Memoria de Calculo Casa A50

7/23/2019 Memoria de Calculo Casa A50

1/49

Dadj~kg la eieqij $ ojpkdaeg

DADJ^KG LA EIEQIJEGUG MGNK\GEKH

EGUG G$12


2/49

DADJ^KG LA EIEQIEgug mgnk|ge

G^W( OJU PKE\J^ DAHAUAU EGDR

DADJ^KG LA EG IEQIJJN^G? EGUG MGNK\GEKH

R^J[AE\KU\G? G^W( ^KEG^LJ D(

R^JRKA\G^KJ? IGQ^G N( L( @(

QNKEGEKH? EK^EQK\J G( %

RG^WQA P( UH( GHL^U EMJIQIG( RQANIG( D]KEJ


3/49



GFÂFGLJU

F~qauj?Ai |gdgj d}kdj lai gf~afglj f~qauj j f~gpg ua~ g ig |a~ea~g rg~|a lai ra~gi|a la qhg ijug dgekzg j

aurauj~ la ig egrg la ejdr~aukh ah qhg ijug r~a`gn~keglg(

@khj? Ai gf~afglj `khj) lana~ eqdrik~ ejh iju ~awqkuk|ju la hj au|g~ ejh|gdkhglj) |aha~ qh dlqij la `khq~g la

geqa~lj g ij auraek`keglj(

GFQG? Ua lana~ eqklg~ ai ejh|ahklj eij~q~ju { uqi`g|ju ah ai gfqg wqa ua q|kikea rg~g ig `gn~kegekh la dj~|a~jejhe~a|ju) gladu la apk|g~ ai ejh|ahklj la dg|a~kg j~fhkeg j gi|ju ejh|ahklju la uiklju lkuqai|ju) {g w

ejdhdah|a ua eij~g ai gfqg lai uku|adg la uqdkhku|~j(

GEA^J LA Â@QA^_J?Ai ~a`qa~zj ijhfk|qlkhgi j pg~kiigu lana~ ua~ ej~~qfglj a}ear|j rg~g au|~knju) uafh ai egu

Igu pg~kiigu ej~~qfglgu la ~a`qa~zj ejh ~auku|ahekg g ig ìqahekg auraek`keglg -`{+ wqa a}ealg iju 22 cf*ed) rqal

adriag~ua ukadr~a wqa -`{+ uag ai au`qa~zj ej~~aurjhlkah|a g qhg la`j~dgekh la 2(51 !(

Ig dgiig aiae|~jujilglg ejh ~a`qa~zj ikuj j ej~~qfglj ejh qhg ~auku|ahekg -`{+ dg{j~ g 1222 cf*ed(

EJHEÂ\JU? Ua lana~ fg~gh|kzg~ r~khekrgidah|a wqa ai ejhe~a|j eqdrig ejh ig ~auku|ahekg auraek`keglg ah

r~j{ae|j { rj~ ejhuaeqahekg ua guafq~g~ uq lq~gnkiklgl( Rj~ ij |gh|j) igu ~auku|ahekgu r~jdalkju lai ejhe~a|j lana

a}eala~ ukadr~a ai pgij~ aurae`keglj la è rg~g ij eqgi ua la|a~dkhg~ ah |jlju iju eguju uq algl la r~qang


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^AEQN^KDKAH\J DHKDJ LA EJHE^A\JUFaha~giau? 7(1 ed(

Lku|ghekg ikn~a ah|~a pg~kiigu? 7 pg~kiig) ra~j hj 9 >(1 ed 7(1 paeau lai gf~afglj f~qauj adriagl

EKDAH\GEKH

Au|g ua lkua la geqa~lj g iju ~auqi|glju r~jrj~ekjhglju rj~ ai au|qlkj la daehkeg la uqaiju) gu ejdj lai ghi

lai r~j{ae|j { la ig au|~qe|q~g( Rj~ ij |gh|j?

\krj la ekdah|gekh? Ijug la ekdah|gekh la ejhe~a|j g~dglj(

R~j`qhlklgl la laurigh|a? Auraek`keglj ah ai righj la ekdah|gekh(

Gea~j la ~a`qa~zj? Pg~kiigu `{ 4 22 cf* ed>

\krj la uqaij? KK

Egrgeklgl la eg~fg gldkuknia lai |a~~ahj? 71 |jh*d>


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Igu eg~fgu ua~h igu ukfqkah|au?

EG^FGU DQA^\GU? Ujh igu eg~fgu ra~dghah|au lanklj gi rauj r~jrkj la iju dg|a~kgiau(

EG^FGU PKPGU? Ujh igu eg~fgu f~gpk|gekjhgiau wqa jn~gh ah qhg ejhu|~qeekh { wqa hj |kahah eg~e|a~ ra~dghah|a(

EG^FGU GEEKLAH\GIAU? J nkah eg~fg pkpg khu|gh|hag) ig eqgi ua ejhukla~g~ rg~g ai lkuaj uudkej la ig au|~qe|q

ua~ dahj~ wqa ig eg~fg pkpg f~gpk|gekjhgi(

GHIKUKU LA AIADAH\JU AU\^QE\Q^GIAU\jlju iju aiadah|ju au|~qe|q~giau uagh dq~ju) ejiqdhgu) |~gnau) ijugu { ekdkah|ju lana~h lkdahukjhg~ua la |gi `j~

wqa eqdrigh ejh igu haeauklglau lai r~j{ae|j grafglgu gi e~k|a~kj lai lkuaj) ra~j r~khekrgidah|a ujda|klju g

ejdnkhgekh du e~|keg la eg~fgu { ngoj |jlju iju au|glju rjukniau la au`qa~zju - `ia}kh) eg~fg g}kgi( ej~|gh

|j~ukjhgh|a) a|e +( Rj~ ij eqgi) `qa~jh ghgikzglju la geqa~lj g ig |aj~g faha~gi ge|qgi la ig ~auku|ahekg la dg|a~kg

r~jrj~ekjhhljhju au|a e~k|a~kj qh dg~fah la uafq~klgl ah ig au|~qe|q~g(

[g wqa rg~g la|a~dkhg~ ig ~auku|ahekg ~awqa~klg g `ia}kh rj~ eg~fgu dqa~|gu { pkpgu ua rg~|k la?

Dq 4 7(< Dl # 7(6 Di Ljhla3

Dl 4 djdah|j rj~ eg~fg dqa~|g


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EG^GE\AÛ\KEGU LA IJU DG\A^KGIAU [ ÂUQDAH HQD^KEJ(Ai r~auah|a ~auqdah ghgi|kej au ai r~jealkdkah|j adriaglj ah ig ujiqekh lai r~j{ae|j au|~qe|q~gi lai r~j|j|krj

eqau|kh qhlgdah|glj ah?

AURAEK@KEGEKJHAU H(\(E( L(@( ->22(

âuku|ahekg g ig |ahukh? `| 4 1622(22 cf* ed>(

Gig~fgdkah|j g ig ~qr|q~g ah 72 ? =!

Ljniglj g 7=2 ujn~a ai dghl~ki? Pa~ |gnig ah iju righju au|~qe|q~giau(

Gea~j au|~qe|q~gi? G(U(\(D( G


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Rauj rj~ da|~j eqgl~glj? 7=2 cfu(

Gi|q~g? pg~kgnia

p ~auku|ahekg hjdkhgi? 5(1 cf* ed>(

` / d ~auk|ahekg hjdkhgi g ejdr~aukh? 52 cf* ed>(

Ah dlqij la aigu|keklgl? >72 222 cf* ed>

(

DJ^\A^JU -rg~g guah|g~ |gnkwqa+

\krj? KKK

R~jrj~ekh -eadah|j $ g~ahg+ 7?7?0

Ejhe~a|j rg~g egu|kiiju? ` e 4 712 cf* ed>(

IJUGU\KRJ? Pkfqa|g { njpalkiig la >2 ed) Dgekzg la ejhe~a|j g~dglj ejh aurauj~ la 72

pa~ righju


8/49



r(d} 4 2(61 rn

rn 4 2(=1 N i - ` e*`{ 0771*0771 # `{ + - rj~eah|goa rg~g ~a`qa~zj g ig |ahukh +

Gu 4 7< nl* `{

Gu 4 2(60 rn} - nl +

Gu 4 Gu - ah ai eah|~j lai eig~j*2 ed) ai ~au|j ejh`j~da gi eieqij au|~qe|q~gi(

Ejh`j~da g igu H\E L@ >22


9/49



Righju

Au|~qe|q~gekh r~jrqau|g

\gnigu la rauju la dg|a~kgiau { eg~fgu

G_J\AG RIGHG G_J\AG KHEIKHGLG AH\^ARKUJ

\AOG 11

EQGL^GLJ 5=

F^GHK\J 0 5> 5>KDRA^DAGNKIK_GH\A 72 72

AH\J^\GLJ

^AIIAHJ IKFA^J 7>1

IJUG >02 >02 >02

[AUJ 52 52 52

IJUG LA PKFQA\G [ NJPALKIIG LA >2 ED


10/49



G_J\AG RIGHG G_J\AG KHEIKHGLG AH\^ARKUJ -NGJ+

\AOG 11

EQGL^GLJ 5=

F^GHK\J 0 5> 5>

KDRA^DAGNKIK_GH\A 72 72

AH\J^\GLJ

^AIIAHJ IKFA^J 7>1 752

IJUG >


11/49



F^GHK\J 0=

@GE\J^ LA EG^FG 7(

F^GHK\J 0=(22 01(0 7(;2 ;66(=2 7=16(=> ;0(22 >27;( G_J\AG \7

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v

DQ^J

V

R^A\KI

IJUG

Dv IJUG

V

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EGLAHG

EKD

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CF*D

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G

A

A& >(1 5>= =>2 5(51 ;66(= 5>61(0 7;> =6(05 RIGH\G \1

@

6

= 7(52 2(22 2(22 2(51 ==1((22 127(=; G_J\AG \>

;

NGOGLG LA EG^FGU 7 gzj|ag

NGOGLG LA EG^FGU > righ|g gi|g


13/49



IJUG DGEK_G -UA EIEQIJ EJDJ PKFG GHEMG+

PAÛKJH 7(2 25$aha$2; @AEMG LA EIEQIJ? 52$hjp$77EJH@J^DA GI GEK $ 57= 2(2 ed ~aeqn~kdkah|j lai gea~jgi|q~g la ig pkfg ra~gi|a m 4 >2(2 ed

ghemj la ig pkfg n 4 >2(2 edDjdah|j qi|kdj Dq 4 7>)0=7(22 cf$d

~auku|ahekg lai ejhe~a|j @&e 4 >12(22 cf*ed>

@[ 4 22(22 cf*ed> ~auku|ahekg lai gea~j

R^KDA^J EGIEQIGÂDJU UK IG PKFG ÂUKU\A EJDJ UKDRIADAH\A G^DGLG

g+ Rj~eah|goa dg}kdj la gea~j4 2(=1 Rg~g ejhe~a|j &e47=2 Cf*ed>

dg} 2(27;7

n+ Djdah|j D7?4 2(5>7 Khlkea la ~auku|ahekg

D74 @&e n lX> -7$2(1; +D74 56;1;1 >206 cf$ed

EGIEQIJ LA QHG PKFG LA EJHEÂ\J LJNIADAH\A G^DGLG


14/49



Uafqhlj? Egieqig~adju ai g~ag la gea~j G&u lai rg~ la gea~j egrgz la |jdg~ D>

D> 4 Dq $ D7D>4 =)==1(21 cf$dG&u4 7 ai ~auqi|glj qa dqi|krikeglj rj~ 722 { Au|a au ai gea~j lai iaemj uqra~kj~

Rj~ ij |gh|j Gu 4 -Gu $ G&u+ # G&u 4 >7(16 ed> Gea~j ah iaemj khà~kj~

\a~ea~j? pa~k`kegdju uk ai gea~j ah ejdr~aukjh ìq{a

2(2715

2(27;7

2(27;7 8 2(2715 UA LANA E QDRIK^ AU \G LAUK FQGILGL PA^LGLA^J

Rj~ ij |gh|j ai gea~j ah ejdr~aukjh ìq{a ah ig ~qr|q~g { ig pkfg |~gngog ejdj ljniadah|a ~a`j~zglg

EJHEIQUKJHAU WQA UA UAFQK^GH EGIEQIGHLJ \^GNA \2 22 ed QUG^ IJUG DGEK_G M4>2ED


15/49



\^GNA 7

EGIEQIJ LAI DJDAH\J DG]KDJDdg} 4 7)=6 rn4-`.e * @{+ } -/@e

wX> $ > w # 2(221>17 # n} # e 4 2 } 4 $n -n> $$ > w # 7)=6g 675)=50(=2

g 4 7(222 $2(1 w> # w $ 2(221>17(222$

2(221>1717; $g


16/49



EGIEQIJ LAI GEA^J AH \AHUK JHAu|a gea~j gnuj~na~g ig ia}kh la ig pkfg { ua aheqah|~g ah ai iaemj kh a~kj~

Gu 4 5(>0 ed> Gu4r}n}l

gigdn~h 2(576 2(055 2(;12 7(>06Hj( Lapg~kiig 7 > 5 < 1 0 6 = ;

5 2(675 7(1 >(75= >(=12 5(105 61 (15< 5(=22 1(206 0(55< 6(027 =(=06 72(75< 77((=12 1(622 =(117 77( >>(=2> >1(01>6 5(=6; 6(61; 77(05= 71(17= 7;(5;6 >5(>66 >6(710 57(250 527 >2(>0= >1(551 52( 51(1(01> 5>(201 5=( 77(5>(0=> 55 (20;

pg~kiigu hqda~j

1 5 4 5(10 ed> gwq auejoj iju pgij~au la ig |gnig la g~ ~kng

4 ed> gwq auejoj iju pgij~au la ig |gnig la g~ ~kng

4 5(10 ed>

ugeglj la ig |gnig -r `khgi+ 5(10 5(>0 ai |aj~kej haeaug~kj

Au|a pgij~ lana ua~ ukadr~a ikfa~gdah|a kh a~kj~ j rg~aeklj ÂPKUGDJU AI R @KHGIEJ^ÂE\J 8 2(27722 2(27

r `khgi 4 2(27722 r `khgi4Gu*-n}l+ EJ^ÂE\J 8 2(27722 2(22

E E J E J J

G~ag

ahed>

Hda~j la pg~kiigu


17/49



EGIEQIJ LA IJU AU\^KNJUIju au|~knju gnuj~nah igu `qa~zgu ej~|gh|au faha~glgu gi kh|a~kj~ la ig pkfg

egieqij la ig `qa~zg ej~|gh|a la ig pkfg ukdriadah|a grj{glg

Pq 4 >);;=(;1 cf @qa~zg ej~|gh|a Pq4-Vq}Ijhf+*>uk r 2(271

egieqij la ig `qa~zg ej~|gh|a wqa |jdg ai ejhe~a|j ah ig pkfg

Pe~ 4 7)560(6; cf

eieqij la ig uarg~gekjh la au|~knju

Ga 4 2(05 ed G~ag la ig pg~kiig wqa qug~adju ejdj au|~knj } > ~gdgu

@{ au|~knj 4 >)522(22 cf*ed ^auku|ahekg la aug pg~kiig( Gigdn~h4>5223 pg~kiig422

U7 4 7>(;5 edU> 4 55(62 edU5 4 11(0>$ ed HJ\G? Ai Pq ua ejhpka~|a ah ai R) wqa au ig eg~fg ejh wqa uU< 4 71(>2(22 edngua n 4 7=(22 ed~aeqn~kdkah|j ~ 4 >(22 edIjhfk|ql la pkfg 4 >(12 d


18/49



\^GNA >

PAÛKJH 7(72 7=*72*>22= EJH EG^FG QHK@J^DADAH\A ÂRG^\KLG @AEMG LA EIEQIJ? 52$hjEJH@J^DA G IGU H\E$L@) D]KEJGQ\J^? G^W( OJUA PKE\J^ DAHAUAU EGDRJU ojpkdaegBmj|dgki(ejd IGU EAILGU GDG^KIIGU U JH IGU WQA UA I IAHGH EJH LG\JU

HJDNÂ LA IG PKFG \> au|a au ai hjdn~a wqa iiapg ah ai righj

l 4 5= ed au ai pgij~ la m $ ~~aeqn~kdkah|j ~ 4 > ed ~aeqn~kdkah|j lai gea~j g |ahukjh

gi|q~g la ig pkfg ra~gi|a .m. 4 ed ua ~aejdkahlg ig dk|gl la m

Ig~fj la ig pkfg Ijhf 4 12(22 cf*ed> 7 Auejfku|a ig jrekjh >22 cf*ed>


eqgh|kg rj~ |adra~g|q~g 4 2(225 2(22> uk ig pkfg hj au|g g ig kh|adra~ka

2(225 uk ig pkfg au|g g ig kh|adra~ka

@GE\J^ LA ALQEEKJH G @IA]KJH @~ 4 2(;2@( LA ALQEEKJH G EJ^\GH\A @~ 4 2(=2

egieqij la ejhu|gh|au` / e 4 702(22 cf*ed> `/e42(=2 @&e` . e 4 750(22 cf*ed> `.e42(=1 ` / e

EGIEQIJ LA QHG PKFG UKDRIADAH\A GRJ[GLG

LG\JU


19/49



EGIEQIJ LA IG EQGH\KG LA GEA^JDdg} 4 7)=>7(;5 cf$d D~4@~}N}l}l}`.e}w}-7$2(1}w+

w>

$ > w # D^ZZZZ 4 2

Lauraoghlj w { ukfqkahlj ai r~jealkdkah|j g ig la~aemg @^/n/l>/@ewX> $ > w # 2(22767=25> 4 2

g}X> # n} # e 4 2 } 4 $n -n> $$ > w # 7)=>7(;5 4 EA^J

âujipkahlj ig aeqgekjh eqgl~g|keg faha~gi >g >)7>2);2

g 4 7(222 $2(1 w> # w $ 2(22767=25> 4 EA^Jn 4 >(222$

2(22767=25> } 722 e 4 2(767=257=2722 au rj~ I4722 ed

w7 4 7(;7221 $n # -n > $g

Ua qug au|a pgij~ w> 4 2(2=;;1 $n $ -n > $g

r 4 2(22>;7 rg~g lkdahukjhg~ r4w> } -`.e * @{+ ua grikej au|g `j~dqig

âpkukh la R dg} { R dkhr dg} 4 2(2770;7 2(277;7 2(22>0 rg~gda|~ju) au qhg pkfg ejh gea~j ngigheaglj gi 61!EGIEQIJ LAI GEA^J AH \AHUKJH

A | n n i ì k l i k | i i m k ` k


20/49



EGIEQIJ LAI GEA^J RJ^ \ADRA^G\Q^GAu|a gea~j ua aheqah|~j ah ai iaemj uqra~kj~

Uk ig pkfg ua aheqah|~g a}rqau|g g ig kh|ahra~ka ua qug~g 2 (225Uk ig pkfg ua aheqah|~g r~j|afklg la ig kh|adra~ka ua qug~g 2(22>

eqgh|kg 4 2(225G&u 4 7(56 ed Gu4n}l}eqgh|kg

pg~kiigu hqda~j

> < 4 >(15 ed>

$ 2 4 $ ed> 4 >(15 ed>

>(15 7(56

Uk ai ra~gi|a ~angug iju 61 ed) ua ejijeg~g ah dalkj la au|a)gea~j rj~ |adra~g|q~g rg~g apk|g~ gf~ ka|gdkah|j ah ig pkfg



Pq 4 7)uk r 2(271


Pe~ 4 7)


21/49



\^GNA 5

PAÛKJH 7(72 7=*72*>22= EJH EG^FG QHK@J^DADAH\A ÂRG^\KLG @AEMG LA EIEQIJ? 52$hjEJH@J^DA G IGU H\E$L@) D]KEJGQ\J^? G^W( OJUA PKE\J^ DAHAUAU EGDRJU ojpkdaegBmj|dgki(ejd IGU EAILGU GDG^KIIGU U JH IGU WQA UA I IAHGH EJH LG\JU

HJDNÂ LA IG PKFG \5 au|a au ai hjdn~a wqa iiapg ah ai righj

l 4 >= ed au ai pgij~ la m $ ~~aeqn~kdkah|j ~ 4 > ed ~aeqn~kdkah|j lai gea~j g |ahukjh

gi|q~g la ig pkfg ra~gi|a .m. 4 52 ed ua ~aejdkahlg ai 72! lai ig~fj la ig pkfg I

ghemj la ig pkfg n 4 7> ed ua ~aejdkahlg ig dk|gl la m

Ig~fj la ig pkfg Ijhf 4 >(51 d

eg~fg qhk`j~da v V 4 12(22 cf*ed> 7 Auejfku|a ig jrekjh >22 cf*ed>







LG\JU


22/49



EGIEQIJ LA IG EQGH\KG LA GEA^JDdg} 4 5)>;;(06 cf$d D~4@~}N}l}l}`.e}w}-7$2(1}w+

w>

$ > w # D^ZZZZ 4 2

Lauraoghlj w { ukfqkahlj ai r~jealkdkah|j g ig la~aemg @^/n/l>/@ewX> $ > w # 2(221652==> 4 2

g}X> # n} # e 4 2 } 4 $n -n> $$ > w # 5)>;;(06 4 EA^J

^aujipkahlj ig aeqgekjh eqgl~g|keg faha~gi >g 7)717)15;(>2

g 4 7(222 $2(1 w> # w $ 2(221652==> 4 EA^Jn 4 >(222$

2(221652==> } 722 e 4 2(1652==76;722 au rj~ I4722 ed

w7 4 7(0155= $n # -n > $g

Ua qug au|a pgij~ w> 4 2(5 $n $ -n > $g

r 4 2(277>> rg~g lkdahukjhg~ r4w> } -`.e * @{+ ua grikej au|g `j~dqig

^apkukh la R dg} { R dkhr dg} 4 2(2770> 2(277> 2(22>0 rg~gda|~ju) au qhg pkfg ejh gea~j ngigheaglj gi 61!EGIEQIJ LAI GEA^J AH \AHUKJH



23/49





eqgh|kg 4 2(225G&u 4 7(27 ed Gu4n}l}eqgh|kg

pg~kiigu hqda~j

> 5 4 7(

$ 2 4 $ ed> 4 7(

7(


24/49



\^GNA 1PAÛKJH 7(72 7=*72*>22= EJH EG^FG QHK@J^DADAH\A ÂRG^\KLG @AEMG LA EIEQIJ? 52$hjEJH@J^DA G IGU H\E$L@) D]KEJGQ\J^? G^W( OJUA PKE\J^ DAHAUAU EGDRJU ojpkdaegBmj|dgki(ejd IGU EAILGU GDG^KIIGU U JH IGU WQA UA I IAHGH EJH LG\JU

HJDNÂ LA IG PKFG \1 au|a au ai hjdn~a wqa iiapg ah ai righj

l 4 ed ~aeqn~kdkah|j lai gea~j g |ahukjh

gi|q~g la ig pkfg ra~gi|a .m. 4 2 ed ua ~aejdkahlg ig dk|gl la m

Ig~fj la ig pkfg Ijhf 4 12(22 cf*ed> 7 Auejfku|a ig jrekjh >22 cf*ed>







LG\JU


25/49



EGIEQIJ LA IG EQGH\KG LA GEA^JDdg} 4 72)01>(

$ > w # D^ZZZZ 4 2

Lauraoghlj w { ukfqkahlj ai r~jealkdkah|j g ig la~aemg @^/n/l>/@ewX> $ > w # 2(22 # n} # e 4 2 } 4 $n -n> $$ > w # 72)01>(g 0)51>(22

g 4 7(222 $2(1 w> # w $ 2(22(222$

2(22 $g

Ua qug au|a pgij~ w> 4 2(>6> $g

r 4 2(22==> rg~g lkdahukjhg~ r4w> } -`.e * @{+ ua grikej au|g `j~dqig

^apkukh la R dg} { R dkhr dg} 4 2(2770 2(277 2(22>0 rg~gda|~ju) au qhg pkfg ejh gea~j ngigheaglj gi 61!EGIEQIJ LAI GEA^J AH \AHUKJH



26/49





eqgh|kg 4 2(225G&u 4 >(1= ed Gu4n}l}eqgh|kg

pg~kiigu hqda~j

> < 4 >(15 ed>

$ 2 4 $ ed> 4 >(15 ed>

>(15 >(1=

Uk ai ra~gi|a ~angug iju 61 ed) ua ejijeg~g ah dalkj la au|a)gea~j rj~ |adra~g|q~g rg~g apk|g~ gf~ ka|gdkah|j ah ig pkfg



Pq 4 ;)6;1(uk r 2(271


Pe~ 4 5)>6=(66 cf


27/49



\^GNA 0


28/49



EGU\KIIJ C$7

PAÛKJH 7(> >2$dg~$77 @AEMG LA EIEQIJ? >2$dg~$77EJH@J^DA G IGU H\E$2 auejfkj jrekjh % 7

âuku|ahekg lai gea~j @{ 4 cf*ed> auejfkj jrekjh % 72 } >1

G~ag Ge 4 122 ed>F

@GE\J^ LA ALQEEKJH G @IA]KJH @~ 4 2(;2@ LA ÂLQEEKJH G EJ^\GH\A @~ 4 2 =2

EGIEQIJ LA QHG EJIQDHG ÂE\GHFQIG^ G EJDRÂUKH UKDRIA

JEQI\G^ R^JEAUJ DJU\ G^ R^JEAUJ


29/49



EGIEQIJ LAI GEA^J


5 2(675 7(1 >(75= >(=12 5(105 61 (15< 5(=22 1(206 0(55< 6(027 =(=06 72(75< 77((=12 1(622 =(117 77( >>(=2> >1(01>6 5(=6; 6(61; 77(05= 71(17= 7;(5;6 >5(>66 >6(710 57(250 527 >2(>0= >1(551 52( 51(1(01> 5>(201 5=( 77(5>(0=> 55 (20;

pg~kiigu pg~kiig % EGH\( PG^KIIG % @KIG PG^KIIG % G^AG LA PG^KIIGU

= 5 1 71(=51

EJRKG^ PGIJ^ LA IG \GNIG

pg~kiigu pg~kiig % EGH\( PG^KIIG % @KIG PG^KIIG % 5(=22

< 7 5 >(=12


uqdg la pg~kiigU Gu 4 7=(0=

egieqiglg rj~ eqgh|g Gu 4 7=(=2Gu dhkdj eqgh|g ~agi r 4 2(25;=

UK RGUG 8

Hda~j la pg~kiigu


30/49



EJHEIQUK JHAU RG^G LKNQOG^ AH AI RIGHJ ^AUQI\GLJUGEJDJLJ LA AU\^KNJU AH EJIQDHGU

EJIQDHG C$7

DALKLGU Iglj n 4 >2 edIglj m 4 >1 ed~aeqn~kdkah|j ~ 4 7(1 edIjhfk|ql la ig ejiqdhg 4 >( R_GU LA PG KII G

AU\^KNJU Au|~knju lai hda~j 4 > GIGDN^JHUarg~gekh la au|~knju gi eah|~j 4 72 edUarg~gekh la au|~knju ah hqlju 4 1 edIjhfk|ql laurqau la iju rgju 4 02 ed ljhla pgh iju au|~ knju ea~~glju

^APKUKH RG^G PA^ UK EQDRIA IG UAEEKH [ IJU G^DGLJU R^JRQAU\JUEGIEQIJ LA IG A]EAH\^KEKLGL

a 4 2( d a4Dq*Rq

AIAEEKH LAI LKGF^GDG


31/49




32/49



EGU\KIIJ C$>PAÛKJH 7(> >2$dg~$77 @AEMG LA EIEQIJ? >2$dg~$77EJH@J^DA G IGU H\E$2 IGU EAILGU GDG^KIIGU UJH IGU WQA UA IIAHGH EJH LG\JUIjhfk|ql la ig ejiqdhg I 4 >)2>6 cfDjdah|j Dq 4 =)77= cf

âuku|ahekg lai ejhe~a|j @&e 4 cf*ed> auejfkj jrekjh % 7

âuku|ahekg lai gea~j @{ 4 cf*ed> auejfkj jrekjh % 7=(12 ed

qu|al uaiaeekjhj ig ukfqkah|a uaeekh?7> } 52

G~ag Ge 4 502 ed>F

@GE\J^ LA ALQEEKJH G @IA]KJH @~ 4 2(;2@ LA ÂLQEEKJH G EJ^\GH\A @ 2 =2




33/49



EGIEQIJ LAI GEA^J


5 2(675 7(1 >(75= >(=12 5(105 61 (15< 5(=22 1(206 0(55< 6(027 =(=06 72(75< 77((=12 1(622 =(117 77( >>(=2> >1(01>6 5(=6; 6(61; 77(05= 71(17= 7;(5;6 >5(>66 >6(710 57(250 527 >2(>0= >1(551 52( 51(1(01> 5>(201 5=( 77(5>(0=> 55 (20;


< 5 1 6(;76


pg~kiigu pg~kiig % EGH\( PG^KIIG % @KIG PG^KIIG % 5(=22

< > < 1(206


uqdg la pg~kiigU Gu 4 7>(;=

egieqiglg rj~ eqgh|g Gu 4 75(0=Gu dhkdj eqgh|g ~agi r 4 2(25=2

UK RGUG 8 5( 7>(;= 75(0= 9 UK RGUG ^APKUG^ AU\A E^K\A^KJ

G~agahed>

Hda~j la pg~kiigu


35/49




36/49



EGU\KIIJ C$5PAÛKJH 7(> >2$dg~$77 @AEMG LA EIEQIJ? >2$dg~$77EJH@J^DA G IGU H\E$2 auejfkj jrekjh % 7

âuku|ahekg lai gea~j @{ 4 cf*ed> auejfkj jrekjh % 7 } >2

G~ag Ge 4 >F

@GE\J^ LA ALQEEKJH G @IA]KJH @~ 4 2(;2@ LA ÂLQEEKJH G EJ^\GH\A @ 2 =2




37/49



EGIEQIJ LAI GEA^J


5 2(675 7(1 >(75= >(=12 5(105 61 (15< 5(=22 1(206 0(55< 6(027 =(=06 72(75< 77((=12 1(622 =(117 77( >>(=2> >1(01>6 5(=6; 6(61; 77(05= 71(17= 7;(5;6 >5(>66 >6(710 57(250 527 >2(>0= >1(551 52( 51(1(01> 5>(201 5=( 77(5>(0=> 55 (20;


> > < >(15 < 1(206


uqdg la pg~kiigU Gu 4 6(02

egieqiglg rj~ eqgh|g Gu 4 =(==Gu dhkdj eqgh|g ~agi r 4 2(25

UK RGUG 8 >(>> 6(02 =(== 9 UK RGUG ^APKUG^ AU\A E^K\A^KJ

G~agahed>

Hda~j la pg~kiigu


39/49




40/49



EIEQIJ LA IG EKDAH\GEKH


41/49



PAÛKJH 7(2 7=$dg{$2;EJH@J^DA G IGU H\E$L@) D]KEJ GQ\J^? G^W( OJUA PKE\J^ DAHAUAU EGDRJU ojpkdaegBmj|dgki(ejd

LG\JU LA LKUAJeg~fg la lkuaj R 4 5) IIAHG^ IIAHG^ IJU LG\JU LA AH\^GLG -KHRQ\

Ghemj la lkuaj n 4 722(22 ed UA LKUAG^G IG PKFG EJH QH PGIJ^ QHK\G^KJ n 4Ra~gi|a la ijug m 4 71(22 ed

âeqn~kdkah|j ~ ~ 4 22(22 cf*ed>




LKU AJ RJ I\KDG ÂUKU \AHEKG -GEK+

@ge|j~ la eg~fg 4 7((12 cf*d

EGIEQIGDJU EJDJ IJUG DGEK_G

EIEQIJ LA QHG IJUG LA EKDAH\GEKH

EIEQIJ LA IJU DJDAH\JU


42/49



EGIEQIJ LA IGU EQGH\KGU LA GEA^J

AI DJDAH\J UA LG^G AH QHKLGLAU CF$DDjdah|j hafg|kpj a}|a~kj~

7 4 2(75>0/`.E+T/722r7 4 2(22;1 r4- /`.e+*`{

Djdah|j rjuk|kpj> 4 2(>>65; 4SDq*-@~/N/lX>/`.E+T/722r> 4 2(22650 r4- /`.e+*`{

Djdah|j hafg|kpj kh|a~kj~5 4 2(5156> 4SDq*-@~/N/lX>/`.E+T/722r5 4 2(277


43/49



EGIEQIJ LAI GEA^J RG^G \JDG IJU DJDAH\JU

Gu7Gu 4 ed> Gu4r}n}l uarg~gekh= PG^KIIGU LAI Hj( 5 Gu4 1(622 U4 7>(1 ED

Gu>Gu 4 =(72 ed> Gu4r}n}l6 PG^KIIGU LAI Hj( < Gu4 =(=06 U4 7(02 ed> Gu4r}n}l6 PG^KIIGU LAI Hj( 1 Gu4 75(=11 U4 706Hj( Lapg~kiig 7 > 5 < 1 0 6 = ;

5 2(675 7(1 >(75= >(=12 5(105 61 (15< 5(=22 1(206 0(55< 6(027 =(=06 72(75< 77((=12 1(622 =(117 77( >>(=2> >1(01>6 5(=6; 6(61; 77(05= 71(17= 7;(5;6 >5(>66 >6(710 57(250 527 >2(>0= >1(551 52( 51(1(01> 5>(201 5=( 77(5>(0=> 55 (20;

EGIEQIJ LAI GEA^J RJ^ \ADRA^G\Q^GAu|a gea~j ua aheqah|~j ah ai iaemj uqra~kj~ig IJUG ua aheqah|~g a}rqau|g g ig kh|ahra~ka ua qug~g 2(225

G~agahed>

Hda~j la pg~kiigu


44/49



EJHEIQUK JHAU WQA UA LK NQOG^GH AH AI RIGHJ

ra~gi|a m la ig ijug 4 71(22 ed~aeqn~kdkah|j ~ 4 4 5(2= d

uarg~gekjh ah ed hqda~j la pg~kiig

Djdah|j hafg|kpj a}|a~kj~ 4 7>(1 % 5 iaemj kh a~kj~ Djdah|j rjuk|kpj 4 7*< g>*

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Memoria de Calculo Casa A50