Math 165
Spring 2001
Final Exam
- (20 pt) Compute the
following limits:
a) b) c) d)
- (20 pt) Find the derivatives of the following functions:
a) b) c)
d)
- (25 pt) Find the
following integrals:
a) b) c)
d) e)
- (10 pt) A spherical
bubble’s volume is increasing at 10 cm3/s. Find the rate of
change of its surface area when the radius of the sphere is 20 cm.
- (10 pt) Show that among
all rectangles with fixed area A, a square has the smallest perimeter.
- (10 pt) Sketch the
curve
- (5 pt) Use the
definition of the derivative to find the derivative of Check your answer.
- (5 pt) Find the tangent
line to the curve at the point
- (5 pt) Suppose that you
are using Newton’s Method to find a root of Suppose is continuous and has two derivatives everywhere. Also
suppose that there is an interval containing the root where the function is both increasing and concave down. If Newton’s Method
converges to this root, will the approximations be too big, too small,
random, or is there not enough information to tell? Explain.