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{SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 207 15 "Finding Limits " }
{TEXT 207 0 "" }}{PARA 201 "" 0 "" {TEXT 208 44 "Example 1. Finding th
e following limits (i) " }{XPPEDIT 18 0 "limit(x*sin(1/x),x = 0);" "6#
-%&limitG6$*&%\"xG\"\"\"-%$sinG6#*&F(F(F'!\"\"F(/F'\"\"!" }{TEXT 208 
4 "(ii)" }{XPPEDIT 18 0 "limit(x^2*sin(1/x),x = 0);" "6#-%&limitG6$*&%
\"xG\"\"#-%$sinG6#*&\"\"\"F-F'!\"\"F-/F'\"\"!" }{TEXT 208 8 "  (iii) "
 }{XPPEDIT 18 0 "limit(x*cos(1/x),x = 0);" "6#-%&limitG6$*&%\"xG\"\"\"
-%$cosG6#*&F(F(F'!\"\"F(/F'\"\"!" }{TEXT 208 7 ", (iv) " }{XPPEDIT 18 
0 "limit(x^2*cos(1/x),x = 0);" "6#-%&limitG6$*&%\"xG\"\"#-%$cosG6#*&\"
\"\"F-F'!\"\"F-/F'\"\"!" }{TEXT 208 71 " first without using technolog
y and use technology to very your answer." }{TEXT 208 0 "" }}}{EXCHG 
{PARA 202 "> " 0 "" {MPLTEXT 1 0 17 "f:=x->x*sin(1/x);" }{MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 21 "plot(f(x),x=-10..1
0);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 16 "limit(f(x),x=0);" }
{MPLTEXT 1 0 0 "" }}{PARA 202 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 202 
"> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 
0 23 "limit(f(x),x=0, right);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 202 
"> " 0 "" {MPLTEXT 1 0 38 "plot(\{f(x),x,-x\},x=-1..1,thickness=2);" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 208 84 "Remark: Do
 you see that we can use the \"Squeezing Principle\" to find the limit
 here." }{TEXT 208 0 "" }}{PARA 201 "" 0 "" {TEXT 209 11 "Exercise 1."
 }{TEXT 208 55 " (1) Use graphs with Maple to find the limits of (iii)
 " }{XPPEDIT 18 0 "limit(x*cos(1/x),x = 0);" "6#-%&limitG6$*&%\"xG\"\"
\"-%$cosG6#*&F(F(F'!\"\"F(/F'\"\"!" }{TEXT 208 7 ", (iv) " }{XPPEDIT 
18 0 "limit(x^2*cos(1/x),x = 0);" "6#-%&limitG6$*&%\"xG\"\"#-%$cosG6#*
&\"\"\"F-F'!\"\"F-/F'\"\"!" }{TEXT 208 0 "" }}{PARA 201 "" 0 "" {TEXT 
208 77 "(2) Explain how the Squeezing Principle can be used to find th
e limits above." }{TEXT 208 0 "" }}}{EXCHG {PARA 201 "" 0 "" {TEXT 
208 0 "" }}{PARA 201 "" 0 "" {TEXT 208 58 "Example 2: Find the followi
ng limits with technology: (i) " }{XPPEDIT 18 0 "limit(x*sin(1/x),x = \+
infinity);" "6#-%&limitG6$*&%\"xG\"\"\"-%$sinG6#*&F(F(F'!\"\"F(/F'%)in
finityG" }{TEXT 208 7 ", (ii) " }{XPPEDIT 18 0 "limit(x^2*sin(1/x),x =
 infinity);" "6#-%&limitG6$*&%\"xG\"\"#-%$sinG6#*&\"\"\"F-F'!\"\"F-/F'
%)infinityG" }{TEXT 208 0 "" }}{PARA 201 "" 0 "" {TEXT 208 0 "" }}}
{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 18 "f:=x-> x*sin(1/x);" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 202 "> " 0 "" {MPLTEXT 1 0 23 "plot(
f(x),x=-100..100);" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 201 "" 0 "" 
{TEXT 208 0 "" }}{PARA 201 "" 0 "" {TEXT 209 11 "Exercise 2." }{TEXT 
208 53 " Use the graphs with Maple to find the limits of (i) " }
{XPPEDIT 18 0 "limit(1/x-sec(x),x = 0);" "6#-%&limitG6$,&*&\"\"\"F(%\"
xG!\"\"F(-%$secG6#F)F*/F)\"\"!" }{TEXT 208 7 ", (ii) " }{XPPEDIT 18 0 
"limit(x*sin(x)/(sec(x)-1),x = 0);" "6#-%&limitG6$*(%\"xG\"\"\"-%$sinG
6#F'F(,&-%$secGF+F(F(!\"\"F//F'\"\"!" }{TEXT 208 6 " (iii)" }{XPPEDIT 
18 0 "limit((x-sin(x))/(cos(2*x)-1),x = 0);" "6#-%&limitG6$*&,&%\"xG\"
\"\"-%$sinG6#F(!\"\"F),&-%$cosG6#*&\"\"#F)F(F)F)F)F-F-/F(\"\"!" }
{TEXT 208 0 "" }}{PARA 203 "" 0 "" {TEXT 210 0 "" }}}{PARA 204 "" 0 ""
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