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{SECT 0 {EXCHG {PARA 257 "" 0 "" {TEXT 256 13 "MATH 156 F'07" }{TEXT 
261 1 "\n" }{TEXT 260 6 "TEST1B" }}{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 -1 280 "1.) a.)   Fi
nd the equation of the ellipse with center (5,-4), minor axis parallel
 to the x-axis with length 9 and major axis parallel to the y-axis wit
h length 4.\nb.)  Draw the graph of this ellipse using  scaling=constr
ained so that the ellipse will maintain its correct shape. " }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "2.)    \+
Let   f(x) = " }{TEXT -1 42 "tan(x) \na.)  Plot f(x) for the domain  x
= " }{XPPEDIT 18 0 "sqrt(Pi/4) .. sqrt(Pi/3);" "6#;-%%sqrtG6#*&%#PiG\"
\"\"\"\"%!\"\"-F%6#*&F(F)\"\"$F+" }{TEXT -1 3 "   " }}{PARA 0 "" 0 "" 
{TEXT -1 537 "\nLet R be the region  bounded above by the the graph yo
u just drew and below by the x-axis.  \n b.)  Draw the Riemann rectang
les corresponding to left sums with n=30.  Is this an overestimate or \+
an underestimate?\n c.)   Estimate the area of R using left sums with \+
30 intervals.\n d.)   Estimate the area of R  using right sums with 30
 intervals.\n e.)  Estimate the area of R  using the trapezoid method \+
with 30 intervals. \n f.)   Find the exact value of the same area usin
g Maple to integrate for you.\n g.)  Which approximation is best?  \n
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 38 "3.)   a)   Find the exact val
ue of    " }{XPPEDIT 18 0 "Int(sqrt(x+1),x = 3 .. 8);" "6#-%$IntG6$-%%
sqrtG6#,&%\"xG\"\"\"F+F+/%\"xG;\"\"$\"\")" }}{PARA 0 "" 0 "" {TEXT -1 
130 "b)  Find the smallest value of n for which left hand sums with n \+
subintervals 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) usin
g trapezoid" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 94 "4)  a)  What is the error of approximation when left ha
nd sum with n = 10 is used to compute  " }{XPPEDIT 18 0 "Int(sin(x),x \+
= 1 .. 4);" "6#-%$IntG6$-%$sinG6#%\"xG/F);\"\"\"\"\"%" }{TEXT -1 1 ".
" }}{PARA 0 "" 0 "" {TEXT -1 29 "b)  Repeat a) using trapezoid" }}
{PARA 0 "" 0 "" {TEXT -1 85 "c) Use a loop to repeat a) and b) with n=
 20,40, 80,160 and 320.  What do you notice?" }}}}{MARK "4 0 1" 0 }
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