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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 256 13 "MATH 156 F'07" }{TEXT 
261 1 "\n" }{TEXT 260 6 "TEST1A" }}{PARA 256 "" 0 "" {TEXT 257 18 "Ans
wer 3 questions" }{TEXT 258 0 "" }}{PARA 256 "" 0 "" {TEXT 259 81 "Put
 your name and which 3 questions you want graded at the top of your wo
rksheet." }}{PARA 258 "" 0 "" {TEXT -1 59 "\nSome of these commands ne
ed with(student) and with(plots) " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 281 "1.) a.)   Fi
nd the equation of the ellipse with center (-2,1), minor axis parallel
 to the x-axis with length 6 and major axis parallel to the y-axis wit
h length 10.\nb.)  Draw the graph of this ellipse using  scaling=const
rained so that the ellipse will maintain its correct shape. " }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "2.)    \+
Let   f(x) = sin(x^2) . \na.)  Plot f(x) for the domain  x= 0.." }
{XPPEDIT 18 0 "sqrt(Pi/2)" "6#-%%sqrtG6#*&%#PiG\"\"\"\"\"#!\"\"" }}
{PARA 0 "" 0 "" {TEXT -1 537 "\nLet R be the region  bounded above by \+
the the graph you just drew and below by the x-axis.  \n b.)  Draw the
 Riemann rectangles corresponding to left sums with n=20.  Is this an \+
overestimate or an underestimate?\n c.)   Estimate the area of R using
 left sums with 20 intervals.\n d.)   Estimate the area of R  using ri
ght sums with 20 intervals.\n e.)  Estimate the area of R  using the t
rapezoid method with 20 intervals. \n f.)   Find the exact value of th
e same area using Maple to integrate for you.\n g.)  Which approximati
on is best?  \n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "3.)   a)   Fin
d the exact value of    " }{XPPEDIT 18 0 "Int(ln(x),x=1..2) " "6#-%$In
tG6$-%#lnG6#%\"xG/F);\"\"\"\"\"#" }}{PARA 0 "" 0 "" {TEXT -1 130 "b)  \+
Find the smallest value of n for which left hand sums with n subinterv
als gives an approximation whose error is less than .01." }}{PARA 0 "
" 0 "" {TEXT -1 29 "c)  Repeat b) using middlesum" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "d) Repeat b) using trapez
oid" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 94 "4)  a)  What is the error of approximation when left hand sum w
ith n = 20 is used to compute  " }{XPPEDIT 18 0 "Int((x-1)^2,x = 2 .. \+
5);" "6#-%$IntG6$*$,&%\"xG\"\"\"F)!\"\"\"\"#/%\"xG;F+\"\"&" }{TEXT -1 
1 "." }}{PARA 0 "" 0 "" {TEXT -1 29 "b)  Repeat a) using trapezoid" }}
{PARA 0 "" 0 "" {TEXT -1 82 "c) Use a loop to repeat a) and b) with n=
 40, 80,160 and 320.  What do you notice?" }}}}{MARK "5 0 1" 0 }
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