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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 20 "Taylor Polynomials I" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 32 "Part 1. \+
 Polynomial Coefficients" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 23 "Load the plots package." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 104 "Answer the questions in Part 1 here.  One at a time, det
ermine appropriate values for the coefficients  " }{XPPEDIT 18 0 "a[0]
" "6#&%\"aG6#\"\"!" }{TEXT -1 7 ", ..., " }{XPPEDIT 18 0 "a[4]" "6#&%
\"aG6#\"\"%" }{TEXT -1 82 ", and replace the 0's in the following defi
nitions.  With each new definition of  " }{XPPEDIT 18 0 "q(x)" "6#-%\"
qG6#%\"xG" }{TEXT -1 106 ",  the plot will be automatic when you enter
 the following block of commands.  Compare with the graph of  " }
{XPPEDIT 18 0 "p(x)" "6#-%\"pG6#%\"xG" }{TEXT -1 18 "  in the web page
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "a[0]:=0
; a[1]:=0; a[2]:=0; a[3]:=0; a[4]:=0; " }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 45 "q:=x->a[0]+a[1]*x+a[2]*x^2+a[3]*x^3+a[4]*x^4;" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 44 "plot(q(x),x=-2..10,y=-600..200,thickness=2);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 38 "Part 2.  Polynomial Appr
oximations to " }{XPPEDIT 18 0 "e^x" "6#)%\"eG%\"xG" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "Answer questions 1 and \+
2 here." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 69 "Enter functions and coefficients here, and plot  f
  and  p  together." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 20 "x:='x':f:=x->exp(x);" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 45 "a[0]:=0; a[1]:=0; a[2]:=0; a[3]:=0; a[4]:=0; " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "p:=x->a[0]+a[1]*x+a[2]*x^2+a[3]*x^3
+a[4]*x^4;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "plot1:=plot(f(x),x=-3
..3,y=-2..16,thickness=2, color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 58 "plot2:=plot(p(x),x=-3..3,y=-2..16,thickness=2, color=red):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "display(plot1,plot2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Plot the error function, and an
swer question 4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 44 "plot(f(x)-p(x),x=-3..3,y=-1..1,thickness=2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "Answer question 5 here." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 259 43 "Part 3.  Polynomial Approximations to sin x" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "Answer questions 1
 and 2 here." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 69 "Enter functions and coefficients here, an
d plot  g  and  p  together." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 20 "x:='x':g:=x->sin(x);" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 54 "a[0]:=0; a[1]:=0; a[2]:=0; a[3]:=0; a[4]:=0; a[5]:=
0; " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "p:=x->a[0]+a[1]*x+a[2]*x^2+a
[3]*x^3+a[4]*x^4;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "plot1:=plot(g(
x),x=-Pi..Pi,y=-2..2,thickness=2, color=blue):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "plot2:=plot(p(x),x=-Pi..Pi,y=-2..2,thickness=2, color
=red):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "display(plot1,plot2);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "Plot the error function, \+
and answer question 4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 38 "plot(g(x)-p(x),x=-Pi..Pi,thickness=2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 23 "Answer question 5 here." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT 260 16 "Part 4.  Summary" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 34 "Answer the summary questions here." }}
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0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "25" 0 
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