Math
165
Spring 2001
Exam 1
- (25 pt) Evaluate the
following limits:
a) 
b) 
c) 
d) 
e) 
- (24 pt) Compute the
derivatives of the following functions:
a) 
b) 
c) 
d) 
- (16 pt) Use the definition
of the derivative to compute the derivatives of the following
functions:
a) 
b) 
where 
is a constant.
- (20 pt) I am standing
on the top of a tall building and I throw a baseball straight up. The
ball’s height above the ground (measured in feet) at any time
is given by 
a)
How
high is the building?
b)
How
fast did I throw the ball?
c)
How
long before the ball hits the ground?
d)
How
fast is the ball going when it hits the ground?
e)
How
high does the ball go?
- (5 pt) Show that there
is a positive number,
such that 
(10 pt) Consider the
following two functions:
y=f(x)
(0,1) y=g(x) (0,1)
a)
Find
b)
Find
- (10 pt) Sketch the
graph of the derivative of the following function pictured below:
