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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 "2*x^2*y-9*x*y+6*x^2-27*x+10*y+30 = 0;
" "6#/,.*(\"\"#\"\"\"*$)%\"xGF&F'F'%\"yGF'F'*(\"\"*F'F*F'F+F'!\"\"*&\"
\"'F'*$F)F'F'F'*&\"#FF'F*F'F.*&\"#5F'F+F'F'\"#IF'\"\"!" }{TEXT -1 17 "
 to the variable " }{TEXT 258 3 "eqn" }{TEXT -1 50 ", factor the polyn
omial, and solve equation for x." }}{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 "Problem
 2. " }{TEXT -1 112 "Write a program that prints out all of the 3-elem
ent lists that can be made from the list  without repeating an " }
{XPPEDIT 18 0 "[1, 2, 3, 4, 5];" "6#7'\"\"\"\"\"#\"\"$\"\"%\"\"&" }
{TEXT -1 79 " without repeating an element. (i.e. [1,1,1] should not b
e in your answer set)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 264 9 "
Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 260 11 "Problem 3. " }{TEXT -1 31 "Write a progr
am that evaluates " }{XPPEDIT 18 0 "exp(x);" "6#-%$expG6#%\"xG" }
{TEXT -1 33 " as a floating point decimal for " }{XPPEDIT 18 0 "x = -2
;" "6#/%\"xG,$\"\"#!\"\"" }{TEXT -1 4 " to " }{XPPEDIT 18 0 "x = 4;" "
6#/%\"xG\"\"%" }{TEXT -1 13 " counting by " }{XPPEDIT 18 0 "2/3;" "6#*
&\"\"#\"\"\"\"\"$!\"\"" }{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 that " }{XPPEDIT 18 0 "sin(
pi) = 0;" "6#/-%$sinG6#%#piG\"\"!" }{TEXT -1 60 ".  Why does the follo
wing command not return the value of 0?" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "sin(pi);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 262 9 "Solut
ion:" }}{PARA 0 "" 0 "" {TEXT -1 3 "   " }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }{TEXT 266 10 "Problem 5." }{TEXT -1 60 "  Explain the d
ifference between local and global variables." }}{PARA 0 "" 0 "" 
{TEXT 267 9 "Solution:" }{TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 268 10 "Problem 6." 
}{TEXT -1 31 "  Let f be defined by the rule " }{XPPEDIT 18 0 "f(x) = \+
exp(cos(x))+sin(x)*exp(x);" "6#/-%\"fG6#%\"xG,&-%$expG6#-%$cosG6#F'\"
\"\"*&-%$sinG6#%\"xGF/-F*6#F'F/F/" }{TEXT -1 109 ".  Use two of the th
ree methods (arrow, unapply, procedure) to define this function in Map
le and test it for " }{XPPEDIT 18 0 "x = 0,pi/2;" "6$/%\"xG\"\"!*&%#pi
G\"\"\"\"\"#!\"\"" }{TEXT -1 6 ", and " }{XPPEDIT 18 0 "pi/4;" "6#*&%#
piG\"\"\"\"\"%!\"\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 271 9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
269 10 "Problem 7." }{TEXT -1 2 "  " }}{PARA 0 "" 0 "" {TEXT -1 56 "Wh
at is the Maple command to factor 2297295 into primes?" }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }{TEXT 270 9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
275 10 "Problem 8." }{TEXT -1 48 "  One of the earliest definitions of
 the number " }{TEXT 298 1 "e" }{TEXT -1 110 " came from summing the f
actorial function.  Use Maple to confirm this.  Write a program that c
omputes the sum " }{XPPEDIT 18 0 "sum(1/n!,n = 0 .. 1000);" "6#-%$sumG
6$*&\"\"\"F'-%*factorialG6#%\"nG!\"\"/%\"nG;\"\"!\"%+5" }{TEXT -1 53 "
 and evaluates the sum as a floating point decimal.  " }{TEXT 276 39 "
DO NOT USE MAPLE'S BUILT-IN SUM PROGRAM" }{TEXT -1 51 ".  Confirm that
 your computed value and the number " }{TEXT 299 1 "e" }{TEXT -1 36 " \+
are identical to 50 decimal places." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
{TEXT 277 9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }{TEXT 278 10 "Problem 9." }{TEXT -1 6 "  The " }
{TEXT 279 13 "golden ratio " }{TEXT -1 133 "occurs in a rectangle when
 the sides of the rectangle have the following property:  If the lengt
hs of the sides of the rectangle are " }{TEXT 280 4 "a+ b" }{TEXT -1 
5 " and " }{TEXT 281 1 "b" }{TEXT -1 33 ", then the ratio of the sides
 is " }{XPPEDIT 18 0 "(a+b)/a = a/b;" "6#/*&,&%\"aG\"\"\"%\"bGF'F'F&!
\"\"*&F&F'F(F)" }{TEXT -1 31 ".   Assume for simplicity that " }
{XPPEDIT 18 0 "b = 1;" "6#/%\"bG\"\"\"" }{TEXT -1 13 ".  Solve for " }
{TEXT 282 1 "a" }{TEXT -1 95 " to find what the golden ratio is.  Expr
ess it as a floating point decimal.  Keep in mind that " }{TEXT 283 1 
"a" }{TEXT -1 91 " is a length and is therefore not negative. You may \+
use Maple's solve procedure to aid you." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }{TEXT 297 9 "Solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT 284 11 "Problem 10." }{TEXT -1 2 "  " }{TEXT 285 0 "" }
{TEXT -1 70 "Write a program that will take the set of all primes less
 than 50 (S=\{" }{XPPEDIT 18 0 "2,3,5,7,11,13,17,19,23,29,31,37,41,43,
47;" "61\"\"#\"\"$\"\"&\"\"(\"#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 -1 202 "  In Lecture 3 we discussed a program that counts the nu
mber of times each digit appeared in a number.  Alter that program to \+
find the number of even digits that appear in the number N=2^50+3^60+5
^80.  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}{TEXT 296 26 "Extra Credit (10 points): " }{TEXT -1 328 "In class, we
 have discussed the use of lists and sets as a potential way of storin
g information on a computer.  A better way of doing this is through th
e use of an array.  Interstingly enough, a two-dimensional array can b
e thought of as a matrix.  In fact, Maple has a method of converting t
wo-dimensional arrays to matrices.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT 305 101 "Create a two dimensional array named \+
myarray with 10 rows and 10 columns using the following command:" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 300 28 "myarray:=array(1..10,1..1
0);" }{TEXT -1 3 ".  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 157 "You can specify where in the array you want to look b
y using the row number and colums number.  The entry of the ith row an
d jth column can be checked using " }{TEXT 302 12 "myarray[i,j]" }
{TEXT -1 77 ".  For instance, the value of 5th row and 3rd column can \+
be checked by using " }{TEXT 301 13 "myarray[5,3];" }{TEXT -1 155 ". S
imilaraly, assignments into the array are done the same way.  If I wan
ted to assign the value of 15 to this place in the array, I would use \+
the command " }{TEXT 303 17 "myarray[5,3]:=15;" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 306 121 "Fill in the array in th
e following way: each entry of the array should be the product of the \+
row number and column number" }{TEXT -1 19 ".  In other words, " }
{TEXT 304 16 "myarray[i,j]=i*j" }{TEXT -1 125 ", so that if you were t
o test myarray[8,7], you should get 56; and if you were to test myarra
y[5,9], you would get 45, etc.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 308 125 "Once the entries of the array have been
 filled in, use the following command to convert the array to a matrix
 named mymatrix:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 307 35 "mymat
rix:= convert(myarray,matrix);" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 54 "In the end you should get this:          \+
             " }{XPPEDIT 18 0 "matrix([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
, [2, 4, 6, 8, 10, 12, 14, 16, 18, 20], [3, 6, 9, 12, 15, 18, 21, 24, \+
27, 30], [4, 8, 12, 16, 20, 24, 28, 32, 36, 40], [5, 10, 15, 20, 25, 3
0, 35, 40, 45, 50], [6, 12, 18, 24, 30, 36, 42, 48, 54, 60], [7, 14, 2
1, 28, 35, 42, 49, 56, 63, 70], [8, 16, 24, 32, 40, 48, 56, 64, 72, 80
], [9, 18, 27, 36, 45, 54, 63, 72, 81, 90], [10, 20, 30, 40, 50, 60, 7
0, 80, 90, 100]]);" "6#K%'matrixG6#7,7,\"\"\"\"\"#\"\"$\"\"%\"\"&\"\"'
\"\"(\"\")\"\"*\"#57,F)F+F-F/F1\"#7\"#9\"#;\"#=\"#?7,F*F-F0F3\"#:F6\"#
@\"#C\"#F\"#I7,F+F/F3F5F7F;\"#G\"#K\"#O\"#S7,F,F1F9F7\"#DF=\"#NFB\"#X
\"#]7,F-F3F6F;F=FA\"#U\"#[\"#a\"#g7,F.F4F:F?FEFI\"#\\\"#c\"#j\"#q7,F/F
5F;F@FBFJFO\"#k\"#s\"#!)7,F0F6F<FAFFFKFPFT\"#\")\"#!*7,F1F7F=FBFGFLFQF
UFX\"$+\"Q(pprint06\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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