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{PARA 0 "> " 0 "" {MPLTEXT 1 0 930 "NewtonRaphson := proc(f:\{name,pro
cedure\},x_0:\{realcons\},L)\noption `Copyright: Brian E. Blank, 1996-
2005`;\nlocal j, k, epsilon, derivative_flag, NRiterates, top, bot;\n
\n\nif not member(nargs, \{2,3\}) then\nERROR(`NewtonRaphson expects t
wo or three arguments.`);\nfi:\n\n\nDigits := 20:\n\nderivative_flag :
= 0:\nNRiterates[0] := evalf(x_0):\nepsilon := 5*10^(-17);\n\n\nfor j \+
from 0 to 99  do\nbot := evalf(D(f)(NRiterates[j])):\nif bot <> 0 then
\ntop := evalf(f(evalf(NRiterates[j]))):\nNRiterates[j+1] := NRiterate
s[j] - top/bot;\nelse\n  derivative_flag := 1:\n  break;\nfi:\n\nif ab
s(NRiterates[j+1]-NRiterates[j]) < epsilon then\n  break;\nfi:\n\nod:
\n\nif nargs = 3\nthen L := [seq(NRiterates[k],k=0..j)]:\nfi:\n \n\nif
 derivative_flag = 1 then\nprintf(`Root of derivative encountered.`);
\nDigits := 10:\nRETURN();\nfi:\n\nif j = 100 then\nprintf(`Warning: C
heck convergence. Process reached maximum iteration bound.`);\nfi;\n\n
\n\nDigits := 10:\nRETURN(NRiterates[j]);\nend:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 40 "L1 := 'L1':   L2 := 'L2':    L5 := 'L5':" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "f1 := x -> (x^2-2);   f2 := \+
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20 "6#>%#f1G:6#%\"xG6\"6$%)operatorG%&arrowGF(,&*$9$\"\"#\"\"\"!\"#F0F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "NewtonRaphson(f5, 1, L5);" }}{PARA 
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{MPLTEXT 1 0 53 "testeq( (a*c-b^2)/(c-2*b+a) = c - (c-b)^2/(c-2*b+a));
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"" {MPLTEXT 1 0 13 "Digits := 20:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 84 "a := 1.4065737204691698392:  b := 1.40810583845004107
52:\nc := 1.4093300324880319502:" }}}{EXCHG {PARA 0 "> " 0 "" 
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