Math 165 Section A
Professor Lieberman
September 1, 2004
PRACTICE FIRST IN-CLASS EXAM
CLOSED BOOK! SHOW ALL WORK!
This test merely shows the number of questions and difficulty to expect on Friday’s exam.
Questions on other topics (from Chapter 2) may appear.
1. (20 points) Show that there is a number x between 0 and 1 so that
(cos x)x3 + 6 sin5 x − 3 = 0.
2. (26 points) Determine the horizontal and vertical asymptotes to the graph of the
function
x2 + 4
.
y= 2
x −1
3. (9 points each) Evaluate the limits.
x2 − x − 12
x→−3
x+3
2
lim (x + 1)(x2 + 4x)
(a)
lim
(b)
x→1
lim−
(c)
x→5
6
x−5
4. (27 points) For what value of the constant c is the function
(
cx + 1
if x ≤ 3
f (x) =
2
cx − 1 if x > 3
continuous on (−∞, ∞)?