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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 13 "Mid-Term Exam" }}{PARA 
19 "" 0 "" {TEXT -1 6 "Name: " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
256 253 "Directions (Level 1): Do 10 of the 12 following problems.  Do
 not do more than 10.  You may use your lecture notes, homework assign
ments, lecture review questions, and Maple's built-in help.  Do the te
st on this file.  When you are finished, save it as " }{TEXT -1 0 "" }
{TEXT 272 20 "YourName-MidtermExam" }{TEXT 273 1 " " }{TEXT 274 43 "an
d e-mail it to me at kkillian@cas.usf.edu" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT 257 12 "Problem 1.  " }{TEXT -1 20 "Assig
n the equation " }{XPPEDIT 18 0 "x^3-6*x^2-7*x+60 = 0;" "6#/,**$%\"xG
\"\"$\"\"\"*&\"\"'F(*$F&\"\"#F(!\"\"*&\"\"(F(F&F(F-\"#gF(\"\"!" }
{TEXT -1 17 " to the variable " }{TEXT 258 3 "eqn" }{TEXT -1 44 ", fac
tor the polynomial, and solve equation." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }{TEXT 265 9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 259 11 "Pro
blem 2. " }{TEXT -1 90 "Write a program that prints out all of the 3-e
lement lists that can be made from the list " }{XPPEDIT 18 0 "[1, 2, 3
, 4, 5];" "6#7'\"\"\"\"\"#\"\"$\"\"%\"\"&" }{TEXT -1 1 "." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }{TEXT 264 9 "Solution:" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 11 "Problem
 3. " }{TEXT -1 31 "Write a program that evaluates " }{XPPEDIT 18 0 "e
xp(x);" "6#-%$expG6#%\"xG" }{TEXT -1 33 " as a floating point decimal \+
for " }{XPPEDIT 18 0 "x = 1;" "6#/%\"xG\"\"\"" }{TEXT -1 4 " to " }
{XPPEDIT 18 0 "x = 5;" "6#/%\"xG\"\"&" }{TEXT -1 13 " counting by " }
{XPPEDIT 18 0 "1/2;" "6#*&\"\"\"F$\"\"#!\"\"" }{TEXT -1 1 "." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }{TEXT 263 9 "Solution:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 261 10 "Problem 4." }{TEXT -1 34 "  From trigonometry, we know t
hat " }{XPPEDIT 18 0 "cos(pi) = -1;" "6#/-%$cosG6#%#piG,$\"\"\"!\"\"" 
}{TEXT -1 61 ".  Why does the following command not return the value o
f -1?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "cos(pi);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT 262 9 "Solution:" }}{PARA 0 "" 0 "" 
{TEXT -1 3 "   " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 266 
10 "Problem 5." }{TEXT -1 60 "  Explain the difference between local a
nd global variables." }}{PARA 0 "" 0 "" {TEXT 267 9 "Solution:" }
{TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }{TEXT 268 10 "Problem 6." }{TEXT -1 31 "  Let f be
 defined by the rule " }{XPPEDIT 18 0 "f(x) = exp(sin(x))+cos(x)*exp(x
);" "6#/-%\"fG6#%\"xG,&-%$expG6#-%$sinG6#F'\"\"\"*&-%$cosG6#F'F/-F*6#F
'F/F/" }{TEXT -1 109 ".  Use two of the three methods (arrow, unapply,
 procedure) to define this function in Maple and test it for " }
{XPPEDIT 18 0 "x = 0,pi/2;" "6$/%\"xG\"\"!*&%#piG\"\"\"\"\"#!\"\"" }
{TEXT -1 6 ", and " }{XPPEDIT 18 0 "pi;" "6#%#piG" }{TEXT -1 1 "." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 271 9 "Solution:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 269 10 "Problem 7." }
{TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 56 "What is the Maple comma
nd to factor 7657650 into primes?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 270 9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 275 10 "Problem 8." }
{TEXT -1 40 "  Write a program that computes the sum " }{XPPEDIT 18 0 
"sum(1/(2^n),n = 1 .. 1000);" "6#-%$sumG6$*&\"\"\"F')\"\"#%\"nG!\"\"/F
*;F'\"%+5" }{TEXT -1 53 " and evaluates the sum as a floating point de
cimal.  " }{TEXT 276 39 "DO NOT USE MAPLE'S BUILT-IN SUM PROGRAM" }
{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 277 9 "Solution:
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }{TEXT 278 10 "Problem 9." }{TEXT -1 6 "  The " }
{TEXT 279 13 "golden ratio " }{TEXT -1 133 "occurs in a rectangle when
 the sides of the rectangle have the following property:  If the lengt
hs of the sides of the rectangle are " }{TEXT 280 4 "a+ b" }{TEXT -1 
5 " and " }{TEXT 281 1 "b" }{TEXT -1 33 ", then the ratio of the sides
 is " }{XPPEDIT 18 0 "(a+b)/a = a/b;" "6#/*&,&%\"aG\"\"\"%\"bGF'F'F&!
\"\"*&F&F'F(F)" }{TEXT -1 31 ".   Assume for simplicity that " }
{XPPEDIT 18 0 "b = 1;" "6#/%\"bG\"\"\"" }{TEXT -1 13 ".  Solve for " }
{TEXT 282 1 "a" }{TEXT -1 95 " to find what the golden ratio is.  Expr
ess it as a floating point decimal.  Keep in mind that " }{TEXT 283 1 
"a" }{TEXT -1 91 " is a length and is therefore not negative. You may \+
use Maple's solve procedure to aid you." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }{TEXT 297 9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 284 11 "Problem 10." }{TEXT -1 2 "  " }{TEXT 285 0 "" }
{TEXT -1 70 "Write a program that will take the set of all primes less
 than 50 (S=\{" }{XPPEDIT 18 0 "2,3,5,7,11,13,17,19,23,29,31,37,41,43,
47;" "61\"\"#\"\"$\"\"&\"\"(\"#6\"#8\"#<\"#>\"#B\"#H\"#J\"#P\"#T\"#V\"
#Z" }{TEXT -1 29 "\}), and changes each element " }{TEXT 286 1 "n" }
{TEXT -1 4 " to " }{XPPEDIT 18 0 "(n+1)/2;" "6#*&,&%\"nG\"\"\"F&F&F&\"
\"#!\"\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 287 
9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 288 12 "Problem 11. " }{TEXT -1 1 " " }}{PARA 0 
"" 0 "" {TEXT -1 42 "(a). Explain the difference between using " }
{TEXT 290 5 "break" }{TEXT -1 4 " or " }{TEXT 291 6 "return" }{TEXT 
-1 25 " to end a loop/procedure." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 289 10 "Solution: " }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 41 "(b) Explain the difference between u
sing " }{TEXT 292 5 "print" }{TEXT -1 4 " or " }{TEXT 293 6 "return" }
{TEXT -1 16 " in a procedure." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
294 9 "Solution:" }{TEXT -1 3 "   " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 295 11 "Problem 12." }
{TEXT -1 167 "  In Lecture 3 we discussed a program that counts the nu
mber of times each digit appeared in a number.  Find the number of tim
es that each digit appears in the number " }{XPPEDIT 18 0 "exp(1);" "6
#-%$expG6#\"\"\"" }{TEXT -1 99 " when it is expanded to 1000 decimal p
laces.  You may use either of the methods discussed in class." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 " " }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
296 26 "Extra Credit (10 points): " }{TEXT -1 116 "Sir Isaac Newton pr
oved through calculus that the final position of an accelerated object
 is given by the equation  " }{XPPEDIT 18 0 "x[f] = x[i]+v[i]*t+a*t^2/
2;" "6#/&%\"xG6#%\"fG,(&F%6#%\"iG\"\"\"*&&%\"vG6#F+F,%\"tGF,F,*(%\"aGF
,*$F1\"\"#F,F5!\"\"F," }{TEXT -1 8 ", where " }{XPPEDIT 18 0 "x[f];" "
6#&%\"xG6#%\"fG" }{TEXT -1 38 " is the final position of the object, \+
" }{XPPEDIT 18 0 "x[i];" "6#&%\"xG6#%\"iG" }{TEXT -1 26 " is the initi
al position, " }{XPPEDIT 18 0 "v[i];" "6#&%\"vG6#%\"iG" }{TEXT -1 40 "
 is the initial velocity of the object, " }{XPPEDIT 18 0 "a;" "6#%\"aG
" }{TEXT -1 40 " is the acceleration of the object, and " }{XPPEDIT 
18 0 "t;" "6#%\"tG" }{TEXT -1 131 " is the amount of time it was movin
g. Write a program that calculates the amount of time the object was m
oving given the variables " }{XPPEDIT 18 0 "x[f],x[i],v[i],a;" "6&&%\"
xG6#%\"fG&F$6#%\"iG&%\"vG6#F)%\"aG" }{TEXT -1 264 ".  Have your progra
m take into account that since this is a quadratic equation, is might \+
be possible for the equations to result in a negative solution, and su
ch solutions should be disregarded.  You may use and modify the QSOLVE
R procedure you wrote for homework." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 212 "Use this program to find how long it wo
uld take a person who jumps out of a plane at 10,000 m with an initial
 velocity of 1 m/s to fall to the earth (where the height is 0) when i
t is being accelerated at -9.8 m/" }{XPPEDIT 18 0 "s^2;" "6#*$%\"sG\"
\"#" }{TEXT -1 2 ".\n" }}{PARA 0 "" 0 "" {TEXT -1 166 "HINT: Modify th
e output of the QSOLVER procedure so it will only return positive solu
tions (you might want to put any positive solutions in a set and retur
n the set)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }