2
SAMPLE EXAM
Problems marked with an asterisk (*) are particularly challenging and should be given careful consideration. 1. Consider the following graph of f .
4 3 2 1 4 1
2
5
3
(a) What is lim f t ? lim f t ? lim f t ? lim f t ? t
0
t
0
t
t
2
(b) For what values of x does lim f t exist? t
x
(c) Does f have any vertical asymptotes? If so, where?
(d) Does f have any horizontal asymptotes? If so, where?
(e) For what values of x is f discontinuous?
2. Find values for a and b that will make f continuous everywhere, if f x
3x ax x2
1 b
136
if x if 2 if 5
2 x x
5
t