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245 "" 0 "" {TEXT 237 14 "1. Give Answer" }{TEXT 237 0 "" }}{PARA 241 
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{EXCHG {PARA 245 "" 0 "" {TEXT 237 13 "4.Give Answer" }{TEXT 237 0 "" 
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234 1 "\n" }{MPLTEXT 1 234 1 "\n" }{MPLTEXT 1 234 1 "\n" }{MPLTEXT 1 
234 1 "\n" }}{PARA 242 "" 1 "" {XPPMATH 20 "6#$\"\"\"I*undefinedGI*pro
tectedGF&" }{TEXT 20 0 "" }}}{EXCHG {PARA 241 "> " 0 "" {MPLTEXT 1 
234 36 "LimitTutor((x^2-6)/(3-3*x^3),x=1.9);" }{MPLTEXT 1 234 0 "" }}
{PARA 242 "" 1 "" {XPPMATH 20 "6#-I&LimitG6$I*protectedGF&I(_syslibG6
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" }{TEXT 20 0 "" }}}{EXCHG {PARA 245 "" 0 "" {TEXT 237 47 "5.Use limit
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" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "
\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 
1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 
237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }
{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n"
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{MPLTEXT 1 232 32 "DiffTutor(x^3*(x^2+1)^(.5)+3*x);" }{MPLTEXT 1 232 
0 "" }}{PARA 242 "" 1 "" {XPPMATH 20 "6#-I%DiffG6$I*protectedGF&I(_sys
libG6\"6$,&*&I\"xGF(\"\"$,&*$F,\"\"#\"\"\"F1F1$\"\"&!\"\"F1F,F-F," }
{TEXT 20 0 "" }}}{EXCHG {PARA 245 "" 0 "" {TEXT 237 157 "6. Find the d
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PO)." }{TEXT 237 0 "" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 
1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 
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{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n" }{TEXT 237 1 "\n"
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{PARA 245 "" 0 "" {TEXT 237 59 "7. In regard to problem 3, find best d
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"\n" }}}{EXCHG {PARA 246 "> " 0 "" {MPLTEXT 1 0 44 "#g:=diff((x^2-6)/(
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{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 246 "> " 0 "" {MPLTEXT 1 0 57 "g1 \+
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0 "" }}{PARA 242 "" 1 "" {XPPMATH 20 "6#>I#g1G6\"f*6#I\"xGF%F%6$I)oper
atorGF%I&arrowGF%F%,&*&9$\"\"\",&\"\"$F/*$F.F1!\"$!\"\"\"\"#*(,&*$F.F5
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{XPPMATH 20 "6#$!+ieHvY!#5" }{TEXT 20 0 "" }}}{EXCHG {PARA 247 "" 0 ""
 {TEXT 225 47 "This says that delta is approximately .05/.467;" }
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" }{MPLTEXT 1 0 0 "" }}{PARA 242 "" 1 "" {XPPMATH 20 "6#$\"+7Qmq5!#5" 
}{TEXT 20 0 "" }}}{EXCHG {PARA 247 "" 0 "" {TEXT 225 0 "" }}}{EXCHG 
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{MPLTEXT 1 234 52 "EpsilonDeltaPic:=proc(a,L,epsilon,delta,g,xGap,yGap
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{EXCHG {PARA 245 "" 0 "" {TEXT 237 181 "9. Suppose one wishes to make \+
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{TEXT 237 30 "So approximate delta is .00044" }{TEXT 237 0 "" }{TEXT 
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{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 249 "" 0 "" {TEXT 238 128 "10. Repea
t problem 9  for arbitrary epsilon, but in this case use the derivativ
e (slope) to approximate the largest error delta." }{TEXT 238 0 "" }}
{PARA 249 "" 0 "" {TEXT 238 0 "" }}{PARA 249 "" 0 "" {TEXT 238 19 "del
ta=epsilon/113.9" }{TEXT 238 0 "" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" 
}{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n
" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "
\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 
1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 
238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }{TEXT 238 1 "\n" }
{TEXT 238 1 "\n" }{TEXT 238 113 "\n11.  Sketch the derivative of the f
unction below. Using the grid, you should be able to make a very good \+
sketch." }{TEXT 238 0 "" }{TEXT 238 53 "\nThat is the graph below is f
(x) sketch diff(f(x),x)." }{TEXT 238 0 "" }}{PARA 249 "" 0 "" {TEXT 
238 0 "" }}}{EXCHG {PARA 250 "> " 0 "" {MPLTEXT 1 239 0 "" }}}{EXCHG 
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{EXCHG {PARA 251 "" 0 "" {TEXT 240 134 "12.  Sketch a graph f(x) whose
 derivative diff(f(x),x) is given below.  Using the grid, you should b
e able to make a very good sketch." }{TEXT 240 0 "" }{TEXT 240 96 "\nT
his is the opposite of the problem above. That is given that this is d
iff(f(x),x) sketch f(x)." }{TEXT 240 0 "" }}{PARA 250 "> " 0 "" 
{MPLTEXT 1 239 27 "PlotWithGrids(f,-3,5,-5,5):" }{MPLTEXT 1 239 0 "" }
}{PARA 251 "" 0 "" {TEXT 240 0 "" }}}{EXCHG {PARA 250 "" 0 "" 
{MPLTEXT 1 239 71 "plot([f(x),int(f(x),x)],x=-3..5,y=-5..5,discont=tru
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