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{SECT 0 {PARA 256 "" 0 "" {TEXT 256 19 "Calulus Worksheet I" }}{SECT 
0 {PARA 3 "" 0 "" {TEXT -1 19 "Types of functions:" }}{SECT 1 {PARA 4 
"" 0 "" {TEXT -1 28 "The absolute value function:" }}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 55 "plot(abs(x),x=-1..1,\nscaling=constrained, th
ickness=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "plot(abs(abs
(x)-1),x=-2..2,\nscaling=constrained, thickness=2);" }}}}{SECT 1 
{PARA 4 "" 0 "" {TEXT -1 28 "Piecewise defined functions:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "f:=(x)->if x<=0 then -x else x fi:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "plot(f,-1..1,\nscaling=
constrained, thickness=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
41 "g:=(x)->if x<=0 then x^2 else sqrt(x) fi:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 48 "plot(g,-2..4,\nscaling=constrained, thickness=2)
;" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 26 "Combinations of functions:
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "plot([sin,cos,sin+cos],-
Pi..Pi,\ncolor=[red,blue,magenta],\nscaling=constrained, thickness=2);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "f:=(x)->sqrt(x): g:=(x)
->x^2+1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "(f@g)(x):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "(g@f)(x):" }}}}{SECT 1 {PARA 
4 "" 0 "" {TEXT -1 16 "Power functions:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 98 "plot(\{x,x^2,x^3,x^4\},x=-1.2..1.2,\ncolor=[red,blue,
magenta,tan],\nscaling=constrained, thickness=2);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 80 "with(plots):\ndisplay(\nseq( plot(x^n,x=-1.1
..1.1), n=1..6),\nscaling=constrained);" }}}}{SECT 1 {PARA 4 "" 0 "" 
{TEXT -1 18 "Scaling functions:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 52 "plot([sin(x),2*sin(x)], x=-Pi..Pi,color=[red,blue]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot([sin(x),1+sin(x)], x=-P
i..Pi,color=[red,blue]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 
"plot([sin(x),sin(2*x)], x=-Pi..Pi,color=[red,blue]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "plot([sin(x),sin(x-0.4)], x=-Pi..Pi
,color=[red,blue]);" }}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 42 "Approxim
ating the area of the unit circle:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 76 "with(plots):\nngon0:=(n)->[\nseq([cos(2*Pi*k/n),sin(2
*Pi*k/n)],k = 0..n-1) \n]:" }}{PARA 7 "" 1 "" {TEXT -1 42 "Warning, `k
` in call to `seq` is not local" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 136 "display(\{\npolygonplot(ngon0(5),color=magenta),\nplot([cos(t
),sin(t),t=0..2*Pi],color=blue,thickness=2)\n\},\nscaling=constrained,
axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "display(\{
\npolygonplot(ngon0(20),color=magenta),\nplot([cos(t),sin(t),t=0..2*Pi
],color=blue,thickness=1)\n\},\nscaling=constrained,axes=none);" }}}}
{SECT 1 {PARA 4 "" 0 "" {TEXT -1 21 "The Riemann integral:" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 188 "with(student):\nri1 := rightbox(x^
2, x=0..2, 10,\ncolor=red, thickness=3, numpoints=100):\nri2 := leftbo
x(x^2, x=0..2,10, \ncolor=red,thickness=3,numpoints=100):\ndisplay(ri1
,tickmarks=[10,0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "disp
lay(ri2,tickmarks=[10,0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
173 "ri3 := rightbox(x^2, x=0..2, 50,\ncolor=red, thickness=3, numpoin
ts=100):\nri4 := leftbox(x^2, x=0..2,50, \ncolor=red,thickness=3,numpo
ints=100):\ndisplay(ri3,tickmarks=[10,0]);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "display(ri4,tickmarks=[10,0]);" }}}}{SECT 1 {PARA 
4 "" 0 "" {TEXT -1 14 "More plotting:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "plot((x^2+5*x+6)/(x+2),x=-4..4);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 28 "simplify((x^2+5*x+6)/(x+2)):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "f:=(x)->if abs(x)<=1 then abs(x) el
se 1 fi:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "plot(f,\nthickn
ess=2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "plot(f,-3..3);" 
}}}}{SECT 1 {PARA 4 "" 0 "" {TEXT -1 35 "Polynomials and rational func
tions:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "plot(1/x,\nx=-1..1
,y=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "plot(2*x^6-
x^4+(2/5)*x^3+sqrt(2),x=-3..3,y=-40..40);" }}}}{SECT 1 {PARA 4 "" 0 "
" {TEXT -1 17 "Zeno's paradoxes:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 3 "Pi:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "3/4:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "6/8:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 10 "evalf(Pi):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "s:=(n)->sum(1/2^k,k=1..n):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 5 "s(3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 
"evalf(s(100),50):" }}}}}}{MARK "0 0" 19 }{VIEWOPTS 1 1 0 3 2 1804 }