Review Problems MATH 224 Final Fall 2008
1.
Be sure to look over all old quizzes, assignments, midterm exam and the midterm review.
Approximately 1/3 of the exam will be on material covered before the midterm and 2/3 on
material after the midterm.
2.
Prove by induction starting at
N = 1
, that
B(N,1) = N
based on the recursive definition given
in class.
(See PowerPoint slide
Recursion.ppt
.)
3.
Which of the following are onetoone functions. For the functions that are not onetoone,
provide values of x that confirm this.
a.
f(x) = 4x
2
+ 2x 10 where the domain equals is the set of real numbers.
b.
f(x) =
floor (x) where the domain is the set of integers
c.
f(x) = 2x, where the domain is the set of real numbers.
d.
f(x) = 1/x if x ≠ 0, and f(0) = 0, where the domain is the set of all real numbers.
e.
f(x) = x+1 if x is an odd number, and f(x) = x1 if x is an even number, where the domain
is the set of positive integers.
4.
Set S contains
N+1
positive integers all less than or equal to
2N
.
Prove by induction starting
at
N = 1
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 Fall '08
 Waxman
 Math, Negative and nonnegative numbers, Natural number, real numbers., N+1 positive integers

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