Math 165
Spring 2001
Exam 2
- (30 pt) Compute the
derivatives of the following functions:
a) b)
c) d) e)
- (10 pt) Use implicit
differentiation to find the tangent line to the curve defined by at the point
- (15 pt) For the
following function, find all critical points and then find the maximum and
minimum values of the function on the interval [0,3]:
.
- (15 pt) Find the
maximum and minimum values of the function on the interval
- (15 pt) You are
standing on a long straight beach. Off the coast is located a lighthouse
which has a beam that make 1 revolution every 3 seconds. Additionally
assume that you are standing on the point on the beach closest to the
lighthouse and that the lighthouse is 4 miles away. How fast is the beam
of light moving towards you down the beach at the instant that it is 4
miles away from you?
- (10 pt) Let , find a formula for
- (15 pt) You have a
circular drum whose height and base diameter are equal. You measure the
height and find it to be 5 feet with an error of ± 0.5 inches. Estimate
the maximum error obtained by using this measurement to compute the volume
of the drum. Also compute the relative error.