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7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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CHNG 2
GII GN NG
PHNG TRNH PHI TUYN
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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I. T BI TON :
Bi ton : tm nghim gn ng caphng trnh
f(x) = 0vi f(x) ! hm !i"n t#c tr"n $ho%ng&ng 'a * ha+ $ho%ng m, (a)-
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1. Kho!" #$#h %& !"h'()
.ho%ng &ng ha+ m, tr"n & t/n ti 12+ nh3tnghim ca phng trnh g4i ! $ho%ng cch !+nghim
*!h %+ :
562 hm f !i"n t#c tr"n on 'a* tho% i72 $inf(a) f() 8 0 th phng trnh f(x) = 0 c& nghim tr"n'a*-
562 hm f n i2 ng9t th nghim ! 12+ nh3t-
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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,- /0 % KCN #3- 45 6h'
78-9 78/9 ;
!" ?@' A5DE! ?o
a
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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F A :m cc $ho%ng cch !+ nghim ca pt
f(x) = ;x< !nx= 0
>i%i :
f?(x) = @x Ax C0 xC0
f hm tDng ng9t n"n pt c& tEi a A nghim
FG+ $ho%ng cch !+ nghim ! (0-H0-I)
f(0-;)= J0-K; f(0-H)=J0-HH f(0-I)=0-0IL
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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F A :m cc $ho%ng cch !+ nghim ca pt
f(x) = x;J ;x A = 0gi%i :a !Mp %ng gi trN ti cc iOm 9c it
5hn vo %ng ta th3+ pt c& nghim trong cc $ho%ng(J
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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>i%i
f?(x) = Px J
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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f?(x) = coSx RxSinx JHx ;a !Mp %ng gi trN ti cc iOm 9c it
5hMn xQt :
f?(x) 8 0 x'A
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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2. C$#h "'' "J! ?!" 45 78L9 M ;
BA: tm t3t c% cc $ho%ng cch !+nghim
B
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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C$# 4h!" 4h$4 "'' "J! ?!"
Uhng php chia Vi
Uhng php !9p n Uhng php !9p 5PWton
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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. C>!" 5hQ# -' S 5@!" $5 :
*!h %+ :>i% SX f(x) !i"n t#c tr"n 'a* $h% vi tr"n (a)562 xY x ! nghim gn ng v nghim chZnh
xc ca phng trnh v[f?(x)[ \ m C 0 x (a)
th Sai SE ]c nh gi thPo cVng th^c :
[xY J x[ [f(xY)[ m
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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F A :_Qt phng trnhf(x) =
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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F A :_Qt phng trnhf(x) = Ix J
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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II. Ph!" Ph$4 Ch'- >'
_Qt phng trnh f(x) = 0 c& nghim chZnh xc xtrong $ho%ng cch !+ nghim 'a* v f(a)f() 8 0-W !"hX- h!h hZ#
ao oxo
aA A
xA xi% SX ch4n gi trN an 2 xo= A- _c Nnh SE !n!9p n $hi x3p x nghim pt vi Sai SE A0J`
(1ng cVng th^c ti"n nghim)>i%ia- g(x)=coSx
g?(x)=JSinxg(x) ! hm co vi h SE co = SinA0-`HAI 8 Ay9t $hc g(x) =coS x '0A* n"n pp !9p hki t#
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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xG+ 1ng 1+ !9pxo= A
xn= coS xnJA_c Nnh SE !n !9p zng cVng th^c ti7n nghim
FM+ SE !n !9p n = AA;
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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Nh! L\5 :
Ec k hki t# ca pp !9p n ph# th2kc vo gitrN ca h SE co
cng nh{ (gn vi 0) th pp !9p hki t# cngnhanh
cng !n (gn vi A) th pp !9p hki t# cng
chMm
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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IF. Ph!" Ph$4 [4 N]^5o!
ykt phng php !9p $hc ! pp !9p 5PWtonn62 hki t# S cho tEc k hki t# nhanh hn
>i% SX hm f $h% vi tr"n $ho%ng cch !+ nghim'a* vi f(a)f() 8 0 v f?(x) 0 x'a*
Uhng trnh f(x) = 0 tng ng vi pt
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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dO tm nghim gn ng ta ch4n A gi trN an 2
xo'a* t+ - _G+ 1ng 1+ !9p xnj thPo cVngth^c
eVng th^c n+ g4i ! cVng th^c !9p 5PWton
ng 2t 1+ xnj c& thO hki t# ho9c phGn $s
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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W !"hX- h!h hZ#
& M 78L9
xoxAxi% SX hm f(x) c& o hm 6n c3p < !i"n t#c v
cc o hm f?(x) v fu(x) $hVng i 132 tr"n on'a*-
.hi 3+ n62 ch4n gi trN an 2 xoth{ai72 $in |o2riPr
f(xo)fu(xo) C 0
h 1+ !9p xnj xc Nnh thPo cVng th^c 5PWtonS hki t# v7 nghim ca pt
7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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Ch + :
di72 $in |o2riPr ch ! i72 $in $hVngph%i ! i72 $in cn
}2i t~c n gi%n ch4n x0th{a i72 $in
|o2riPr :n62 o hm c3p A v < cng 132 ch4n xo= -5g]c !i tri 132 ch4n xo= a
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dO nh gi Sai SE ca pp 5PWton ta 1ngcVng th^c Sai SE tng 2t
[xnJ x[ [f(xn)[ m
m = min [f?(x)[ x'a*
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B-' 5-4 : eho phng trnh
tr"n $ho%ng cch !+ nghim '0i%iA-.iOm tra i72 $in hki t2
f?(x)=;x
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7/25/2019 Chuong 2 - Giai Gan Ding Pt y f x
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n xn n0