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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 32 "Maple oppgave om Newtons metode
." }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 "Oppgaven" }}{PARA 0 "" 0 "" 
{TEXT -1 73 "Denne oppgaven ble gitt som en innleveringsoppgave i MAT1
00C h¿sten 2001." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 20 "I denne oppgaven er " }{XPPEDIT 18 0 "g(x) = x^3-3*x+1;" 
"6#/-%\"gG6#%\"xG,(*$)F'\"\"$\"\"\"F,*&F+F,F'F,!\"\"F,F," }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "Deloppgave
 a)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 16 "Te
gn grafen til " }{XPPEDIT 18 0 "g(x);" "6#-%\"gG6#%\"xG" }{TEXT -1 59 
" og la Maple finne tiln¾rmede verdier for nullpunktene til " }
{XPPEDIT 18 0 "g(x);" "6#-%\"gG6#%\"xG" }{TEXT -1 1 "." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "Deloppgave b)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 72 "Forklar a
t dersom vi bruker Newtons metode for Πfinne nullpunktene til " }
{XPPEDIT 18 0 "g(x);" "6#-%\"gG6#%\"xG" }{TEXT -1 9 ", fŒr vi " }
{XPPEDIT 18 0 "x[n+1] = (2*x[n]^3-1)/(3*x[n]^2-3);" "6#/&%\"xG6#,&%\"n
G\"\"\"F)F)*&,&*&\"\"#F)*$)&F%6#F(\"\"$F)F)F)F)!\"\"F),&*&F2F)*$)&F%6#
F(F-F)F)F)F2F3F3" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "F¿lgende \+
program regner ut " }{XPPEDIT 18 0 "x[n];" "6#&%\"xG6#%\"nG" }{TEXT 
-1 34 " (for ikke Œ bŒndlegge variabelen " }{XPPEDIT 18 0 "x;" "6#%\"x
G" }{TEXT -1 24 ", kaller jeg f¿lgen for " }{XPPEDIT 18 0 "c[n];" "6#&
%\"cG6#%\"nG" }{TEXT -1 12 " istedenfor " }{XPPEDIT 18 0 "x[n];" "6#&%
\"xG6#%\"nG" }{TEXT -1 17 "). Se side 156 i " }{TEXT 256 26 "Getting S
tarted with Malpe" }{TEXT -1 24 " for lignende eksempler." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 96 "c:=proc(n::nonnegint)\noption remember:\nif
 n<1 then c0\nelse (2*c(n-1)^3-1)/(3*c(n-1)^2-3) fi end:" }}}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "Dette programmet v
irker pŒ denne mŒten. Etter du har spesifisert startverdien " }
{XPPEDIT 18 0 "c0;" "6#%#c0G" }{TEXT -1 23 " i Newtons metode, vil " }
{MPLTEXT 1 0 12 "evalf(c(n));" }{TEXT -1 24 " gi deg verdien til det \+
" }{XPPEDIT 18 0 "n;" "6#%\"nG" }{TEXT -1 12 "-te punktet " }{XPPEDIT 
18 0 "c[n];" "6#&%\"cG6#%\"nG" }{TEXT -1 63 " i prosessen. Her er et e
ksempel der vi regner ut verdiene fra " }{XPPEDIT 18 0 "c[0];" "6#&%\"
cG6#\"\"!" }{TEXT -1 5 " til " }{XPPEDIT 18 0 "c[5];" "6#&%\"cG6#\"\"&
" }{TEXT -1 5 " nŒr " }{XPPEDIT 18 0 "c0;" "6#%#c0G" }{TEXT -1 8 " er \+
lik " }{XPPEDIT 18 0 "-.3;" "6#,$$\"\"$!\"\"F&" }{TEXT -1 1 ":" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
96 "c:=proc(n::nonnegint)\noption remember:\nif n<1 then c0\nelse (2*c
(n-1)^3-1)/(3*c(n-1)^2-3) fi end:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "c0:=-.3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c0G$!\"
$!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "for i from 0 by 1
 to 5 do\nevalf(c(i));\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!
\"$!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+he!3'Q!#5" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#$\"+2tOmM!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#$\"+Q='HZ$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+`N'HZ$!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+`N'HZ$!#5" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "Deloppgave c)" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 64 "Bruk prog
rammet ivenfor til Œ regne ut de 5 f¿rste verdiene nŒr " }{XPPEDIT 18 
0 "c0;" "6#%#c0G" }{TEXT -1 16 " er henholdsvis " }{XPPEDIT 18 0 "-2;
" "6#,$\"\"#!\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "0;" "6#\"\"!" }
{TEXT -1 4 " og " }{XPPEDIT 18 0 "2;" "6#\"\"#" }{TEXT -1 68 ". Hvorda
n stemmer dette overens med de nullpunktene du fant i punkt " }{TEXT 
-1 3 "a)?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "Deloppgave d)" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 70 "Hvilken rot tro
r du Newtons metode vil tiln¾rme dersom du starter med " }{XPPEDIT 18 
0 "c0 = -.8;" "6#/%#c0G,$$\"\")!\"\"F(" }{TEXT -1 111 " ? Kj¿r program
met ovenfor med startverdien og forklar resultatet geometrisk. Hva skj
er dersom du begynner med " }{XPPEDIT 18 0 "c0 = -.65;" "6#/%#c0G,$$\"
#l!\"#!\"\"" }{TEXT -1 2 " ?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}
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