = 0; 4sin 3, sin r cos 4r = 0!
l"sin:.r=0, [3.r n,,,nFz. l' "{.^'z'sinx 0. x=nk,ktZ, x-fik.k.L.cos 4r = 0:cosar=u:
fax n t nm.n.z: l"=E-T.^,r
BiAntuiAb:
:::iitiiiitiii!: AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hxn piBeHb *:l 467
oe;rr-.atxu 9=nh: n=3h.ro3
BianosiAb: +,Iezi4) 1- cosr.=ts,r siD.x: oA3: ,.; "",^czi r-cos.t lll';-"'"',
sin.rll-cosr) cosx(l -cosr, sin.r(1-cosx) ^.
tc=21th,keZ,ctg.t-1-0,
x +f,+ nn, n ez;
BianoaiAb:2fik. k e Z. \+nm,me7.4
5) sin t + sin 3:t = 4cos2 xi 2sin 2r cos r 4cos' * = 0;2cos x(sin 2x 2cos t) = 0;zcos (2sin t cos r - 2 cos t) = 0; 4cos'z r(sin t - 1) - 0;
ln. lt=-1fin-naL.cos.r=U, | 2
lstnx-t=o: I nL lx= 2LfiR.neL.
Big6ip ropesis:'gas. pzcyso$.
BiorLoliOb: ;+ nn, n ez.
6) cos 2r = \E(cos, - sin r); (cos' * - sin' r) -'E(co"t
z=L+2nh,kez;
7) sin'a + sin'2ju sin'z3r sin'z4r = 0;(sin'? r - sin'z 3jr) + (sin'z 2r - sin' 4r) = 0;(sin, - sin 3r)(sin r + sin 3r) + (sin 2r - sin 4r)(sin 2, + sin 4r) = 0;-zsi'l r cos 2x . 2sin 2x cos x - 2sin r cos 3r . 2sin 3r cos r = 0;2sin r cos x . zgin 2, cos 2r + 2sin r cos r . 2 sin 3r cos 3, = 0;sin 2r sin 4r + sin 2r sin 6r = 0; sin 2r(sin 4r + sin 6r) = 0;sin 2iu . 2sin 5, cos r - 0;+-.meL,a4
lnl-t"lI= +-,meL.184
fr-*"-=0,I cosr - sin.r = 0,
lco" r * or
sin2r = 0,
sinsx = 0,
cos r = 0;
Bidnoafit: t. keZ: L+nl.LeZ.
fzx=nn,neZ,i
l'x=nk.hez.lx=!+nl,leZ:LZ
2
5
t=!+nI,IeZ.(1- cosxxcos.r - sjn t)
^.
lx=2\k.kez.t=L+nm.meZ,
4tirlr + t+ n4 n e L.
8) cos'? r + cost 2r + cos' 3$ + cos' 4x = 2;1 + cos 2r . 1 + cos 4ru 1+cos6, 1+cos8r ._
-+-+-+-
2224 + (cos 2t + cos 8t) + (cos 4* + cos 6r) = 4;2cos 5r cos 3r + 2cos 5r cos r = 0;2cos 5r(cos 3x + cos r) = 0; 2co3 5r. 2co8 2r cos, = 0;
5r=!+nn.nL7. l,=" "'lcoss:=o. ^-'-*"" "' '-10l-n,rk-Icos2r 0. 2x " Inh,k-7. x" -tr'!).6a7.lcosr=o: -
l
' x=!-nt.teZ: lx=!-ttt.tcz.L2L2-nnkBidnoBidb: to|--,nezt i,;,k -r.
- sin t) = 0;
r 3r;
3': +n
62x
+
:+2fi
2cos
cos :
IL6r
eZ-
6x
z,
s9t
2cos
;
nl+-nh
o;2r
1
2'
t-+
cos 9x + 2cos 3x = 0;
cos 3r = 0; cos 3js(2cos 6rc + 1) = 0;
nn-lnnn3163
I
+2th h ezt l, = +!*!! e "z193
(cosr - sinrxcosr + sinr) - 1E(cos.r - sint) = O;
, cosx-sinr=0,lcos-r - sin.rllcosx ' sinx-J2l 0l L' lcosr'sinx-Vz - 0i
cosr sinr=0rctg.t-I -O:ctgx li x=ft -nn.n.Zt
cosr+sinx-rE=0r cos x + sin r = .lz : ,Er {cos'+{sin'=r;'12 .12
. n n .... ,. .-rn -l=r, ,-\=I -znp.*eztsin4cosx rcos-arnf rt srnl- I -t.) 4 z
x=!+nn,nez,
, =I * 2nk, k.z.
BfinosiAb: !+rm.meZ.4
468 :}il: AITEEPA Mep3rrKA. r, ra iH. aKaaeMiegnr piaent li{lll:}i.iilil:.i
,- . 1Fcosl2r 1-cos10.r'22
2+cos 12x + cos 10.t = 2; cos 12r + cos 10r = 0; 2cos 11r cos r = 0;
, cos11x = o. rtx=|-nn,ncz. -=h-#.,,t.| "."' = o,lcos'rru:
,x n nh,he7: x !.nh.k.Z.
.^finn22 11
iitiili_:ilii-1t1:jii AITEEPA Mep3reKA. r. ra iH. AKaaeMi{Hrt piBeHb lt! 469
I
" 1 lrcos2.r I cos4r I+cos6r' I2) cos' ,r - sin' 2-r + cos 3-r ;: - 2 --Z *- 2 =2i1 + cos 2r - 1 + cos 4t + 1 + cos 6t = 1; (cos 2t + cos 6r:) + cos 4ir = 0i
2cos4xcos 2, fos4x=Licos4r(2cos2.r+t) ., l;x;;:; =.,I " I n nn n,n!.n-z.l4x=-21nn.nLL. lx=B) 4.neL. " e q'. -.
.t t-cmzx= j; 1r' rt'2nh.k(L
lx -!':t nh.k(z-
si3n66166; La!!.16y.a43) cos 2t - cos 4]' = sin 6t; 2sin.r sin 3r2sin 3t(sin t - cos 3t) = 0;
sinSr = 0,
sin. cos3t = 0;
flx=nn.nez,
l"', ","{r ,,1 = o,I \2 I ("-i)=''
4\ sin2r + cos2x = ."E"i" r; f "inzr+f cos2r=sin.t;
sin2rcosl+cos2rsin|= "t'' "t"(r,ni) "t"' = o'
. [,",:_lJ n,.r.[l*ll-"l.'"*ll =0, I \2 I
-"-..{ 2 8'"""r 2 st - L"*fr;_l .,
l* -n.on.n-2. Ir n+2rn,ncz,12 8 I 4
l:' s,, - I n 2nkt ^ ,:::"nk-hL7,: tx=-1 .hLz.L2 8 L 4 J
.n2nhBidno6i.Jb: ;+znn,ntzi ;
-;'.kez.
5.) cos' x , cosz 2.r. cos2 3r I cos2 4.r:
l-cos2x l-cos4r l'cos6r I cos8.r.2-t 2 T 2 '
2.os 3' cos r 2cos 7t cos .! = 0:2cos t(cos 3t - cos 7jr) - 0;2cos t zsin 5r silr. 2t = O.
47o tii AITEEPA MepsntKa. l-. ra iH. AKaaeMi'{Hl4i piBett ll!.i:iilliiiJtl;i
] sin 5.r = 0,
Lsin2r = 0i
BiA6ip rcopeniB:
BiAnogiAb:
ItJ'= s'1,,1,,*r.l2
2sir 3, cos 3t = 0;
lonl3l'"*[* ;)-"
,meZ.
Bianosiab: !!, h ez., S,nez.
2x=nn,neZ,
"o" r, = 1,
2
u, ","u'=r-"13*z*J; "i,' o" = 2sin 2.r; sin 6x sin2x sin2j 0;- lsin 2.r. - 0.
2sjn 2-rcos4n sin 2,r = 0: sin 2"r(2 cos 4x - 1) = 0: lr_"0,_r =0,
l'=+.".'. l,=+.^.'.'lqx =,! - zn*. * -2.. l, =, L -!!. o. t.31t22
o.z, xL +4. * ez.12 2l,=+.".'. '=!.,.2.lr, "=nu.o.r. l, ;-f;.r,t.l,'i=;'"^,..2, I' i rm.mcz.
Bianoliab: T,n ez: !,S,n.z; f,+rm,^ez
2
!6 &F ? = r.r.2
s65. 11 -l2 l,'x+2 2 r31 6+5r+10,n.
tx+2ltx-21
3-1
3 5 3 5 3(x 2\t5(x t 2\x-2 x-2'x-2 x-2-"' lj.+2)(x-2) -"'
8.r.- 4 ^ 8.x+4 - fsx+4=0,
->o: -=u:
Itx -2ltx -2t tx-2Xx-21 [(ir-2X-r-2)+0i
l2tIr n| +-=nn.neL-t2 aIl3v rr r_+_= +nk.ReLi242
sianouiao, ( -2, -!]u o, t *t.\ zl
o, 2 . A 2 _ 3 .n. ztxr5) 3(l 2-r) <^.-' I 2x .x+5' l-2x x-5-" {1-2xxr r5) --'2'+10-3+6' 8r,? lS.r-7=0.<0:
-<0: 1(l - 2.r)(-r + 5) (1-zrxr{5) l(l - 2r)(.r - 5) + 0:
--i\ /'-:\,-i\ /- -57
8
Bidno'idb: l', l].-1 i, --l
::il::i1:$:i:,jt:l AITEEPA Mep3ncK A. r. ra iH. AKaAeMi,{Hrai piBeHb !lt:
1u2
I cnraB..5'7
II crnaB vxr ' 7"
Paaonr x+Y=28 !'+!,=tE7 7'
866, ,qns po3B'nsyBassa BaAa.{i crina,qeMo ra6,1sitto. S69, 1) sin3 4r + coss 4r = 1 - 0,5 sin 8r;(sin 4.r + cos 4r)(sin'z 4r sin , cos 4r + cos' 4x\ = 1 - Eirr 4, cos 4t;(sin 4r + cos 4rX1 - sin 4r cos 4r) - (1 - sin 4r cos 4r) = 0;(1 sin 4, cos 4rxsin4r + cos 4a - 1) = 0;(1 - 0,5 sin Srxsin 4r + cos 4r - 1) = 0:
I - 0,5sio 8r = 0, I sin Sr = 2, I ueruac xopeaia,
fsina-r+cosar - I 0t lsin ar r cos4x.li lsin4r+cos4x=1.-L"i"n',1.*n'=1, .i"a'"""I-.""a'.inr 1,J2J2J2nnJt
MaeMo cucreMy:
Po3B'fi )ri€Mo Apyre piBsssEs:
!-et y=6U7 =zt, s=zr,
[x=2a !t,
J ze-o *so -,n.177t40 -Ua +aa _u. tno;rn
=rn,
lc = zt'
1tn
2
fifih-
lx+v=za.
ll'.1,='n'zo 2-!
= t a,:7
BiAnosiAb: 7 Kt I cnnaBy; 21 rr - II cn;rary.
867. sin r + cos r = 1 + sin r cos r;siIIr sinrcost+cos, 1=0;sin r(1 - cos t) - (1 - cos r) = 0'(1 - cos t)(sin , - 1) = 0;
T-- d-- ,t-cos.r=0, lcos* t, rr=ztrn'nF7'
lsinr - 1- o; "in,=r; lx={ .2nk,hcz.L2
Bi,q6ip EopeHiBr arB. ptcysorc.
BiAnoai()b: 2nn. n €2 . fr +2nk.heZ.2
1
868. 1, sin 3x cos 2x = sin 5r; i(sin x ' sin 5r) = sin5x:2
sin a + sin 5r - 2sin 5x: sin t - sin 5, = 0;-2sin 2t cos 3t = 0;
lsin2r = 0, lzx=nn'nez'fcosa' = or
lzx = f,+ n*, * ez;
BiA6ip &dpeEiB: Ar.rB. prcysoK.
^fifih-Blonoetob:6+n',ReL.
I2t 2coslx t 2o'i cos .r = cos 40"t 2 ;
(eoE 20'+ cos(2,. { 20")) cos4o"i
cos 20'+ cos(zt + 20') = cos 40'i cos(2t + 20') = cos 40'- cos 20'icos(24 + 20") = 2 sin 30" sin 10"j cos(2t + 20') = -sin 10';2, + 20'= 1(180" arccos(sin 10') + 360"4, n € Z;2r=+(180' - arccos(sin 10') 20' + 360', n e zi
\; = 1l 96' '-srqqeslsin tO't - 10'+ 180' n, n € Z.t2)atanoaiad: t(so" ] *""o",",n r0")l - ro' I t8o' n, n cz.\2)
472 i.l,* ,'IiIIEEPA Mep3reK A. f- ra iH. AKaaeMi.rHran pieexr !ii:iiff.;..;.;!!i
,"t(
"'"(*-lJ=#, +,+f,=ttt'!*n .,€z' 4' =( D"f, f,+nn,nez;y = 11y L - !- 1Y. n a7.16 164Bianosiab: err" + - #+ f, , n e z.
2) sinBr + Ja cosBr = z*"s'; |"lna,*fcos3'=cosbr;sin3rsin i cos3rcos
f, - cossr: coslar-iJ -cos5.!=0:
-zx-!. g*-!-2sin 6sin 6=o:
22
3) cos 2.r + sin2: = rD(cos'2r - sin'2*);cos2r + sin 2r = Jt(cost 2.r + sint 2rxcos' 2r - sin'? 2r);(cos 2r + sin 2r) \E(coszr - sin 2r)(cos 2t + sit2al =O;
, tcos 2-r r sin 2,r - o.(cos2-r + sin 2rl(l - V2(cos2x - sin 2.r), . 0i
r-rc2.r=o, II v2(coszt sin2t)=o;
l+=-.r,-"*r,.lJza) 1+ ts 2r=0; ts2x=1; 2z=-!+nn,nez; x=-[+l,nez;
6) cos 2ir sin 2r- | ; *"o" z* - *"tn z* = 1;'J2J2J22
coslcos2x-sinlsinz'=1, *"lz'.') r' 2, , ! = -\ * z,*. * . z,4 4 2 \ 4) 2 4 3
zx = t!- l+ znn, x ez; z = tfi -[+ n*, n ez.
^ fiItn _ 1l 1rBi0no6i0b: ;t ,neZt !:-:+nk,kcZ.
ilili:i:tjlli-itiAnrEEPA Mep3rtKA. r. ra iH. AxaaeMiqHxi piBeHb::it 473
'1
azo. 1') 2cos4:21= x, + 4r + 6: 2"o,t !!1 = ," ,, 4r,, 4,,2.
2"o"t-!3a = 6 + z)" , r, "o"t1?' = !r'+ 2)2 + r; piBBrEEs Ma€ RopeHi,
"*uo |{,+zl" =o; t = z.
BiAnosiob: -2.
2l grn!1 = "
- 4" * 5; "i.n14- = "" - 4r * n+ 1; sin 11 = (r - 2), + 1,
piBEsEss Mae KopeEi, rKryo (t - 2rz = O; t = 2.BiAnoqidb:2.
7. Po3B'r3yBaHHr Haf npocriulrnx rpl,iroHoMerpr{Etax HepiBrlocyefi
821. r) su.t < ];-U+2nn<r<!+2nn,nez.
BiAnMiA6:
(-!*zn,t!,zn^\.o.2.\trtj)
t;2
-!+znn<x<!+znn-nez-44
BiAnMiA6:
(-i,2,,,! * z^1.,.t.
Z) si.rr > -f ;
-!+2nn<x.s!+znn,nez.
BiAnosiAb:
|-!*rnn ! n ro,], n.t.
t;4) cos r 5 J9;
n l7n-+zfinSx<-+2fin,neZ,
5) te, < -l;nfi
-- + nn < t < - - + ,tn, n e Z.
BL0noqidb:(x z l\ -+nnt- +nn),nez.
?) ctgr < \f3;n
-Bianosiab: lt+
thi n* n,)., n.z.
9) sinr < ;;-n - arcsinl + 2nn <.r < arcsinl + 2nn,
ne Z.
or tsx>f ;
[+nn<x<!+nn,rez.
Bia,o6ia,,li
t>-1t3r4
sianoaioa: (trn: ! + nn), n ez.
10) tgr > 3;
-|+ nn < t <|+ no, o ez.
+ftn;-+nn).neZ.
nn, n eZ.
8) ctg
i
BiAnosidb:
f;, r^,t!t n r^,],,.t.BiAno6iAb:
(-,, - *""in I * znr; *""i" 1* zn"),ne Z.
;i:llilillllilii Ai|-EEPA Mep3.nr( A. r. ra iH. A(aaeMi.rHri piBeFb li:i: 47S
Bi0nosiAb:(" z \
l-t+lutt+nn),nez.
+ in < x < T + Itn, n aZ.
a7a l:i!i urespl Mep3reK A. r. ra iH. AKaaeMi{r.nr pieenu Lll!ill{:!ili.:;!
ezz. t) sinx <!;-! + znn < z <f,+ znn, n ez.
BiAnosi1b:lsn ' - l| -- + 2ftn. +21tnl.nez.144)
rr "n.
r < 1,'2L+zn<t.!!+zn".nez.
BiAnogiAb:
lL*z^.,4*z^,].,.2.L3 3 I
5) tgr>-1;-\+rn<t<\+nr.nez.42
2r sin r > -1:2
-! * 2nn 3 ,3!A a 2n1. ,y 67.66
BiAno6i0b:
I ! , z,^,!! * zon). n .2.16 6 )
1;nr "."" f r
-L+2nn<tsL+2nn.neZ,66
BiAnoqiAb:
-\l-:*2"";:*2"")'".2
O; tg .t < -",6;
-|+rn<'<-!+n","e2.
BiAnoaiAb:
ln n )I t+ ltnt - 3+nn),neL.
t;'3
nn<t<-+nn,ne Z.
aianoeiat: (nn;!+ nn), n ez.
s) cosr > f;-"r""o" | + 2n, . ". ur *",f; * zn,,
(- **." | * ,no, u."" o"f,, zn ),
o .
873. 1) sin 2.r > f ;
!+2nn<2x<!+znn,nez;! +nn < x <1+ nn, n ez.
8)ctgx<1;
f,+nn<x<n+nn,nez.
Bianosi1b: (arcclg 2 + nn, fi + nn),ne z.
a €(-;) .v6' ,ei, Ji'rtn--+1tn<-<-+Itn,naz,
!+4nn<x<2n+4nn,nez,
BiAtuosiAb: !+n",L+"n.1.".2.\,6 3 )
\l--+nn: +ttnl-n€L.L4 2 )
BiAnoeiAb: Bia oBi,b:
| -1! + 4nn; 2n + +nn l. n e z.\ir)f, ra iH. AKaIeMi.{Hr,rfi pieenu llJ
sianoaia': I! + nn n+n^)..e14 )
10) cLgr <2iarcctg2+nn<t<n+nn,ne
476 iii: AnTEEPA Mep3nr( A. r. ra iH. aKaAeMi'rHrr pieexu it!:illtli:iJ:::!, :ilil:igllll*ti AnTEEPA Mep3"K a.
3) cts 5' > 1;
n+nn<5r<!+nn.neZi4
finn+ .n€L.5205
Bidnosdb: ( ! | L + !!). n E z.\5 20 5)
ll4) cos( 3x) > ;: cos3r > t:
11-arccos; r 2,'In 3x. arc.os I
t2^n,n-Zi
tt2nnIl2nnI <Ja<-STCCOS +- ,na/.333333( I 1, 2nn 1 I z,Tnl
Bidrodidb. l-5a'ccos3r- r
3ar.rosA I 3In
a74. 1r sin{ < 1r
-U*2,,.!.!42nn-,E7.6367fi
--+tifin<r<-+tftn.ne4.22
,, *'l {) '"6, cts{. "6;5]Ir--+nn<-<T+nn.neLi!!+znn<x<2x+2nn.nez.3
Bionotiab: (+ + 2nnt 2n + znn), n e z.
3) te 2,r < -;:L+n,<z'<-\+nn.nez:26
nfin+-<I<--+.neL.
!nftn n nnlBidno6i0b: \-i+ tt - i+ t ).
n e L.
1
411
arccos i + 2nn - ar < 2,T arccos- 'znn,n-7i44l lrn nl 1nn4422442
,l I nn r I 1 nn\Bidnosidb: \iirreos- - 2i 2-iarccos-+nl.ncL.
/-\875. 1) tq x-llsJS;t r/
_!*nn., r.\ +nn.,.2,
-1+ 1+ jrn<r<I+ L+n,.net,n2n
- +nn<r<-+nn-ne7-63T-
llLalnoBLtlh: - +ftn- +frn ne),L6 3 l
2nn2nnT+ 6-2nn\2t< Z t-+2nn.n€Zi
!+2nn<2t<!+2na.ae7'26fi5fi--+1ln<x< +fin,neL,
- (n 5Jr )it@no8db: l-i+ nni-+ \n ), tr e L.
' "*(;-r'#, "-(,-l,),*, "ic(,-i).-;, v
2nr+ltn<x-:<fi+nn.n€7i
2fitifti+i+^n<x<n+ +nn,neZl
llfi 5'I _+nn<x<-+1tn.n€L.
(tln hn \Bidnogidb: l + nni
- + fin ).4 eZ.
4) 2srnlI-3xl< J:: sihl ax- Il- '6. "i"l s,-Il' - /3.\ti ,r \ 6) 2 \ 61 2
:: + 2ttn < 3, _ t: < ::: + znn n e 7 :363! 1! n 211n. 3r. !! + ! + 2nn. n e 7.:3636
-L + znn <sx <1! + zn,. n e 2.,62n 2fin n 2nn- + t)aa_+-.nF/.-1832s
I n 2nn n zrn)llidnoaidb: - + : +- ne7118 s 2 3lsr "n"l{*rl<-f,\2 4J 2
!.z, <|*|<!+2nn,n.z'
t+zfin<-<n+znn,ne7:T+ 4nn<r<2n+ 4nn, ne Z.BiAnMiAb: ln + 4nn; 2n + 4nnl, n e Z.
47g li:l ATTEEPA Mep3rer A. r. ra iH. aKaaeMi.iHur piaexs :i:iiiJlil{l:ii;i i :iiiii:iiiltii:ti AITEEPA Mep3rqK A. r. ra iH. A(aAeMi,{Hrr piBeHb !:!l: 479
6) sjntr _ zrr . [email protected] ^
-"'' -T' -"'n,r" -tt. -f ; sj,r2.r _r)>i + 2nn < 2x - t. ! * roo.,.,.n"
I' 'r' "- "* ,T ' t '2on. n u z,
"-r..*"..t-j,+na.nez.Bidnoaidb: (! + : +
^r, 3 * f * _- ), , ,,,,I,nez.
e7o. rr "t"f,*Il- E -| 6/:vt'i nn<x4lI<fttr A'6+n"'o.r'-E+^h<rSnn,nez
s, -"1*_rl,l.\ 6)-2,-Ir2*r*_[r{*r*.,.r,-i+u +2nn s,rsr*
!+2nn,nez,-u+2xn<r<[+znn,nez.
ffi
3nn;--+2nn<a,n\ ni- ' 2'i-;+2nn.neZiii*2"".|.ff*znn,ouz,r 77n
sinl r-:11-, s)-
3) -2<tgr<8. n aZ.
4) -1< cte, s JB. c2
Bi0noaiOb:{-.arctg2+,rri srctg g +fin),n€2. Bidnostab:
",u*",u", f_ ; * rn,, | * zo,l. o u z.er ":n/e.*I)- 6.2n n tt =-V: -f - zxn t o, - ! , - I -
"o,, n-]-5 .2nnsr*s -[. lr, rnn. n.r,
-;=+2nn<z-- Bn,,j -.^ =_G+2nn,neZi
-ff*f s*s-?l-^, _ _tE z ,,, . z.Bidnosiob: l' !7! , nn 2n __-
- i 60 i'-l;-V1.,.2.877. lt r*
= "o",. lz -^'t ^ r, _, s sinr <
!rnon.,.$*on,,o,i.a'a^"tu"' (! r nnn: tJr
r axnl, n e z.ar z"i"/f -*j.r, _"in/* _tl. t.-
:-,^*.. #.,:, r^,.,!,,'
^i. t' ^^,..,. ! . !.,,,. ^.,,i*rnn.,.#*rnr.n.r.
"'u'*tu,' ( [ - r*, ! + zt,), o e z..,*(;.;1.f, [-,8*2",'-]*z"n)ut,/ I * ,--. sz I\3 -"'"8+z^n].nez. [-,6
* zo", un":" ] r znnJu
tl o -"""un!*zn, 3I* 2o,,],
ii:ii:iiiiii:;iii AnrEEpr rrr.p"r"^;. ""'"4
Ld " nn; ::: - M I' n . z.rh !,, r4e,nM. r l
--"'^^' r' ra iH. Arag.ri""r,i pi".r" ii,ji,, +8t
./3 r878. 1) -; < cos x <
Bionoaida: | 5n, znn, 2! r'1. l?-*"'T
zr J<"r*'<j.
3) -4<ctgt<1,5. ll -@. tg'. r.
BiAnosiAb:(arcctgl,s + fin; n arcctg 4 +
"tn.r, ":r:=4(€-t)=Va-Ja Ja(Va-rld*"" * sit^""- "Eii("t; r a"6)
'' ,t^4iii . sG r'r*,,t,t' - {n ' 311;i + a{nm + sJi (G t aa,E)'
a+8 ({; *z\(e["" -zli*n)
8so. 1) E !E:!)' .o' 1lfSf = o,
BiAnMiAb: L3; -2)u (-2i 1).
t'-st+4 x'z 5x+42l
->0: -=U:
'r'-6r+8 -r' 6r+8
f.r=4a6oir=1;lxr4a6ox+2.
[t:-rrrx+rt'= 0: [x = 1a6o r = -3r
lrr+zr'?*o; l'. z.
2
-2
-1
* zn,), ,.2.
-4
BiAno6iAb:
nn), n eZ.
=16+1;
XE;
tn n )l- 6+nnt +Itn),neL. finnnnn
6262
(ta-rX"6.r)<Ja -r
;\,'-:\/'-:\/-+
It'z - sx + + = o: lrx- nXr -rt = or
lx'-er+s+o; l{x ax-r-2)+oi
BiAnoqiAb: C*: 1l u (2i 4) u (4; +-).
", (r + l)t.r 3f , ^. (x + 1)lx - 31'?
0;t+4 x+4fr'-tx'-at'-0,' la6o-r=3.
l:c+4+o; lr* +.
BionosiAb: ( 4; -11; {3}.
Aal. noAis A rossa AinLEr.rEa rrrcna 32. Airbllr.:Kr.r 32r 1, 2, 4, 8, 16, 21.,l.l'63
Pl Al = -''n32 16
Bidnoeidt: 316
.l;gg2. t) lcosr 'Y; -'l ' nn- x<'! + nn, n -2.'244
zl Ei"zr.*;rr ,t--+[z<x< +nn.neL:66
n2n-+nn<x< ^ +nn.neL.
Bidno'idb: | ; "J, ;- T).,.r:litlit{i!:llil A'||EEPA Mep3nrKA. r. ra iH. AKaAeMieH}rr piBeHb ::*
+)/-:Y-r\f+ ,
t\/.=\/,'i\/-+
Bianoeiao: I i. "",i. ""1, ".2.
482 itl: AnTEEPA Mep3reK A. r. ra iH. aKaAeMieHltt piBeHb lliilliltl:liiii 443
4) lcts irl > 5.
'.i"'(,-i), "a, "u(, -;]'*,nn < , -! <! + nn, n ez:
ea3. r) sin'f +cos'f '|; "n'f .2"r"'fco"'f +cos'l-zsio';"""';'rlt ^' ".rr 1r2x I - | ,2x flsin';" cos'fJ -2"'r"T,2: r-
2srn T>2t
-' '1"T,-t, r-"os1'<2: "o"rr.r,2223Uar 3rr 3nrt
cos a> l: ;?n -2nn.nezi xa 4--.ncz
Bianoliab: r e n,"vi* !+!,nez-a ",(; - "). """(r - "; ..,e, "'"[i - (t. l). "*(; -,)',r,*"(; - I -
"""(; - I > Jr; 2"o"fi "o"' >.,6, r. f "o", = n6,
cos t>!1 x=2nn, n€ 2.BiAnosiAb:%n,neZ.3) sin , > cos ,; sint-cosx>0;,-\"i" ' - sin{
tr-.rl>or z"tnl *-I]cosn =0,- "^ "'l2 ""1- -' --"-l 4) 4
,","1 ' 4] @=0, "i,'l' 4l zo,\. 4) 2 \ 4'2nn< r -L <n + 2nn. n eZ:
4
L+zn <x<4+2nn.nez.44BidnBiab: i+zttnt - + zltn I n e L.
+t ]lajYr J5; oA3: sin'-cos,*o; te'+1;
"in"-"i.1 ft
'l z"t^**"l." "l" -"'\2 '-) t; 4 \ 4). t;.ln I - I ,rl ,I
sin .r - sin | 2 - .r J zsrn ['x - ;.]cos 4
rrttfi,-+Tn< x < 6+i+fin,nez:fi5,I+rrn<x<-+1ln.neL.
^ lft 5n )Blono6tdb: \ + ^ni -
+ ftn ),
n e L.
sea. ry rcosrcosl x+l''G, ,'"o, z, '[1 -"il' fe,6, t
"o.l z'* 1l- €'4, *"1 z**11'0,\6122\6,/
+2nn<2t+ <-+zftn-nel:2622n 1t+znn<Zr<-+Zltn.neLi
1l It--+fin<x< 6+trn,neL,
Bianosidb: l -L + nn. ! + no l - n e z.
2) 3 + 2sin 3r sin.r > 3cos 2r;3(1 - cos 2r) + 2sin 3, sin .' > 0;csin'z, + 2sin 3, sin r > 0; 2sin r(3sin t + sin 3t) > 0;2sin r(2sin r + 2sin 2r cos r) > 0; 2sin r(zsin .r + 4sin, cos'?r) > 0;
| - - + frn: - + fin l. n e L.\3 3 t
BiAnosio': (nn: atcctg 5 + trt) uu (n -- arcctg 5 +MI|fi+nr"),tueZ.
.4sin'z r(1 + zcos'z r) > 0;1+2cos2r>0npl,lr€-Risin': , * 0i sin Jr + 0; x+|tn, ne Z.BiAnoaiAb:x+ML,neZ.
885, 1)2cos'z,+3cosr- 2 <0.SaMiEs: cos, = t,, € [-1; 11.
It_-t+-+Ilk,ReL.
2t,+3t-2<0i2t'+3t 2-0iD=25:
-3r5 1t\,,= a i tt=tl
t = 2: -l<t<!: -r<"o"r.1.2/- \
Bfinoeidu lL
+ znnl !: + 2nnl|, n ez.
z1 ts" +(2 - "ls)rs
x 2h <0.
al lte '1. Ja.
-----+->.2-\/z'? .
SaMiira: tg r = t. -2 -./6t' + (2 - s)t - zJz = o; t" * (z - Ja)t - zJa = o;
i::::;:::::::ii:i:::::i:: AIrEEPA Mep3ntl( A. f. ra iH. AKaAeMi,rHri piBeHb i:ii:484 ii:: anrEEPA Mep3neK A. r. ra iH. AKaaeMi'{Hrt piBeflb li{llliiiit:alti
r
.o = (z - J5)' * e'6 = a r.,E + (.6)' + s"E =
= + * +.,6 *(.,8)' = (z n Ji\' ;
. z*'6t(z*.F),,"= 2 ,
t,= 2; t,=.ft; -2 . I . 1E; - Z . tg r < Jt .
!n)Bidnoqidb:
l-arctc2 ' n ;-n ),nc7-
| ", 2,,, 3n . -zn,), (
" - r"", lt' r,',,.] - f
s., znn: 2n t 2nn). n c z.Ls 5 \ 5 / \h )
8, BnpaBll Are noBTopeHHr Kypcy anre6pra ra noqar(iB aHari3y lO Kracy
1. MHoxnHx. OnepaqiiHaA MHoxnHaMn
886..4 ^
a a. C - MHoxxHa HBaapariB.
AA7.A., B=C,C MHolrrHa kBanpariB.
888-I)AwA=At 2rA^A=4.2\A\JB=4.0; 489. 1).4^B=B;
A9O. 1) 35 - 10 = 25 wsip ozeqaprB i Oi3r-rlcy, i MareMarnriy;2) 25 20 = 5 ]J"{]liB saiiMamrbcs nsEre abistrRoro;3) 11 5 -G y.rriD 3aiiuanrrcs i nareuarqriolo, i ibi3lrRolo.Brdnosidb: 6 y.!1i'.
2, OyHKrr;r_, piBHrHHr, HepiBHocri
Agl.l) /(xr=JJ-5: ,ln:r 5>0ijrt5:xc 15:,€l:
zl fto- -]:; D(fr:4 - x> ot r,4; r e (-*;4r;.J4 t
3r /txt ,.s ,; Dtlttx'z-5aoi x*.Js: *.{ *, Jr)r{ Js,Js),-{Jsr '-},4t ft*\=f;AtDtntx€Ri
5) i (*) 7j+]3r D(t)t x'-7x+o.x(x - 7)-{):.r-ua6or* ?i
r'-7t.r€ ( 6; 0)u(0 7)u(7;+-);6) /(irJ r,;
DtD; I,rl -3-o;lxl*3; x--3a6o s:uiJju€ ( -; 3)u( 3; 3)u(3; +-);
Zl 1111=
--L. Dtf). x e Rt
ln +l)
81 /1r1= ll , D(f): l-Yl .r' / 0:,r > oi ,rr ,r , 0: ,r(,r - l) ' 0:lx+r'r + O e6o x + -1, BpaxoByroql,I., > 0, r I 0.r < Ot x' - x + Oi x(x - 1) + oi t + oi t + 1; Bpar{oByroqr .! < 0,,c I 0;r € (--; 0) u (0; +-);
fr , 5:0: fr u 5:9) /(r)= J.r - 5 - V3 - n; ,(n: 1 I x.t5; 3l;lJ-r.]U: l.raU:
. r+r lr-l>o: l::r:10) /(r, Jr It " ,--i D(l)t I { .rc tl: l0)u(10; -):x-10 Lr/1ol ljr/l0r
3),""",(,+;)'","(;-r, r; z".r(,*i)-as.[j-[t'',,)).'''.,/_\
r""Jl '+11 :cosi r+al+1>0.\ 6l \ 6.r
/.\saMiHa: coslr -;J /. I . [-1: I l. 2t' - 3t t
2t, - 3t + 1=o; D =1; t.,=f; r,=r;
Il nrli^= ; -l:i.;r licosl,r r6J<t:
L n 2nn 5 t 1L.5! 12nn, n .7,363
[+znn.".!*zn,,n.z.Bidnosrdb: II t znn:T ' 2,,), n.z.
\6 2 )
4) tg x > 2ctg t; tgt - 2ctg .r > 0jl1̂t+ +ftn-neLi
oA3: I 2
lx+\k,keZ.tg" x 2 > o. BaMiEa: tgr= 1.
tgtt'-2.o. r-2=0.
{r, -.Eacoi. --Jz:
t t [t+0i-nE <t.o a6o r > J2;
,,E<tst<o a6o tg'>'12.
Bidnoaida: I-arcteJ2 ',.nrnn)t u'.ug.,6' ,.r, |-nnl.,.z2t5) sin 2, - sin 3.,. > 0; -z"inf *"f ' o; 2"i^;."s5+ < ot 2st";*"? = 0;
l .i' l = 0, x^ nk- k cZ: l,
^o. u -t, lx = 2nh. k'zl
| 2 l2 lz i ft 2nn
J*"tj =0, l'i i-",.^.r, lsx=n t znn'ncz: l' s+ b 'ncL
486 Iti: AJII.EEPA MepsreKa. l-. ra iH. A(aaeMieHnr piBenr ili:llfJi:i:j:.tji iia:j:iaii{iilti: AITEEPA Mep3rqx a, r, ra iH. aKaaeMi,{Hnr piaenr !il! a8z
11)
14)
lr 2 2o. lx>21Jtxt Jx-z, J2-xt Dtht
\z_r,o,, \,. zi,r, t,
q>o: lx>9: r€ u.ftx\ = Jx -9 + --::; D( l -1E-; -" 18-x'0t [n-8:
v _7 lr_2_0: I.r: ,, ,. t_2:21, t2i t_.Jiftxt=J! 2-i o;othtlx 4,oi lxF_2ix t2i,,-T 5x -4Jr+3 .r'-6x+ I
893. 1) /{).) =
-;.x+2
D(f\tx+2+0:)e + 2i
-. tx - 2\(x + 2\flxl=-=x-zia+2f(tl = x 2;
2) fr.rr=r -6r+9:
,(f):3-r*0;x+3i- {x -3)'? (3 -.r)'z ^
f(r) = 3 qI
fx-620t fr>o:Drfl: ]x+3>o: ]*' e:
Lx'?- 8r+7 + 0i I'r + 7 a6o -r * l:r € [6; 7] u (7; +-);rrt ff,l = J-"t- e, + 9; ,(f): x' - 8ri + I > O;
r,+8.r-9<0;x'+8r-9=0; , = 100;It= 9i r,= 1;, e [-9; 1l;
l116) f(x)=-+ '- ;' Jx' +6x_7 x' zx
Drn, I"*6* 7'o' *.*6'-?' o,'' lr, _2x+01t,+6r-7=9tJ\= 7t xz=1){t + 2, + Oi r + Ot t + 2; xe ( -i -7) u (1; 2)
---i\,,-- -\,/--9tjc
- =\/-\/'-,-70 12
l7t ttxt=Jx-6+ _=- l'l x' - 4x -12
lr-6>0r fx:6;D(n'\,' a* - rz, o; 1*' a,-tz,o.
t, 4x-12>o;t! 4x-12=oi\= 2tx,6 r-518r l{x) = Ji;;- Br'
+ xL e i
hs' a'' t o, l3r(5 -.r) > o;o'n'
1"" n , o, 1" -r. x F (0; 3, u (3i 5).
892. 1) l(,)=#+L Z(D: t1; +-); y=G vropv sa I o,qxH4qro;
2\ to4 = 'G 2; E(f\t | 2; +*li v = J7 vsns Ha 2 osr'rql,lqi;
3) c@J=3- tt E(er; ( -;31; y= x'yropy lra 3 oal.rE{qi;4) f(tt = x' + 2i E(nt I2t +-); v = ,' vropv tla 2 oauErqi;5) e(t) = 5 + ItL; E(q): [5; +-);v= r vropv sa 5 oarHlrqb;
6\ h('\-JVa-5; E(t): t-s; +-);7\ t('\ = 'l-x't E(f\t \alt
s, /rn) fira .li - xt ortt: 1; ; . ;, t; . ;, x 3i E(n' toti
s) f(t)=Jl-"'; t(D: to;11;
10) flirt =:r E{n: (0i +-).
488 r::.j:: ATrEEPA Mep3ncK A. f. ra iH. AKaaeMi'{Hr4i piBeHb ::i:::::::::i:::::::::::i:
4.x - 203) I(xl=-'x' 5.f,
D(f): x' - 5x + Oi x(x 5, + 0lr+0tx+5;- 4rx 51 4 4xt= .:=-i J\x)= i
-r(.r - b) x
4\ tG\ = 5=: Dff : x.+ !1; f('\ = 1.
|ga.\ f(4=Jx+7; fl")=o; G+z=o; r+7=o;r=-7i- r"+4x 5 -.Z) /l,rl =
-: /{x, = ui
t? +4x_5 lx,,ar S 0: x=_Sa6on l; _=(l: I x b:
,r-l [x-l*0: lr/l:e1 nx1=uQ at fl')=0; rt' 6=O; x' a=o; r"=a; x=xr6q f @\ = (x - s\Ji-r t(')=o; (n-s)G-=o;x-3=0: lr=3:I r=3a6oJ.=4.LJ'-a=0: r=ar
iili::ttii:;lil{i AITEEPA Mep3riKA. r. ra iH. AKaAeMi.rHrn piaexs lf:i
0 2
v 0
0 2
U I
1 2 8
U 4 2 1 0.5
[-9,o*,qo*<r;I.r
895. 1l frr)= j-x 2.sKDro 4<x<2i8-
L- .'nqojr>z.
u1 1'1 = -9, "l,,"Poo,,u,
499, 1) l(x) = 0 (ro.*ca reperrHy s Or), 2 I(o'pesi;2) flr) = ll Mae xoqa 6 oanH Kopisb, nKqoa e l2i +*\:3) flr) = a Mae aBa KopeHi rpr a € (-2; 0);4) /(jr) = a Ma€ piBHo oarH l{opiEb rrpz d € (1; +-).
i
I
I
I
sifliftfl
rry
9oo. 1) l(r) = 7ic6; D(f)i t i ( -; +*); /( r) = 7( r)t = ?,6, rapEa;2) fG) = 3r5 - 2r1. D(|Ji r € ( *; +*);fl-r) = 3(-'f - 2(-t)? = 3r5 + 2'1 = (3r3 2,?), I{enapl]a;
6) l(r) = x-2,rpsMa;1 1
U 1 3
e) l(r) = -9, .inep6ora;
2 4 8 16
4 -2 -1 -0,5
l(r) spocrae IIa (-*; 411€ sal2; +*); l(r.) crana€ Ha [ 4; 2]'
fs.rxuor<-2:2r ftr) = lx' - 2x - 3, n.Rrrjo -2 < x < 4i
lz' a, u*qo ' > +.
^) f(,, = 5, npsMa lapanenblra o';
6) ^x)=
!) 2x- 3. napa6o,ra. {Birkr'r, eKor
FarpaBned Bropyi r'" =: = t
u"=1-2 3=-4,(1;-4lt
B) l(r) = 2t 3, npnMa;
4 5
a 5 7
f(r) Bpocrae tla [1; +-); l(r) cnanae Ea [ 2; 1].
ee6. r) l(n)=1t-+tE-x; o(ft:
2) f(x\ = J-r' + ';D(f\i a'z+t>0it'- t<O;x(t 2)<Otr € [0; 1].
8s7. lt f tx) = tG s + Ji1: ft: 'at:
I Lgxrrox<2:2t fl)ct = I
U. EKUro 'r > 2i
3,) ftx) x:. nxuo D{/r: (lt.E). ro E(n: {l: 2r'
49O il:::AIrEEPA MepsneKA. f. ra iH. AKaaeMi'{Hraf piBeHb ::::i:::::::i::::::::*:::
z) f(i=+-; DU)t',-5+ot x+):.15;
". (*; - "6). (-"6, l5), (,6; * -);
s) f(x)=\ls-";D(f)t I r' > Ot 11 = -3; r, = 3; r € [-3; 3]!
f1,1= nG - 1-ar = urg ;, ".o"".5\ f(r)= x' - x +Li D(f): r€ R, f( ')=( ')' ( :.\ + t= r'3ararbEoro Bnrnsayj
l6) /(.r) = ,:: Dlf\" 11 ! ' ot !l! I) / oi
.r € (--; -1) u ( 1; 0) u (0; 1) u (1; +-);
3rr-r+liibvHKqin
(*i 2t w (-2; 0) u (0; 2) u (2; +*);tr" 2x't | - 2r"
^ . ovHxtllsG' ax) r'-4x
111/{-r)=- i HPnapHa:' r.Yf (x) x'+x7l f(r\ = (x - 2ll (t + 2)" D(n: )e e ( -t +-)if( :t) = (-:. - 2)l - (-r + 2)a = ( Q+2)ra ( (t 2)r1 =(x+2)4-(r-2f =- -((x - 214 - (t + 2)i), senapHa;
8) /(r)'-'l . DD:Zx+6-0;n=-3:.r=( -: 3)-( 3r -):,(n He c4MerprlrHa BiaEocEo ro.rrcr O, i(r) ibyE&rrir saran6Eoro BlIrrEAy;9) fl,) = r3lxl; r(D: x e (--; +*); l(-r) = -(-,.f-t = 13,r, I]erapHa;
l0r frx)=+;t' 4t
l
I
I
j
I
D(fl. ic& 4x+O; t+Oi r t!2i r e
". I x)"+21 xf x3+2x'z
Gr\" - 4( r) x' + 4x
lr s>o; Jx:5:Lb-.r>o: lrssi
9O1. 1) y = 3t + 9; B'rpu*""to t ""p""
y, t = !:!.
fiosEaqliMo B oaepi*ranifi QopMy,li apryMeEr.repe3 r, a OyEXrIno - qepes y. MaeMo
r-g , I ^Qysnqrrc r= 3 aoo v=t,r r.
n , 6=!;,=!*e. ro3'a.rr.rMo apryMeHrt, , , _6, Brpa}HacMo r qepe3 9: g s
trcpe3 .r. a OyHxniro qepe3 g. MacMo OyqK(iro y 4 - e.
Al a = 1,E:n (ArB. nosclevt.r ao saBAarHs 1);
u5 r 2.rt 2x r.u..,=1_1,, ,=1_1",2 2" ' 2 2
iliilili{iitil A'TEEPA Mep3rrK A. r. ra iH. AKaaeMi,{Hri piBeHb ii;:i 491
4 8 -16
g 2 1 0,5
1 0 2 3
v o -3 0
4) a=2-nli-4; nE-1,=z y; '-4=4 4g+a';t:=g'z 4v+8ta=x' 4r+8'
5ts x'ixc [1r--)r x= Ji, v'"G.6)a=xu;ze(-*;-21; "=-Pli; u= \G-
9O2. 1) Ocld,'lbftr piBEsItEs y = l(r) Mee €AllHuii xopilrb Bi{nocso 3MiIIEoi t, ro rBep-
anieEEs npaB[nEr{e.2) TaIl, oclcitERv piBlInHEfl y = l(t) Mae €Alsri liopiEr, BiAHocso 3MiHHoi r'3) Ei, ocnir6rcr.I piBHnnna y = l(.r) riroxe uatlt ABa KopeEi BiAHocEo sMiEEoi a.4) Hi, y = g1g 1- t.rapHa, y = arccig t - OvHrcqis sara"lrHoro Blrrnaav.
5) Tax, ocRin6&{ y = '3, D(g\, , € RtE(itae n; c={;; D@\ 'e Ri
EG): e c Ri Dlgl ElCl, Elgl = DIV\'
6) Hi, ocni,rrxa y =;rat D( tt.Ii;t(y):[0i +6\ c=!t, D(g)t )ee R.E(g); t0; +-); D(y) + t(s).
9O3. 1) (2t 3X3r + 2Xr 9) < 0. nocniAoBHicrb po3B's3vBaIIIIs:1. 3Eafrrn o,43.2. nepeHecrr Bci q,reHtr HepiBuocri BniBo.3. fiprpiBEsrn niBy.racrxHy,4o Eyrs i sHaiira ftopesi orpnMaEoro piBssHEs.
4, Iloana.rarr.r orp&Maxi qzcna n O,q3 IIa qncnoBiii 4psMii.5, BMrsaqurrj BFak Oyltftrii Ea xoxHoMy npoMir{Ky.6. Senrcarr Bi,qroBiAb.
51 !:I2 6, -1:!r6, IJ36'' r-2 r-2 x-2OAg'.x-2+O;z+2iI:!=0, r-5=o:r=5.x-2BiAnNiAb: (2i 51.
6) 1]]4 s o; '1 * t'-u . o, ': "'! , o,2-5x 5x 2 5x-2
On3| 5t 2+OixxO,4i4i l'6 o, 2x r r.6 - o: -r = ,0.8.5x2
Bi0tuosiA6: ( -; 0,81 u (0,4; +-).
?) (r-ll)(n--4) lo; o,u3:.r - 10 = o; r =' r-1Ot-.1-11)411) = e, (, rll)(J r4) o;r-10fr+11=0: Ir= rrilr+n=or lr=-1.BiAno'iAb: | 11; 4l u (10; +-).
(.r+6X"r-8)
o-Il3: t.r + 6t{r 8) + 0, ' * -"'i*a
r -&l- = 6; x - 2,i =o; x= 2,s.(r+6)(r-8)BiAnoqiAb: (-; -6) u [2,5; 8).
so+. rr tl -!*'1'o; o.zl3:x'?r6.r rE,u;'x'+6.Y+8x'z-5x+4 - " -"" -" !=0; x, _ 5x + 4 = O; x = 4; x =
(.t 4Xr - 1) ^(t+4\(t+2\
BiqnosiAb: (*i -4) u (-2; 1) u (4; +-).
2l^ i '^.O: OJIS: .rr - I - 0; .r * -13.
xr 3x' 2x 0: xq 3x, .t 2x = Oi xtx, - 3x + 2) = 0: xt= O: x2= Ii x,= 2.x'9'!'-])'-!\.0. W(,-3)(r+3) ,B o I z iJ
Bianoeiob: ( -; -3\ u (0; 1) !-) (2; 3).
s, , * 1> 1, o-[3: ,r + o.!2
''1 I'o' 2x'- bx-2 >o 2x,-bx-z=tJ;32 2x
. zt,-zt( r !)D=9:r 2: x^ r: ' z':0.
"22x
- - \.TY=Y* :012^
aianoeiat: (o;!)wP; + *t.\zttillti:jliiliii AITEEPA MepsrrKA. r, ra iH, AKaAeMiqHrfi piBeHh tltj 493
-0,8 o,4
10;
--a,ti\'-\T..-11 -4 lo r
OA3: r € fi.Qx-a\(\t+2)('-s)=0;
i'=r.r=t1,lzx-a=o: | 2
la'*z=0, l*=-f,Lr_e=or lr=e.
niaoouiao, I :, - ?f .i\ ;I 3t tz2)(6+r)(r+2X4-x)>0;O,43:,'eR.'
[,r+o=o;{-r+6X.r+ 2)(x 4l=0: lx+2=0:
lx-4=0;BtAno6i0b: (--t 6) u (-2; 4).
lx + 4:
lx + -2.
1;,1.I
(' + 6)(, + 2Xr 4\>
z--61
0i(r+6X'12)(t-4)<Ol
ffi 4,8 15
3) (' + 4,8X1 - x)(5 - x)<0iQt + 4,8)(, - lxr 5)< 0;O,4B: ' e -8.(t + 4,8Xr - 1)(t 5) = 0;
lr++.8=0r lr=-4,8;ttlx-1=0; lr=1:Ljr 5=0; Lt=5.BionosiAb: F*t 4,81 u [1; 5],
at j-1220, o.[3: x 8.4-0ix/8,4.t 4.4
-_" n- = Ol r 7,2=0ix=1,2.
Bilnosi.Ab: ( -; 1,21 u (8;4; +-).
492 r:i!.: AITEEPA Mep3neK A. r. ra iH. AKaaeMi'rHrr piBeHb :i1ti::rj:r::ii;:{
$ 4!J 3y, oAB: , * o.
lIf 1-r.0. 3'+1-t<0.xt
o"'=o;2x+r=o;
e;a",,ia", l-1, o).L2 )
t1 !! Jr-2t oAs: ' + o.
51 1 5r l2.x -__2>Ua _>U.
"f;'=o, r,-r=;, '=+l\
s;anoaiao: (:: o) u lr:
+ - J.
6) { lsr-?. o.[B:.rr- lr" -1 x Ir3-g x 2 -<U:(r 1Xx'+r.+1) r 1
," 8 t" + 2x' t'+%c-t +2(r 1)(r'?+t+1)
I
;:;:.!:.$
::::::::!l
1
2
2t+1_<{).
gos. t, (* '3t' oi or3r ir r 2: x ' b.(x + 2\(, 5l
(r , 3)' 0i tr J). 0i -r. " J.(.r + 2Xx 5)
BiAnoqiAb: F2, 5).
z, tr*3f .0(x+2)(x-5)
(arr3. trorclleEEn ao saBAaHns 1).BiAnMiAb: e2,5r: \-3]..
B, ql?+ < o; oAB: .r. , + B.(x 3)"
fr+z=o: [r=-2;l" s=o; l'=r.BiAnosidb: l-2;3) u (3; 51.
+V1\(-::V-13 -i"'-;
+Y-+\a:])/'+|E-2br
r\ /--:\ ?.--\/-------.----+.---------.#z [el 5 '
+ 3.
3)=0;rc=0:r=1ix=3.
(jr + 2){x 5) ^---:------:i- = vi311
->ui
at * 5 ^<oi o.&3: xt 2ix."-8.
(x + 2\(x 3)'
::_=o: j 5=0:.r=5.(x + 2J(x 3)'Bion%iab: ( 2; 3) u (3; 5).
, '.,j ", 0:ir,-"r 6 0:.r--3:"r z.fl111\C-(.r rJtir- f.r r i)Bidnosidb: l--, 3i '(l; 2|.
7, LaL.a, on}i x+Ii r+2.x-I .t 22 3 - 2tx-2\ r3{r l)-4(r-lxx 2) ^
x-l x 2 - {r lx,r 2)
z'__1_fL Q:4l1t2x -8 <o. 4-y'/r l7.r-15<0. 4-r?-17.r I l5 ,0.(.r lJ(n - 2) rjr l,lir - 2) {x - l)(x 2)
17+7 I -4x2- 17x I t5=0:' 49: ',. =- ; , nr =1-i r Jr
al' - r1)t" ar\ 4/ ,O.(r. lxir - 2)
Bidnosiab: F*t \t €(r ], z), ra, * -r.
u 2-+4;>z: o1gtr* 1;'+-2.2 3 ^ ^ 2lx t 2l -3lr I) 2l.r + l)(.r 2) ^
x-I r'2 (rrl)(r r2)2x-4-3x 3-2J( -6x 4.n -2r"---!' 3,6, 41L,-3 ,6,
lx JJlx t 2) (.ir - 1,{'( ' 2} l"r - l)lir ' 2)
2t'7rx-3 -.o:2!, x 4=otD 2si r,"=-l+5i t.=21 t" r,s.{x' IXr r 2) --2lx-1)lr.+1,5) -^(r+1)(t+2)
BiAnosiAb: C2t 1,51u (-1i 11.
494 lli: AITEEPA Mep3reK A. f, ra iH. aKaaeMiqHlrn piBeHb :a:a:;::i::::::;:i:::ii
114
6\ l2x + l\'ztx .3 e o: o.[3: x . oi ' t t.,r"(r. + I)'
,.. frz'+rf =or ", ,= ];' f*-z=o: "=, "
BioflosiAb: ( *; 1) u ( 1; 0) u [2; +-).
6) '".41"-g'o: oA3:.r'z 5r r6/oi,r,2rxt3 -4a'z+3t^. : :- 0; 'r1 - 4r' - 3.r = 0: r.(.r' 4xI
r(r 1)(, 3) > 0.
(x - 2\(x 3lBiAnoqiob: t € (0; 1) u (2; 3) u (3; +-).
g06.rrrr -stE- .o. oo". [z-t:o. l.z.2.x t3 [x/ -1.5: [.rr-1,5.
r"-st"E-_r. r,, cr6: = o:2x+3
('-3Xr+3)J2 jl' >0.
2r+3BiAnoqiAb: FB, -r,5); {2; 3}.
x=!3;t-2.
,, rl;'$ a . o, ,, -,1,_fE . o, oo", {i I _1.
rl-llitlr 3 o, r, rf,/i-3 = o, [' , -l'16 r' lr=.3.
(r+r)'rE+3.0.@ q@+4)
BiAnwiAb: | 3; 4r.
-\-a/1z t,s z 3 x
" (:\(34.4 3 FI 4
-)€-]V-.10-t
+ 0t (t - 1r(t' + t + 1) + 0; t + 1.
x' 8 r.r'-2x2+t'z 2t+x 2l .^--- +Su;(r-1)(J'+x+1)
(r 1)(ir' + .r + 1)
(r+2X, 5)=0;
(2r+1)'('-2\r'(r + 1)n
i:l:ittiililiiitli AITEEPA Mep3reKA. r. ra iH. AKaaeMi,{Hri piBeHb r:::i: 495
3, CreneHeBa OyHxqie 3) a=\tlx-2) iD(a)tt-2>D;r>2tteL2i+6).a=t-2
q v-{a4;D(y):reR;y=lx-21.
soz. 1) 4(-i6)' - t,.vm.o - [i ltto)'=-2O-6+40=14i
= -20 0,6.10 + +.640 =
2)
n[, -1".t; = "56- = 1n = t
1lJ2 - {12 2+2$ I,lltz + J2 = {:,z,fz =
3)
4)
5)
6)
t, ,,srr. rr i/{z -.,F)- -,lz =lz-,111-,lt -
"F - z-Jz 2i
srz. t xF = d"" -" = "'tFzl v_a' = _i6".a = _a'16,
il 1862*-j = 418L2*" *"."' "" = z*"o\li^"o" t
Et rls6;W = {ir a'- . ," . om = zry'{iz\;s d-zney' - d-ar. sy1 - zy,!-zy:
al ll."o" = :1"'" .
""W = o%\,lo"r" .
grg. rr 5= = 3@= -sE -stlz.v4 v4 .i/2 v8 . 2
". 12 12.li tz.dz tz.tE ,,1..'' E-ffi Ts--W - s -"'"',, g=94=s4=fia,'V8 {az 2
,, 14 14 V7 :.41,!i .xE.! 4s { 4s.{7 7
ff'.fesf i,[rtu uI=t ,6s lJsb-d=z-.6b+JEs-e=r;= <F -,rlq;,tA = O -;AWn - F - txil = ira - -2.
gog.ri s i/3"-sr D(y):3.r - 5'0, *>r3,
4 a= -t; D(Y)i-,>oi/'<o: '€ ( -;ol;
3\ a = 4!x a: D@ri x e (-*; +-\t
909.
2)
3)
4)
5)
6)
91o.\ u=llx-2); zl y=trG4;D(V\tte(--;+-):,(r):re(--;+-);
12 \relrrt+1:
qt v {6, . lt Det.6x x, zoi xt6 -.r) z oi -:G/- - :-r-0; .r=6:.rc [0161. 0 6
rl .i6; = J"l = o, s*qo a > o;
tltt =lo = -a, slcqo 6 < o;
{zt*t*i =ls^^"'pl= s^'""p, 'Krqo
n < 0;
t,u"Jira"^ = t, t"lz"'l = -2,arn , snqo r 5 0;
,68"- =Uttl "b! b",.e*rqod-o,c<0.
ah. abc abc
496 lll ATTEEPA Mep3rtKa. r, ra iH. a(a,qeMi'{Hrr piaenu il!*:ilfl*it'ii:'r
,' e. s(a*f) s(a*"El _ s(qtuF) _^*,r.4 J7 14-h)14 th) 16 7 s
.. r (Ve' {6'Vr) {6 -.f6_j[."' {a*{t (17tI -(q,E)' 5
z) ^ 6",_ o(a , zVt '.Vzr) o(l - z'6 . Vzr) zlr t z{s . <!zs):2 ts 2, (r/t)" J
g(S*r) e('6-r) e(t6*r) a(Vs 'r)'' plzs lt ' (Vrs - 16 - rX",,6 - r) (vb)',r, 6 - 3
,Er (
:ittilft:r:*l: AII'EEPA MepsfleK A. f. ra iH. AKaaeMi.rHran pieenr ilil1 497
gra.u Wa =iE a =4,8;3) nAG ='vc' . c ='d"';
2' flE{t' = {t.'t" =:{t";q 4e =\lt = Jz;
/,\l(r;)"-,il=(r,_rl)(, _s))=2,_s =1 i_ r,!,
or Isl (o.sq/o.i)"")lr,'" 1""",^,',J l':-i.,ll"l1',. "-l;l',]=
[3r_(1]'j(s:.i;l l={,,r lIj] l' ,, ,,
( rl .
,n, l n',, , 1 t "'" " 1 ' ' l ' l { ni i,Er 'l [r: -titlll(r; -rl;)='"' f- tL""'e r I J'- '-'"' l- ' \ 2t 1'' ' -
=(ri - "')(ri -
r'") =(rl" - p-'t" = z - z' = z - ft = fi .
n,n. ', i"'
l a ll '- rg'r l 'i a: - s';'l ,u"J 7 e'ti, 27'
| 3 3\3125a'-h' t1tt "nrh, 256arh,
!? I'I on. , ; AB) 'c' 625c'3
sl f6ri0 =,Sls='ne. =Je; al *lzJ, =42* =42" = *lr.
gts. rl i6o . {6, .""i"'"" '6 = .Vsl;
zt Jo . .,6, oc&iJlbru i6 = i6e ; Ji = rll%lal l/il r "6, ocrin*' ../5 = 16;q\ {n, 1E,.""i"'"" .'Ei = lF='itr, t/5 = i/d ='F.
nru.,, Jg Jg_(+6-16)('6,' Va) _vo va.Va + Va (V" + Va)
.. s[ z (J"-r) 1
Va a 1i7o - r;1go * 2l \la +2
^-tl^" <1,,t Hn | ., "- -_= :1-= \!m = \!miJn tn tln\tln r)
4.lV +etli +s {V *e{" +s 1
x-27 = (G ;nV-, :V, +o) = if-, a'
!9't7. 1) s = x6l, D(ar: x > o;
2) a=xa3t Dtlt: x oi3) u=(r+ 6\'6;D(A)i:r+6>0,t >-6; n€ [ 6; +-);
8)
494
4) y -(rz -6t-7)-6tD(y)t ? 6x-7>O;x= 1;t=7;re ( -; 1)u(7; +-).
918. 1) 31'. 3 o?.3' { = 3r'o'1:!1
2l tl 3.11 4 .11r, .11 , = 1.121
3) 360r'6-01=6'{.6
4r ::=a=3r =3iBa Bt
sy o,rzs i+o,sri-0,216-,? =1o,sy'+10,s)-'-(0,6)' =(1J'-(*)' (9'=".10 25 ",2 l.
I I 3 3./ .1-* r -rLo, (o,ozzlJ +zse'- lts'iJ =(0.3'r"^ 2so'5-ir=o.a 'z' l
=19*64-1=3*64=62;
uru""" -(.*"" t) ;
* (V*)" - 6,y,, - ii . (roi)' - 5 - 1 + 101 = 14;
" ,]l(,1)' , n-l llr",e,r; -(,;).J l(,1)'.,. ,=
lll: lltrespl wtepsncKA. r. ra iH. AKaser,ri,{srr piee}tu ::llfilillili{li
l"Ih: *"trb:]" l,ib;(,; .b;)l',,, ,jri , =l__;;,,r,lu;r'' ,,0, olo,,
,rr t ,1, ,t\+I o,b, I b, I b,\ol +u) a-, aa)l-l- ,i, rtl a' t\a!-aaba t \a4\a4 b1l)
92O, I) Cnpoqycvo,liBy qscrHdi roror+(Hocri:I I '\ ' / ,\ ,
I ^ , n -n, (n\' \m-n-n+n"n"ln'l;:;; ;.f,,)r^' ^,1^t,^),t(,'i_";)(,"r.":) I l= l '--'\
=m -nt\n'+n')
11!lnL1 n1 = n1 _ nr. IoBeAerro.
2) Copouly.Mo riBy qacrnsy roroxEocri:
otb a-b oi-bi
oZ oa6t a6r aa + a,aba +ba aa bjt t\l 2 r\/ tr 2\ I r\/ r r\la; _6,](a; _a,b; I b") 1,, a,ll,' ta,bs +bsl [,'_a"J(""*a"/
t,r - !M\,, _
""t, _ o') \o', I oibi bi)
rr1111111!rr=at +bt _as +b3 _a3 bs =bt &3. br da =Da a3. AoBeAeEo.
:::::i't:iilijf.!i! A'rEEPA Mep3nex A. f. ra iH. AKaAeMi,{Hlri piBeHb ii:::
3) crporqy€Mo niBy 'racrlltlry rorornsocri:).
I s a3t2 lorr8d3 5 d3 -
fd+8 o; 2j, -a) 1-oi r-ai1l
s aB -2 I as+z
'';'"-;-t-n (,!ffi-; ,)-G" ,"i"131 ?\
- s-ad 4a3 -4 _ 5 - a:_:!as I
a+8 a+8t 2 !\ .\5_as_4arl.a'@ '8t 5a. a_4a3
z'_'--l(a+s).(t-d'/ 1-at
r oi -qotr s-oi sol -a aoi *r ,3 -rol . , s s,? ,,r\ I / 't'(r-oi]tr *,iJ r', o; h ",Jh-orJ r+03
5 = 5. AoBeaelro.4) CnpotrIycMo "1iBy
qacrusy rororkHocri:
t ! \ / c ^\'l',1-+ ''w^' ,l +', -,; I ,
l-i-". .J \,?.+nr )
, ';---n "^:,: (^i
'i)(qi ' ^:^I '^1\ "^:^'"'
^i _^I "" " {,,r ,:)
1 I I / r I L\ I I '\'n' * n;n" - n; s^i ni =l^" *2^'n; *
""1-14, - nll t
t[ ! l]1 I ll 1l ,l' , , , , z zr' t , r \'2 l\n' +nx)tn'-n,ns +nsl_n:l \^, lni^;_ni n;l =\n; _n;n'l =I (,t-,1) )
,t . r\'=n,\m1 -n'l .
It r\'l-t -",t 1 1 1 -t. ffi=
-,. ,. i lotelcno.ni \ni -nz)
gZ't. t\ J+t * m = t + 2; 4t + 20 = ,c2 + 4x+ 4: "
-16= 0; (t 4)(t + 4)=0;lx,=a,
Ii"peulpxa, ", = l, J+++m =++z;6-?,npalurbEo;r,--q, J-le+m =-q+z;
2 = -2, senpagr'Irl'Ho.
BiAnosiA': 4.
Z7 u6-i=Z'-t;6-t=gx'-24r+16i9x'-23x+ 10=0; D = 169:
23113 - 5
",., = fS : xr= 2, x,= g.
soo l{t ArrEsPA Mep3rcK A, r. ra iH, AxaaeMiqur4i piBexu llillii{illtN
2 = 2. flpaEhnbHo; x, = ;:
4+2r-x'-r' 4x+ 4;2x2 -6t= 0; 2r(r 3)=0;
nepeBiprcai ,t = 2: 1Q - z = z z-l,;77- = --, llenpaBlrrEno,
BiqnoaiAb:2.
4 '[G x "='-z;
IlepeBip&a: rr =O: Ja+Z.O-O=O-2;2= 2, ls.e!pasuntiflo; z"=3:.lE+z s-s =z-z; 1= 1, rpalrrnbno.BiAnosiAb:8.
q 1Er" - llt- tl = S - x: 2x2 - L4tt + 13 = 25 - 1Or + a2i 12 - 4t - 12 = O.
nepeBipxa:,,= 2, ;a zy u.{-2)-13 =?: ? = ?. rlpsB nEsor x, = 6:
rE.6"L4'6 +14=-1;1= 1, HeBpaBHnr,Ho.BiAnosiAb: -2.
sr Jr-J''-ir =x-tr r-uG' I =x"-z*-t; '[7 -," =z* '"xt x?.4x2-4x6+f 5x,-4xx=O:.rr(5 4IJ - 0i.irr =0 a6o ,"=i=tti
IlepeBiprc&: .r, = 0: 1= -1. senoalsftso: r.^ = 11,'4
f rs r i r.iI--=-:\164441
4'
=0-1;
BilnoerOt:1!.4
6\ 'li+i-Jui =2t 'li+Lt=2+Js'+7; t+11=4+4Jiiii +sx+r:-2r = t1li7*; -r=Z,,Er+7; x, = 4(3t + 7li t, - 12x - 2A = Oi
fiepeBipria: x,= -2t J-2+11-J-6+7=21 3 - 1 = 2a 2 = 2, npaBtrnEgo;
,"=tc: "Ea+11-Ja2-i -2; 5 7= 1; -2= 2, EerpasrnEgo.
BiAnoqiAb: -2.
7),8 - % - s = J16 + x; ./l - zx =,lla+r + 3; 1 - 2r = 16 + r + 6li6 +.r- + 9;-za-zx 6,h6tx; S-r=2fi6-xr 64+ 16.r+r'?-4(16 r .r)i
64 l6x x, - 64 4x,, x, r 12x = O, x(x + l2t = 0; [x' = 0'
lx" = -12
IlepeBipxa: x, = o: uii-zo-a= u/io*or I a 4t 2 - 4, HenpaBa,rr,Fo;
:t "
= -tzt,ET zi - s, = Jta - n; s - 3 = 2; 2 = 2, rpaBn.rbno.BiAnogiob: -I2.a1 ula-,+,1*-z=r; "6-i =t-"li z; s-t=r-zJt-2+x-2;2Jr-2=22-4; ,Q-Z=r-Z; x 2 = xz - 4t + 4i t2 - 5t + 6 = Ot
nepeBipxa: \ = 2. .tE - 2 + fE - 2 = 1; 1 = 1, npaBgnbHo;
r, = s: .,6-+.v{_z = L 1 = 1, npanr.rnr,ao.BiA 6iAb: 2. B-
i:r:::ilt!li:itlli: ATTEEPA Mep3rqKA. r. ra iH. AKaAeMirHrt pieenu ltl: SOr
sl "t
x+5+"lt-=t: ,!z'+r=t '"b-t; 2x+5=16' }nE .r+a-r;ar rn - -8'6-; s\,6 1 = 14 sq 64(s x) = 196 84r + 9x2;
fg2 64x = lg' - 84;t + 9t2; qx'z 2Or + 4 = 0; D = 256i20rt16 - 2
r,., = rs , x|= zi x2= -.repeBipKa: ,,=2. "E*+Jrz =4; 3 + 1=4;4 = 4, npaBlanr,Ho;
s22-D lE-4{i 5=o; oA3: '>0.saMiga: V;=r, t>0't'z 4t -5=o;t,=lit,=5t I Ire 3a{oBonEEs€ vMoBv
i,t .5; r 62s.Bi0no6iAb:625.
zl Vi + r$[ 18: oA3:x2oSavisa: Vr =t, t2O.t'z +3, 1a=0; t'= 6it2=3t -6 Ee 3a.qoBonbg'e vMgBv
r>0.6t, o. -" 4. - - aro
BiAnoqiAb:729.
U "lV-q' ' q-z'J' 2-3=0r G-2)' 2t[x-2 3 o.
3arina: {t 2=r. ',t2t-3 O:tr= 3; //=1:+lr-z= e; x-2= 27;x= 25i;J,-z =t; '-2= :':3.BiAnosiAb: 25:3.
a) l=8 r.3aMiHa: Vx=r. i -u.2+ -!x
Lt" g_1 . t4 - i ) (2 r-r)(8 i '?) o.2+i .--' 2+t
t2+tn/'-r-6)_0. I{2 +
2+t l2+t
,tQ =g; x-o.-5neDeBiDXa: . 1=8 9: "=-1; l--1'npalurbHo
2+ J9 b
o ,ffi .ffi.1=0. Bauisa: /tt =,, ''o'r 9+1=o; l+l-6-0. t,+t- 6=o;
l';"="? t Heaa'*oBonl'snel.MoBv'>o;
-rr3 xr3 4-r r12 3xt15----:- = 4 - =0; - -=0;x 3 .ir 3 x-3rlepeBipka: ffi uffi.t=0,BiAnosiAb:5.
u) .E ' ./f--: =1, o.qa: -L-0; -j-=0, I'=0 .rc(-*;-l)L{0; -).vlrr ri .r 2 I r xrl l.ir. -l:aa*i,,a: _E=r.r, o, _p=1.!1+r \l r t
,r!-f,=o, 2* 5-t+2-o' zt'z-5t+2=oia=st r,." =tn?t
r x-4-4x -Sr-4=4t =0: =u:1+r 1+' 1+r-32-4=O,1+ r.+ 0l
f r -t
!1+r 2'4x1x 3x1
-=0: -=u:
4(1 + r) 4(l + x)
nanoaiat: -!; !.7, ""-4,-,,8-4, 1=3. saMiHa: k -4'-=L t>o;x,-4r-1=t2t? 4x=t2 + l:xl -l -r-3=0:1,- t-2=O:t|=-lit2=2.-1 ne 33,qoBonbH.se yMoBy t > 0.
'[V - t, -t = z; x.' - 4x - 1 = 4; x' - 4x - 5 = 0; r. = -1; r" = 5.
nepeBipria: 4 - -t; t a 4 - $ a 4 - 1 = 3; 3 = 3, trpaBr.rrbdoi r, = 5;
25 - 20 -,85 - 20 - 1= 3; 3 = 3, npaslrftso.BiAnosiAb: \ 5.
, I a Jral lr Jra l8) 5J.r?+3n-I=2x +6x+I: OA3: xL :r llrl
3a'riua: Jr' . Bx I = r, I : o; ,,., ar ', ut n', ")
), , ,'t l
2f+6t=2t2+2.
5t - 2t' + 2 + lt 2t' - 5t = 3 = O; D = 1;5a1 r,=1,5,a lr,=rr
uE+Sr-t=1A;st Jzz
f +3x L=2,25;x'z+3x 3,25=OtD=22i
vtt J' I t; ,r'2 r 3,r t = t;.r'-3,r -2=ot D =lF, *.^ = ttitt.", 2
.^ 4!Jn s t "/itt'Iono6lob:-:---'-.
4. TpllroHoMerpxqHi OyHKr.tii
023. 1)cosr=a+4; -1 <a+_4<1; -5<a<-3;oe [-5; -3];le" "" ro
2) sinr=6a-az-lo; I - =t' Uo o'z 10<1; a2+6a 11,<ot16" d' l0 > li
iri;iilliitl::;:tl: AITEEPA Mep3rqK A. r. ra iH. AKaAeMi.rHri piEeHb ttii 503
2 6.!2
J-3,r + 15 = 0, J,r = 5.
l:r 3+0: lr+3.+1=0;0=0.
I l. r.L"-r'f__ al'- r'l,* t.ll
l, = :'.13"-r=0,L1+r+0r
n1
12+tlt2-t 8+t'zl ^
-=u:
2+ t 'It =-2'rxi' r -6)=0. li'-i o o, ]l-' ".+O: t+-21lt t -21
502 !!::: AnrEsPA Mep3ns( A. t ra iH. AKaaeMiqHrr piBeH" f;:ittii::,-f:i!li
a.z 6a+ 11.>Ot a!-6a+ 11 = 0; D=-8 < 0, seMa€ EopeEiB,4€ R'6a a2 - g >O; -a2 + 60 - I > 0i a'z- 6a + I <o; (a - 3)'<o; a = 3.
tae R-I - o=3.
BiAnoqiAb: 3 .
924, 1) sin 168" cos 126'< 0, ocl{irbxtI sin 168" > 0; cos 126" < 0;
2) te 206".cos ( 223") < 0, ocliinblcs tg 206" > 0; cos (-223") < 0;
3) cos 4 tg 3 > 0, ocliirr,lca cos 4 > 0; tg 3 < 0.
t;925. ll sin?80'-sinl2 360"-60')" "in60'=;,
2) tg 900" = tg (180' 5 + 0') = te 0" = 0;
3t cosl2O0.=cos(360' 3+120") cosrzo' -cmeo"- -!:4) ctE ( 585') = -ctg (180' 3 + 45') = -ctg 45'= -1;
llr/tr\n.,65) cos6 = coslz,T 6J = cos -6 2,
6r "t,[ 1l^,)=-"i"[r r"-i] -",'l-;l-+
_1b) ,=- srnr;
6.) , = 1,5 cos r.
92a. l) 6inx 5;3].o.zo: t,ctg'x=J; .Lg:=tJ8a 2 ' sin x
dG lv,{Beprii crg.r \ 0i ctsx= .lg-t=-./g=-g.,l z0 \lz5 5
Bionoeiat: -!.5
2) Lg(t=3i n.,r.3l; l-tg'o t, , "o.o=r.[z cos- d \ir . tg" aI-
rr€ III cueDri: cos r < o: cos.r-- /1 - '!lOi
stnc- lvr cos-ci smc<u;
",", = -.,f1 = - E = -: = -'J'.\l 10 Y10 Jro r0
- s"toB tnoa th: -- .10
929, 1 ) sinl o . cosi cr tg c = sin" c - cos:-qsjn a = sin' cr + cos'z c ein o
= sin a(sin'a - cos'?a) = sin a;
2) cos'zd - ctg'dsina c "o"'o "oI19!lll9 = cos' c - cos' c sin' c =
cos2 d(l sin'? d) - cos' s cos' c = cos' c;
3) (sin'?cr + ts'osin'zo)ctgcr = sin'?p(1+ tg?d;"rgo = 4{] "tgo=ts'zo ctss=
1-lsinfI+nos.rl':4)--+=sln d cos d - cigd
= 2ts' a.-""l,"r"--a-lI sin al
926. f(x + T) * l(.r T) * l(I).
927.llg--sil]'x+2i
at r = coslr2
5o4 ill: ATTEEPA MepsrrK A. r. ra iH. aKaaeMieHrar pieenr tiiiltliiill:iilil
93O. l) 2cos'?c-3sin!d. l-cos2a-;tl-cos2d) I cos2d 1.5, 1.5cos2o=
=2,5cos2d 0,5;-1 <cos 2c[< 1;2,5<2,5cos2d<2,5; -B < 2,5cos 2c[ - 0,5 < 2.Hai6inblle - 2; EaiMeHrre - (-3).
iitliiiillliii:| uresPA MepsrqK A. r. ra iH. AKaaeMiqHrafi piBeHb ::i::r 5o5
1- (1 + 2 sino cos d) -2sindcoso 2 sin'zc[sin'd 1cos0. - - -
fr'
2)y=cosn-1;
2) 4 cos'? Cl - tg d ctg cr - ocEinr'(rrarii sHartelrEs rle icEyloTl'.
d*!+ .IJr.neZ "ta ctxfi+nn,nez' ^to
cos(21r+cr)tg(n+(r)
"-[" T) ctg,(sn o) - 1r-r.i--i;(;."1
sina ctg 0 tg a ,.= ".""
te" -'
r-^l 1 ,l- tgd.tclg:d- l) "*[ie'c 'J
-€ct{l -Lg o) tgcr -1.- {l- tg'o) "tgo 11 ts,ct. I (1 tg'd) tg'a
tc(1
932. cos(s + ll) = cos ct. cos P - sin o sin 9; coso= .E-"t"""= n[-o'el = o'o;
si" P = .'/i - co"' cr = u4:o,so = o,a;
cos(c, + B) = -0,6 0,6 (-0,8) ' (-0'8) = -0,36 - 0'64 = -1'
933. 1) ctrpourvFMo niBv cacrl'IEv roroxRocri:r """a cogB\
sjnctsino(ctgd "tg0) sinasinUl;in" - "i"b.J
=
_ sin cr sin g(sin P cos ct 1 cos p sin d) = sin(cr + p);
sin ct sin P
e31. 1) sin(; d) + cos(n - o) + ic(+ + o) + ctgtt + crl =
= cosc[ - cosd -ctgCl + ctgcl = 0;
_ sindqosF + cosdsing = "i"("
* 9J = tg(o * p);
cos cr cos B - sin C[ sin P cos(cr + 0)tg (0 + P) = te (ct + B). Aose,qeEo.
I ^ 7r llt )934. lr cosa+sind=sinl;:-.t]tsino -zsrn4rosl4 - o.]
zl "m(o
* l) "i,,tn - ol. *"(". l) -<z' - d) = cos d sin c, - sin q cos o = 0;
ciue'.J -1 _-ctgCI
3)
4)
sin !9d + P) = sin lq + 91. Aoeese.o.2) CDporrvcMo niB) qacrxnv roror{socrr:
'6 "o"o-z"osl l*oJ vz-"o-rl-"1""",r "r"|"r'"J;{}, #"'* zl.r.i-""'"""1"*'l "o"''"
fjglgl !9i-1 @-tL- -"- 'r , Jz "i"o - "gd; rs a = re d. .Iroseae'o.
J2cosd' J2sinc{ J2sin<r J2costr
^. 2sindcosB -sin{o-p) - 2sinorosp sindcosp-co sinll -'t' cos(o - 0) 2sindsinP-ioscrcos0+sinosinp 2sinosinp
tsn )-"ielt "J1- ig'(3?r - cr)
=J2coslct-;l;
r < """(" - l) < r,,/t < vE-"[" ]J..8. ""out"'*" ",,*""""' -'.8'
506 i:::::: A,rlrEEPA Mep3ncK A- r. ra iH. aKaAeMiqH,i piBeHb :::::::j:::::::i::j:::::;:
2) 10sin o Tcos q; a=10:b= 7,
Ja +t" = Jtls: l0sind-7.osrr. | '"-sinc .'- "o.o .,/t+s
\ Jl49 Jl49 )
= \,/i4g(sin a.os I - sin 9 cos cr1 = u/t49s;n1.r 11'
-1 s sin(d a) < 1; -J149 < sin(a <p) < n4+g. na;oi.'rrme g"a'e"'o - ,{?-6.
935. lr sin2q =
2 sin d los (}
= ts ..,I + cos2fl 2 cos' cr
2) 1 cos 6c[ - cos 2cr + cos 4cl 2 sin' 3cr - 2sin3c{ sin (r' 2sindcos2c, 2sindcos2d
2sin3a(sin3d sins) _2 sin q cos 2q
2sin30 . 2 sin (1cos 2d= 2 sin 3d;
6)
2sin0cos20
3) sin 6a tg 3& + 2 cos' 3d - 2 sin 3o cos 3e !4!q + 2 cos: 30 =cos3d
=2sin3a+2cos'z3cl=2;4) cos{ cr - sint o - cos 2([ + sin2 cr cos' o ==cos: cr(cos'?(1 + sin: o) - sin'zo + 2 sin'zs- 1= cos'z&+ sin'2o 1=0;
5t 2.os 2d + sin 2d --1 I - cos 4a + sin 2d I 1.
sin 2d - sin' 2d +.nq' 2fr sin2d+.nq4d
"-(T --).',"*,("-';)-, cos2d + 2cos'2.I 1
2cosgcrcos2ct + 1+ cos 4C, - 1 2 cos 3cr cos rx
7)
2 "."
'J" =-=cosq
f cosa sinc) nos2c-cos6c (cosocos2a sin2dsinc').2sin4crsin2ctt"trrr "*rrl .lr'5r "lt- ".r""*r.2"t"r""".'i"
-ros8o sin4d 2sin4ct 2sin4d ,.
.os 2.r sin 2d.os 3d 2ein2.t.os2 "i*1" ''
8)sin'z 4.r - 1l
\ 2) cos'4a cos' 4alzn ) l:n \ctcl , +za) +tel 2 - zct.]
cos 2cr sin 2cr
"nr2" "*2"
2cos3([
^1cos'/40.sin2scos20 'os 4(I 2sin2d'os2G cos40.sin4d 1. .-
aos" 2ct sla" 2 cos4d 2 4--" --'
lg2o. + clg2o.
5. TprroHoMerp14qHi piBHrHHr i HepiBHocri
s36. rr "i"l{+I)+2=0,l6 r2,rxr r^_6 12 2
BiAnogiAb: 3,5n + 12nn,
2t 2cosl ! 1*,,6=o,\3 2)
r5trr=+ + +zftn-nF/.263
"r"f{.rl=-r; 1-.n, -\-znn,n c z;\6 r2l 6 12 2
r= 1 an 12nn,nLZ: x=-3,5r- l2nn, ncZ.2
neZ-
"o.[ I 1l J:,: I ln \l znn.n.z;12 3,r 2 2 3 \ 6/
5fl 2nx=!a+ e +4nn.neL.
Bidnoiidb: !! + ! + 4nn. n eZ.33
..:titii::ti:llitla AITEEPA Mep3ncK A. r. ra iH. AKaaeMi,rHrt piBeHh lr.l 507
3) 3+Gicljr-;J =oi
1t 1lx= --+fin,n€Li x
Biinoeilt -ft+ nn, n eZ.
41 4cte @r - 9) - 8 = 0; cte(3r 9\ = 2;
x=z+Iurcctez+T,nez
Bi}noailt: 3 + larcct'e
2 + !, n e z
/ n\ r n -." 'reaz. sin[x ";)=;,
, - =(-j) ;' n''nczr
n = t: (-tt' [ -[+ n = -I-.:- " = ;.Bionoeiat: | .
l,=!+znn.n,z, l, ; ,*.,-..t-^t-L-"'=;, l, -^u*"!-zn*.x.2.
znn, n eZ; t arccosl + 2nk, k eZ,
/n\rts i- l=--;"\ 4' Jg
=--+fin,neL,
nfit--= 6+fin.nELi
4cosr' 3 = 0;
BiAnMiAb: -+2
'=1-1yL-!r,nn,na7'
e38. .osf r, - Tj = . "rO.
* -+ t?! - 2nn. n cz;
z, = -l' I - 2"". ^ ez., - =3{ t !. n"' " -zt
3n fi - -gr-8,I 1t,=0,*.---3-u U = Zi
Bianoeiat: ft
e3e. w;= \ ; -;1nn'n-z: x -f,tznn nez:
tt . 3rI ^ = ft*tn-U,
n=1:rr= i-zlt-Ti n=zt x,' 2 2
BiAno^iAb: 2 Kopeai.
94O. 1) 2cos? r = Ssin x + 2i 2(1 - sjll2 t) - Asin t - 2 = 0;
2-'2siII't 3sin iu - 2 =O;2sin't + 3sir '=
0; sin n(2 sin t + 3) = 0;
lsjn r = 0r ]x =nn,ncZt x.fln,ncZilz"in*-a,0r lsin'=' l,s: Ixopeuie xeuae'hidnosiab:fin.n€2.2) cos2t+sin jr=0;1 2 sin'? x + sin t = O; 2 sin' t - sin a 1= 0'
SaMiEa: sin r = 1, t € [-1; 1].2t,-t-t=O.D=9i
i =1: lsin.r=l: l,=" -znn,ntztl-3 ' | 2i."=- ; I I I I".,- t'lU=_U: l"i,x -r, l,=rtr,L, "x.*.2.Bianoliab ++znn,neZi l-r\*tI+ nk' k ez'
3) 2cos2"t Scosx- 2 O,2(2cos'zx I) 3cosx -2=0ii.*'t -Z 3cos jr -2'O; 4cos -r-3cosx 0: cos n(4cos r- 3)=0;
5oB l{!l ATTEEPA MepsniKA' r. ra iH. AKaaeMi'{Hr4i piBexr ll:i{ii;ii:iiii;i
4) 2s\t\ 2, = tg t + clg x; OfiB; x+!+2nn,nEZi ,+fih,keZ.
2sin2y=llri+!9!J; z"inz, "in'':j9{l ; 2sin2x. 2- ;cos,r srnx .1n2r
2sin^2'-2 2s:tn'?2t-2=o: 11-cos4ir-2 0, l"os4x t:
sin2x " lsln2x*0: l2x ' nt,teZ: x.!!.Lz:
lax n 2nm.n-zt l.=I-Y,^,2; 2
l)42l,*\.t.zt 1_,tl -"
1^= 2" ''Bianoeiad: f,+\,nez.5) 3 tg', 8cos'zr+ 1=0; OA3: x+f,+nn,neZ.
ate,r-j._+1-o:- 1+ tg'.r3tg'zr + 3tgi r 8+ l+ Lg' x
=0;1+ tg- r.Slga {-+ 4tg'x -7
= o: arga r + 4Lg, x 7 o,r+Dg-.r
SaMiEa: tg" = t, t>O.3t, + 4t:7 = 0; ) = 100;[r. = t,-4+lo t. 7tt.z= O ilr^ 7. -t - Be ra4olonLu'c , 2 0:
t' 3f_
- tgx 1; x '\tnh'k-Z'n8"t=tt
t"*=-1, : + fim. m.7-
Bianoaiah: ': +'-Y: h c 742
6) 2 tgx rScrgJ.=5lO.ll3: x*tr -nn.n-Li x r fih, k.Z.2
saMiHa:tsx t; crs.r=l; zr+9-s o; 2!' -!i--2=ot [2" sr 'z=ot
t t / li-0;ffr, - r,rr ,.- ,. lx=alrtst,l-nt,tez;I ltSx=I,b:lr'z-ri lLg'=r; x n tnm.net.lr+ft - L 4
Bidnolilb: ar.tg t,S nt,I.Z: I-nm,m.t.4
7) sin r + 2 cos r = 0: tg t + 2=O; Lg x= 2; x= -erctg 2 +nn, ne Z,BiAnosiAb: arctq 2 + nn, n e Z.
" Ssin? r sin-rcosx 2cos':xdl Jsfn x, srn x cos ,r = z cos; xi ,-F-. =0;cos- J
iiii:ilii{lilll: AITEEPA Mep3rrK A. r. ra iH. AKaaeMi,{Hxi pisexu Itl SO9
3r --9=arctg2+fin,neZi
't!:4.il.:l_.
:::::Urlg!,
13) sin r + sin 5r- = 0; 2 sin 3r cos 2r = 0;
lsin3x=0. lz'=nn'n"' l,' T.,.t'Lcos2r=o; lz,. |. o*.*.2;
L,=X.V.u.r.
i:':{.!-::.i:iu,, lr=r: frs,r= r l'=n +nn.nez:r'.,= a i l, _2.l---_2. I'- 6 f/,=;; lrcr=i, l,=**"?"-^o.u.r.
3lg"+tgt-2=O.gaMifiai tg n = t. 3t2 + t - 2 = 0t D = 25i
I. rlb f,, ?, fr"'- z l'-a'ctez-nn',-ez'r"- 4 ' I o I o
I" 1,,=-t; ltgx=-r; la=-\anp,t?.7.'14Bilnoaida: arcLe?-nn,ncZ: -fr + nh, h eZ.
9\ 2,5sr'l 2, sin, r= 2; 5sin r cos r sinrr- 2(sine:r + cosr.r) =0:- 3sin'zr 5 sin.rcos.r 2cos'-r-USIn''f + bsln I coa ,r - ZCOS/ .f, = U: " I -+-=O:
\rc, x -|tgx-2=o. cos'x
3aMiHa: tg x = l. 3t' 5tt2 O;D=ll
Bilnoaioa: Y, n eZ; itt, n.z.14) 2-sin'z:r + sin 3x sin r= l; 2 sinr, + B sinr - 4 sinrJ._ sin r_ 1= 0;-4 sin3r + 2 sin,r + 2 sin r=O;4sin3, 2 sin?.r- 2sin.t + 1=0.SaMiEa:sinr=r,rEt 1;11.4f - 2t, -2t+1=Oiltlrt=rt 4.;-2. _2:+1=0i 0=0:
I.at' zt" zt+rlt-)4t _ 2r2 t_
14( 2
- -- il+l-2t +1
Bdnoaidt: !.n=Zi l.t)" ! . trk.kcz.z4t7) sin'z.r.cos?2,!+sin'3r--3: l-cos2r ' l+cos4_t. I cos6r 32' 2 ' 2 ' -n- i.3 cos 2.:!+ cos 4r - cos 6r= 3; cos 2, + cos 6, - cos4r= O;
:iiilit:li:jllt; AITEEPA Mep3rex a. r. ra iH. AKaaeMi{Hrai pise6r i.:::i 5r r
Bidnoeida: ! + nn, n e Z: arclp? r nk. h cZ.4 "3
- 2x ^ x ,x -lul cos- - l.Dsrnr=l: cos'- -Jsrn cos - srn' - - cos' - = (r:'222222
.in"!+s'i"ico'X=o:
Ll =ftn,neLi
Itel*a=0,
z=2fin,nEZi
tc|= -z
lx=znn,neZtlx=-2arcts3!2flk,he7.iilnoaila: 2nn, n e Z; -2 arctgg + 2nk, k e Z.
11) 5 sin 2t - 2 sin r = 0; 10 sin r cos r - 2 sin r = 0; 2 sin r(5 cos r -1) - 0;
^ fx=rn,neZ, lx= nn,nez,lsrnr=u, I I
lt"."r-t=0, 1"o", = t , I r = t "r""o"
I + 2nk- h e z.'lst5Bi6ni'oai0o: nn, n e Z; larccos! + 2xk, h eZ,
Bidnoeilo: !2
510 i::i: AIrEEPA Mep3rex A. f. ra iH. AxaAeMi,{Hran piaenr i::,i!!:i:ii:ii:i.;:11
l,i.I = o,sinfl *nj+3.".{l=0, | 22\ 2 2' 'l"i,r-r-"|-o;
[x=2nn,neZ:,
lf,= - arctc} + nh. k ez;
2l=0;
lx ( ,z "x'\( ,x ,.r)"." t-"'' 2i stnzx. lcos---s'n-rJlcor2 +s'n'
2Jt=cos; l;2sinrcosr cosr=0; cosr(2sinr- 1)=0;
f-lcos.r=
0, lr =a+ rll, rez,o, l"i.'= ]; I x = r_tf ! + na. eez,.' -l 6
+ nn, n ezt (-tl'E+ftk,hez.
12') si^2t =
4=xm; *=2m.
aianoaiaa: lfi+!, nezt +,kez.
941. Lg(5 cos .r) = 0t 5 cos x = fin, n e Zi
"o"" = ]nr.rezr r =larccost*2nh,heZ.55Bilnoailt : ! arccos4 + zfik. h e z.
5
942. sin rl= 2 sin r + cos r.1) cos r > 0; 2fin < x < ft + zrn, n e Z:
sin a = 2 sin r + cos r; sin r + cos r = 0;tg"r+ I -0:tg-r tit=-!+nn.nez.
4
3anoBo,r6gse sin x > 0 : x=4+nh.kcz.4
-sinr=2sinr+cosriSsinr+cosr=0; 3 tgr+ 1=0;
l1tsr = --: r=-arctg-+nn-ne/.
1
SaaoBorLsr. sin x. 0; .t = - arctg : + ,rs, s F Z.
Izfi - arcLg;
2 cos 4-r cos 2r - cos 4x = o: cos 4x(2 cos 2x-1)=ot [:""n1=o:' 2aB2a 1=
-n "*te|
.tt943. ltsin3x> 2 i
\ t znn <3x <8 + zxn, n ez;44n 2nn fl 2fin
12 3 4 3
ln 2ftn ^ 2nn\Bino'idb: l'r+ ;t ; + 7- l. n e z.
Ylrr5]I-,\ .or;<
;'';. ^,. ;' -;' 2nn' n ezi
2! n 4nn . , .!! r 4nn, n .7.3U
t ,n 101! )Bid\osidb: l';' - annt; + 4rn l. n ' 7'
s) "i"(,-i) < +; -! * z^,s,,i=!+ 2,1n, n e7'i
- t - ! * "",
t " I - L + 2tn' n ez;
-ff+znn<x<$+znn,nez.
nianoeia,.: | ff , znn; {t+ znn)' , . z'
"'! + '' =znn<zx='lr-) -2nn,ne7t3630
-L * znn < 2x <1! + 2nn, n ez;26n3n
-;+r,n<x<lr+fln.neL-
Bidno'iab: \ ! + n4 #+ nn
). n ez
'h t x [ fr -nn.n-lt5) rcl;F;ls:t, z,nn'i '3'6 """ -',t! * "".a < !+nn,nez;
63tt-2!
+ snn < x < -! + 3nn, n e z.22
-1Bidnolidh: | "i' + 3nn: ')+}nn],ncz'
\ZL)
o, *"1 ?-'-ll >-t: nn.4 !:3!,nn.n,z,\b
L * nn .?! 3!r i! a nn, n a7i554at 2x 19n+nn<-<-+fin,n€L'5521)
19r ,fi+'fin<2xt-+'fln.nELi
r::::iitili::iiti: MTEEPA Mep3rcK A' r' ra iH' AKaAeMi'{Hxr piBeHb i!:i 513
l7Ycl ln l0M,!
4x =!-on.o, 2, l, =;-7.",,. l, =X,T.^.^*"2, ], lr,=,i-rou.o,r, ), -;, ^o.u,r.
Bidnosidb :- :-, n FZt !' | fth. k cZ.84618) cos'1 ,r + cos'z 4,r = cos? 2-r t- cos? 8xil+cos2r l+cos8r l.cos4-r Ircos6t
2 - , = 2 -- 2 '2+ cos2t+ co68r= 2 + cos 4r + cos 6r; 2 cos 5r cos 3r = 2 cos 5.!cos 5t(cos 3t - cos t) = 0; 2 cos 5r sin 2r sin r = 0i
.lnnnl r lr=-+--nc7-lcossr 0- Itx=-!ILn,ncL, | 10 5
ll'lah-lsin2r=0. l2x=nk.hez. , i.,u.r.I sinx = O: lr=nm-mez:
lr=\m,mcZ.
0;
BiAno6iAb: Eane)xaft IOi 2nl, sfi
v
aa
512 lll: AITEEPA Mep3rer< A. r. ra iH. AKaaeMi,{Hxi piaerb l{::iittalij:iii
n .\nn 19n 5xn
2282n :JnD 19n :inn
Brtnardt, i - .n 7.': 2 8 2i
944. I' ,o. .,r,cos'3 Iar.s,' /3 "n"t
I , I n
: 2 2 o 23 6
2r sit.,r.sir', ".".n"' "i,,r f,t -,"'t-r,3:63:
' I ./l tl r3r rs 2,r 'r4 i. .c zi, ^l ...,,
l : ,r it in ;,r1).a 3j'r'."s : 'i" 3 - 0
ctC 6 "tC " "tA r
945. l)a=nrcsilr(.r 5); t!x 5:li4<i<6; 1)(a): [4;6]:2) u = arccos (n! 15); 1 ! xr 15 < 1;
]r' 15.1, ljr' ! 16,
l'' - r; : -rr '"'
: t+;
,tqr: [-r; -,]rJl!,1"r.r; a ;
3) V .arr,tgu/y1 2i r + 2 >0: r>
946. 1) q 2ar(sin:r- 1, -X:"*"r"r'.ii -n:2arcsinj.!r;5n - n 3n t5n3n
r2,rc,r!r. I l:l.ttl141"44
2) , . 5 3 rrcctg 2.r; i) . urcctg l}- r; 37r ' ;l arcctg 2.r ': 0i5 3ir . 5 3 arrctg 2 ' 5i t(y): (1, 3ri 5).
q47 lr.rr,.",r= ll: Y- "1l!/,,
Rr,ln,ntnt,: Y2
::r ar,r:r, 5n. tt,r",,iti, :lt :
6ill
s,1l=0.21
l2
,i l4 .i 1.1
2i D(ul. | 2; t*).
ll2n;Jl arccnsl t 1) . i
Bidnoair)r: ].2
.r1 arctg(:r +.1:)- |: :. r J; = *, . = 4*!, ' = '11
ltan'nutr: ! \-I
