Taller #2 Métodos Numéricos

 

\CBPLY^BKJK KLE PJEEL @jnuetjk kl Bchlcblrïj Lsnulej kl Bchlcblrïj kl ^bstlojs y Ngoputjnbþ c Trghrjoj6 Bchlcblrïj kl ^bstlojs y Ngoputjnbþc - >8;>

[jeelr 9 Jcêebsbs y Oâtgkgs Cuoârbngs  

Jutgrls6 Ngrtâs Ngrtâs Kjvbk ^jctbjhg - :8;> Grgzng Aurtjkg Jelfjckrg - :8;;;>2 Lkwbc Je`gcsg Ogctlrg - :4;;001

Trg`lsgrj6 Ojrbj Tjtrbnbj [rufbeeg \rbil

Cgvbloirl kl 94:2  

Trlhuctjs

 

Trgielos 9.:6 :, 9, >, 1, :4, ::, 9:, 99

Trgielos 9.96 :, 9, >, ;, 1, :, 6 ;, bctrgkunbkj lc le ebirg pêhbcj >2, sl lstjielnl jsï6 | ̉| 5 :4   ∙  

   5 9   ∙   pjrj ijsl :4, pjrj ijsl 96 |  | ^blckg c ej pgsbnbþc klskl kgckl sl trucnj tr ucnj le cöolrg klnboje, ls klnbr sl klsnjrtjc tgkgs egs cöolrgs kl ej pgsbnbþc   : lc jklejctl, pgr eg tjctg, pjrj le ojrn->9

 5 9 |  |

  ∙ 

yj qul le ojrn->9 utbebzj 9> ibts pjrj ej ojctbsj. Tgr öetbog ej ucbkjk kl lrrgr ls lctgcnls 9   ∙ . 9.:.9. ^blckg (:.  . . . )9     le cöolrg ibcjrbg ib cjrbg cgrojebzjkg kl :/:4 

(4.444: 4::44 :44::4 ::44:: 4::.. . . )  ^u rlprlslctjnbþc ibcjrbj ls6  ? (4.44 ^blckg ∙  le cöolrg trucnjkg t rucnjkg j 9; ibts klspuâs kle puctg klnboje y + le cöolrg rlkgckljkg ucj ucbkjk ajnbj jrrbij6 ∙  ? (4.444::44::44::44::44::44:)  +  ? (4.444::44::44::44::44::4:4)  Njkj ucg ngc 9; ibts klspuâs kle puctg `rjnnbgcjrbg. ` rjnnbgcjrbg. Tjrj kltlrobcjr nuêe kl egs kgs lstê oês nlrnj je vjegr rlje kl :/:4sl rlstjc kl ej sbhublctl `groj6

 

   ∘ 9   ∙  ?    :  2 +   ? (:  ) ∘ 9   ∙ ?  ∘ 9 :4 :4

  ∙  ? (4.4 (4.444 44:: ::.. . . ) ∘ 9

  ∙

Tgr tjctg ∙ ls le cöolrg oês nlrnjcg j

  ∙ 

, ( () ) ? ∙ 

Eulhg le lrrgr 9   ∙  ls6 |()  |?  ∘jisgeutg 

Lrrgr rlejtbvg6

|()  | / || ? 9

  ∙ 

9.:.>. j.^blckg (:.   . . . ) Ø 9    le cöolrg lc su rlprlslctjnb rlprlslctjnbþc þc ibcjrbj rlkgckljkj, ·Nuêe ls le lrrgr rlejtbvg kl rlkgcklg7 Trbolrg ngcvlrtbrlogs >/< j ibcjrbg, ngog ls klnboje jhrlhjogs uc nlrg y uc puctg prbolrg6 >/< ? 4.0 4.0 * 9 ? :.9

➟

:

4.9 * 9 ? 4.;

➟

4

4.; * 9 ? 4.1

➟

4

4.1 * 9 ? :.0

➟

:

4.0 * 9 ? :.9

➟

:

. . . Plogs qul le pjtrþc sl rlpltbrê bc`bcbtjolctl, lctgcnls tlclogs6 x ? (>//< * 9-9;  +

+

-

-

-9;

-9;

-9;

x - x ? (x  - x ) - (x - x ) ? 9  - >/< * 9  ? 9/< * 9   Ajnblckg ej ngopjrjnbþc cgs kjogs nulctj qul le vjegr oês nlrnjcg j x lctrl x + y x- ls x+ pgr eg nuje ajnlogs `e(x) ? x+  Le lrrgr kl rlkgcklg rlejtbvg ls6 |`e(x) - x| / |x| ? |9/< * 9-9;| / >/< ? :/> * 9-9>  i. rlspgckj j pjrj le cöolrg 9/8 Rj qul 9/8 ls uc cöolrg klnboje plrbþkbng bc`bcbtg, pjrj rljebzjr ej ngcvlrsbþc kl rlje j ibcjrbg cgrojebzjkg sbchel-prlnbsbgc sl utbebzþ ej e j rlprlslctjnbþc 4.91 ·Nuêctgs Ibts kl prlnbsbþc sl pblrklc lc ej rlstj (:-ngs x) nujckg x?µ 7 Ajnlogs x?:, y? ngs (:/;) ↙ :-(y/x)≁ 4.4>:, 9 ?4.4>:, i? (ec(4.4>:)/ec(9))?- >9112  Lrrgr jisgeutg6

|4.>>>>> >9112  4.>>>>9 2| ? 4.;9111 Ø :4

  ∙  

 Jsuoblckg < pulstgs pulstgs klnbojels pjrj le nabp kle prgnlsjkgr6  (/)  ( /) ? 44.>>>>> .>>>>> 

  ∙  

 

  Lrrgr rlejtbvg6

(|4.>>>>>>9112 (|4.>>> >>>9112  4.>>> 4.>>>>>|) >>|) / 4.>>>> 4.>>>>>>9112 >>9112 ? 4.> Ø :4  

∙  

n.  ?

;: 22< : ;;>19  / ( ) ? :.>>>1 :.>>>199 4;;2:  Lrrgr jisgeutg6

|:.>>>19 |:.>>> 19  :.> :.>>>194;;2 >>194;;2:| :| ? 4.;;2: Ø :4  

∙  

Lrrgr rlejtbvg6

 (/ ) ? :.>>>19   (/) :.>>>194;;2:  (/) / :.>>>194;;2: ? 4.>084: Ø :4

  ∙  

9.>.;. Le cöolrg kl ngckbnbþc kl ej `ucnbþc ` ?   ls bcklplckblctl bcklplckblctl kl x ·Nuêe ls cöolrg kl ej ngckbnbþc7

      ‹() usjogs () lctgcnls     ?j 9.>.