Math 165 Section A
Professor Lieberman
September 23, 2004
PRACTICE SECOND IN-CLASS EXAM
Carry out the solution of each problem: show steps of any required calculations and state
reasons that justify any conclusions. A short sentence is usually enough but answers without
any justification will receive no credit.
This test merely shows the number of questions and level of difficulty to expect on Wednesday’s exam. Questions on other topics (from Chapter 3) may appear.
1. (a) (15 points) Differentiate the function
x2
.
x3 − 2
(b) (15 points) Use implicit differentiation to find dy/dx if y is given by the equation
p
√
x 1 + y + y 1 + 2x = 2x.
g(x) =
2. (20 points) The limit
x4 − 81
x→3 x − 3
represents the derivative of some function f at some number a. Determine f and a,
and use this information to evaluate the limit.
lim
3. (25 points) Two cars start moving from the same point at the same time. One travels
south at 60 mi/h and the other travels west at 25 mi/h. At what rate is the distance
between the two cars increasing two hours after they start?
4. (25 points) Use differentials to find an approximate value for sin( π6 + .1).