{VERSION 5 0 "IBM INTEL NT" "5.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 
257 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 1 14 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 }{CSTYLE "" -1 260 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 
262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 
2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 
{CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 
4 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Ti
mes" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 
2 2 1 1 1 1 }3 1 0 0 12 12 1 0 1 0 2 2 19 1 }}
{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 259 16 "MAPLE HOMEWORK \n" }
{TEXT -1 30 "DUE DATE: DECEMBER 20th, NOON\n" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT 260 35 "Name: _____________________________" }{TEXT -1 1 "\n" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "INSTRUCTIONS: " }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 101 "Complete the followin
g maple worksheet and e-mail it to me (kseniya@uwm.edu) by Noon, Decem
ber 20th. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 82 "Please save the worksheet with your First and Last Names as the
 name of the file. " }{TEXT 269 152 "Make sure, you have only one exte
nsion on the file name and it is .mws! (Example: KseniyaFuhrman.mws, N
OT KseniyaFuhrman.mws.mw or KseniyaFuhrman.mw).  " }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 50 "The subject of the e-mail
 should be in the form: \"" }{TEXT 261 37 "First Name Last Name MAPLE \+
Assignment" }{TEXT -1 183 "\". I will send you a reply message confirm
ing that I got your worksheet. If you didn't get a reply from me, this
 means that I did not receive your assignment and your score will be 0
." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 130 "No \+
late assignments will be accepted. So, please, submit ahead of time to
 get a confirmation from me in case you need to resubmit." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta
rt;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 
"" 0 "" {TEXT -1 10 "Question 1" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 
"Here are two functions.  " }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "f(x) = (1
-cos(x))/x;" "6#/-%\"fG6#%\"xG*&,&\"\"\"F*-%$cosG6#F'!\"\"F*F'F." }
{TEXT -1 6 ", a=0\n" }{XPPEDIT 18 0 "g(x) = -1/sqrt(4-x^2);" "6#/-%\"g
G6#%\"xG,$*&\"\"\"F*-%%sqrtG6#,&\"\"%F**$F'\"\"#!\"\"F2F2" }{TEXT -1 
233 ", a=1\nWhat are the domains of these functions (You don't have to
 use MAPLE to answer this)?\n\nFor  each of them, do the following: fi
rst, try to guess without using MAPLE whether or not the function has \+
a limit at the indicated point " }{XPPEDIT 18 0 "a;" "6#%\"aG" }{TEXT 
-1 118 ". Now, using MAPLE, check (or formulate) your guess numericall
y by evaluating the function at several points close to " }{XPPEDIT 
18 0 "a;" "6#%\"aG" }{TEXT -1 85 "; then graph the function and confir
m that the graph has the expected behaviour near " }{XPPEDIT 18 0 "a;
" "6#%\"aG" }{TEXT -1 19 "; finally, use the " }{TEXT 257 5 "limit" }
{TEXT -1 30 " command to verify the result." }{TEXT 256 0 "" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }
}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Question 2" }}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 4 "Use " }{TEXT 258 9 "piecewise" }{TEXT -1 22 " to de
fine a function " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 19 " which i
s equal to " }{XPPEDIT 18 0 "sin(x);" "6#-%$sinG6#%\"xG" }{TEXT -1 4 "
 if " }{XPPEDIT 18 0 "x < 0;" "6#2%\"xG\"\"!" }{TEXT -1 11 ", equal to
 " }{XPPEDIT 18 0 "-x^2;" "6#,$*$%\"xG\"\"#!\"\"" }{TEXT -1 4 " if " }
{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 40 " is in the interval (0,2), \+
and equal to " }{XPPEDIT 18 0 "2^x;" "6#)\"\"#%\"xG" }{TEXT -1 4 " if \+
" }{XPPEDIT 18 0 "2 < x;" "6#2\"\"#%\"xG" }{TEXT -1 16 ".  Find whethe
r " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 77 " has left and right li
mits at 0, and whether the (two-sided) limit exists as " }{XPPEDIT 18 
0 "proc (x) options operator, arrow; 0 end;" "6#f*6#%\"xG7\"6$%)operat
orG%&arrowG6\"\"\"!F*F*F*" }{TEXT -1 13 ".  Repeat at " }{XPPEDIT 18 
0 "x = 2;" "6#/%\"xG\"\"#" }{TEXT -1 17 ".  Finally, plot " }{XPPEDIT 
18 0 "f;" "6#%\"fG" }{TEXT -1 28 " on an appropriate interval." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
-1 10 "Question 3" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Define a func
tion " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 11 " such that " }
{XPPEDIT 18 0 "f(x) = x^3-x^2+4*x;" "6#/-%\"fG6#%\"xG,(*$F'\"\"$\"\"\"
*$F'\"\"#!\"\"*&\"\"%F+F'F+F+" }{TEXT -1 33 ".  First, find the deriva
tive of " }{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 18 " as a function o
f " }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 11 ", and plot " }
{XPPEDIT 18 0 "f;" "6#%\"fG" }{TEXT -1 103 " and its derivative on the
 same set of axes.  Next, find the equation of the tangent line to the
 graph " }{XPPEDIT 18 0 "y = f(x);" "6#/%\"yG-%\"fG6#%\"xG" }{TEXT -1 
33 " at the point on the graph where " }{XPPEDIT 18 0 "x = 3/2;" "6#/%
\"xG*&\"\"$\"\"\"\"\"#!\"\"" }{TEXT -1 11 ", and plot " }{XPPEDIT 18 
0 "f;" "6#%\"fG" }{TEXT -1 47 " and this tangent line on the same set \+
of axes." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "How are the graphs of f(x) an
d f '(x) related?" }{MPLTEXT 1 0 1 "\n" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 30 "Find the second derivative of " }{TEXT 262 2 "f " }{TEXT 
-1 25 " as a funcion of x, plot " }{TEXT 263 14 "f, f ', f ''  " }
{TEXT -1 24 "on the same set of axes." }{MPLTEXT 1 0 0 "" }}}}{EXCHG 
{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Question 4" }}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 16 "Graph the curve " }{XPPEDIT 18 0 "y^4 = y
^2-x^2;" "6#/*$%\"yG\"\"%,&*$F%\"\"#\"\"\"*$%\"xGF)!\"\"" }{TEXT -1 8 
" . Find " }{XPPEDIT 18 0 "dy/dx" "6#*&%#dyG\"\"\"%#dxG!\"\"" }{TEXT 
-1 3 " . " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT 
-1 10 "Question 5" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Given the fun
ction  " }{XPPEDIT 18 0 "f(x) = 2/(x^2);" "6#/-%\"fG6#%\"xG*&\"\"#\"\"
\"*$F'F)!\"\"" }{TEXT -1 25 " on the interval [1,5].  " }}{PARA 0 "" 
0 "" {TEXT -1 80 "Approximate the area under the curve  using 6 subdiv
isions and right end-points." }}{PARA 0 "" 0 "" {TEXT -1 274 "Approxim
ate the area under the curve  using 6 subdivisions and left end-points
\nApproximate the area under the curve  using 12,25,50,100 subdivision
s and right end-points.\nGuess the exact area under the curve based on
 your approximations.\nFind the exact area under the curve." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Question \+
6" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "The velocity function of an o
bject moving along a straight line is " }{XPPEDIT 18 0 "v(t) = t^3-t^2
-2*t;" "6#/-%\"vG6#%\"tG,(*$F'\"\"$\"\"\"*$F'\"\"#!\"\"*&F-F+F'F+F." }
{TEXT -1 49 ". Find the displacement of the object over [-1,2]" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Question \+
7" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Plot the function " }
{XPPEDIT 18 0 "f(x) = 1-x^2/4;" "6#/-%\"fG6#%\"xG,&\"\"\"F)*&F'\"\"#\"
\"%!\"\"F-" }{TEXT -1 33 " on the interval [-2,3]. Find the" }{TEXT 
268 11 " total area" }{TEXT -1 45 " of the region between the curve an
d x-axis. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{TEXT -1 0 
"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "1 0 0" 
32 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }