{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 3 1}{FONT 0 "-adobe-helve
tica-bold-r-normal--14-*" "helvetica" "Helvetica-Bold" 8 14 0 "He
lvetica-Bold" 12}{FONT 1 "-adobe-times-medium-r-normal--14-*" "ti
mes" "Times-Roman" 4 14 64 "Times-Roman" 12}{FONT 2 "-adobe-couri
er-medium-r-normal--14-*" "courier" "Courier" 4 14 192 "Courier" 
12}{FONT 3 "-adobe-new century schoolbook-bold-r-normal--17-*" "n
ew century schoolbook" "Times-Bold" 8 17 64 "Times-Bold" 17}{FONT
 4 "-adobe-new century schoolbook-bold-r-normal--17-*" "new centu
ry schoolbook" "Times-Bold" 8 17 64 "Times-Bold" 17}{SCP_R 1 0 20
{COM_R 2 0{TEXT 4 39 "Taylor series convergence demonstration"}}
{COM_R 3 0{TEXT 1 387 "Ocie Mitchell 1993\015\015This worksheet i
llustrates the convergence of the Taylor (power) series for a fun
ction bounded and defined on (-1,1).  You can modify the number o
f terms that will be used, and then view the animation as the ter
ms are gradually added from lowest to highest power.  To get star
ted, just press enter after all of the statements.  Then try your
 own f(x) and play with N."}}{INP_R 4 0 "> "{TEXT 0 12 "with(plot
s):"}}{INP_R 5 0 "> "{TEXT 0 57 "af:=(t,k)->Heaviside(t-k)*(t-k)-
Heaviside(t-1-k)*(t-1-k);"}}{COM_R 6 0{TEXT 1 76 "Change N here t
o reflect the number of terms of the series you wish to use. "}}
{INP_R 7 0 "> "{TEXT 0 6 "N:=20;"}}{INP_R 8 0 "> "{TEXT 0 16 "bf:
=array(0..N);"}}{COM_R 9 0{TEXT 1 34 "Put the f(x) you want to us
e here."}}{INP_R 10 0 "> "{TEXT 0 18 "f:=x->sin(2*Pi*x);"}}{INP_R
 11 0 "> "{TEXT 0 56 "for i to N do bf[i]:=evalf(subs(x=0,diff(f(
x),x$i))) od:"}}{INP_R 12 0 "> "{TEXT 0 46 "ts:=(x,t)->sum(bf[n]/
(n!)*af(t,n)*x^n,n=0..N);"}}{COM_R 13 0{TEXT 1 92 "You must chang
e the valuse ulim and llim to reflect the vertical view range you
 want to use."}}{INP_R 14 0 "> "{TEXT 0 11 "llim:=-1.5;"}}{INP_R 
15 0 "> "{TEXT 0 10 "ulim:=1.5;"}}{COM_R 16 0{TEXT 1 34 "This wil
l animate just the series."}}{INP_R 17 0 "> "{TEXT 0 61 "an:=anim
ate(ts(x,t),x=-1..1,t=0..N,frames=3*N,numpoints=5*N):"}}{INP_R 18
 0 "> "{TEXT 0 28 "subs(DEFAULT=llim..ulim,an);"}}{COM_R 19 0
{TEXT 1 60 "This will animate the series and show f(x) at the sam
e time."}}{INP_R 20 0 "> "{TEXT 0 68 "an:=animate(\{ts(x,t),f(x)\
},x=-1..1,t=0..N,frames=3*N,numpoints=5*N):"}}{INP_R 21 0 "> "
{TEXT 0 28 "subs(DEFAULT=llim..ulim,an);"}}}{END}
