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{SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 204 23 "Newton's method example
" }}}{EXCHG {PARA 200 "> " 0 "" }}{EXCHG {PARA 200 "> " 0 "" }}{EXCHG 
{PARA 200 "" 0 "" {TEXT 204 82 "We want to find the square root of 2, \+
which is a solution to f(x)=0, where f is..." }}}{EXCHG {PARA 200 "> "
 0 "" {MPLTEXT 1 205 18 "f := x -> x^2 - 2;" }}{PARA 201 "" 1 "" 
{XPPMATH 20 "6#>I\"fG6\"f*6#I\"xGF%F%6$I)operatorGF%I&arrowGF%F%,&*$9$
\"\"#\"\"\"!\"#F0F%F%F%" }{TEXT 206 1 " " }}}{EXCHG {PARA 200 "" 0 "" 
{TEXT 204 27 "Here's the derivative of f:" }}}{EXCHG {PARA 200 "> " 0 
"" {MPLTEXT 1 205 11 "df := D(f);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#
>I#dfG6\"f*6#I\"xGF%F%6$I)operatorGF%I&arrowGF%F%,$9$\"\"#F%F%F%" }
{TEXT 206 1 " " }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 35 "This defines
 the Newton iterations:" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 
28 "newt := x -> x - f(x)/df(x);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>
I%newtG6\"f*6#I\"xGF%F%6$I)operatorGF%I&arrowGF%F%,&9$\"\"\"*&-I\"fGF%
6#F-F.-I#dfGF%F2!\"\"F5F%F%F%" }{TEXT 206 1 " " }}}{EXCHG {PARA 200 ""
 0 "" {TEXT 204 76 "Here's the initial guess (use 1., not 1, to ensure
 answers are in decimals):" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 
205 8 "y := 1.;" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"yG6\"$\"\"\"\"
\"!" }{TEXT 206 1 " " }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 22 "Here's
 the next guess:" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "y :
= newt(y);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"yG6\"$\"+++++:!\"*"
 }{TEXT 206 1 " " }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 21 "And the ne
xt guess..." }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "y := new
t(y);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"yG6\"$\"+nmm;9!\"*" }
{TEXT 206 1 " " }}}{EXCHG {PARA 200 "" 0 "" {TEXT 204 21 "And the next
... etc.:" }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "y := newt(
y);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"yG6\"$\"+'o:UT\"!\"*" }
{TEXT 206 1 " " }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "y := \+
newt(y);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"yG6\"$\"+iN@99!\"*" }
{TEXT 206 1 " " }}}{EXCHG {PARA 200 "> " 0 "" {MPLTEXT 1 205 13 "y := \+
newt(y);" }}{PARA 201 "" 1 "" {XPPMATH 20 "6#>I\"yG6\"$\"+iN@99!\"*" }
{TEXT 206 1 " " }}}{EXCHG {PARA 200 "> " 0 "" }}{EXCHG {PARA 200 "" 0 
"" {TEXT 204 17 "ok, time to stop!" }}}{PARA 202 "" 0 "" }}{VIEWOPTS 
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