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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 30 "Limit of a function at a \+
point" }}{PARA 19 "" 0 "" {TEXT -1 19 "Wei-Chi Yang, Ph.D." }}{PARA 0 
"" 0 "" {TEXT -1 11 "Exercise 1." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "f:=x->x^2+1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 35 "g:=proc(x,eps) abs(f(x)-5)-eps end;" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "g(x,eps)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "fsolve(g(x,10^(-3)),x,
1..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "delta:=2-%;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "plot(g(x,0.01),x=1.996..2.01
,y=-0.1..0.1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 
0 "" {TEXT -1 12 "Exercise 2. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 36 "f:=x->(x^3-2*x^2+x-3)/(x^4+3*x^2+5);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 41 "g:=proc(x,eps) abs(f(x)-(-1/33))-eps end;" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "g(x,eps);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
28 "fsolve(g(x,10^(-3)),x,1..3);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "delta:=2-%;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "a:=2-delta;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "b:=2+d
elta;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(g(x,0.01),x=1
..2.08,y=-0.1..0.1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Exercise 3. " }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 16 "f:=x->x/(2*x+1);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 35 "g:=proc(x,eps) abs(f(x)-1)-eps end;" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "g
(x,eps);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "fsolve(g(x,10^(
-3)),x,-2..0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "delta:=ab
s(-1-%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(g(x,0.01),
x=-1.5..0,y=-0.1..0.1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Exerci
se 4." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=x->sin(x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=2;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "g:=proc(x,eps) abs(f(x)-sin(a))-eps end;" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 
"g(x,eps);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "fsolve(g(x,10
^(-9)),x,1..3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "delta:=a
bs(2-%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "c:=a-delta;d:=a
+delta;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "plot(g(x,0.01),x
=1...3,y=-0.1..0.1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Exercise \+
5." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f:=x->1/(x-1)^2;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "g:=proc(x,eps) abs(f(x)-50)-
eps end;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 9 "g(x,eps);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "fsolve(g(x,10^(-3)),x,1..2);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 11 "delta:=2-%;" }}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
42 "plot(g(x,0.01),x=1.996..2.01,y=-0.1..0.1);" }}}{MARK "0 2 0" 11 }
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