Test #1
Name:________________________
Read all of the directions carefully and CIRCLE your answers. If I cannot read your writing, no credit will be given. Good Luck!!!
Find the following limits in problems 1-4. If the limit
does not exist, state limit does not exist.
1.) 
2.) 
3.) 
4.) f(x) = 5 x x ≥ 2
2x + 7 x < 2
a.) Find
.
B.) Find
.
C.) Find
.
For each function in 5 and 6, state whether the function is continuous or discontinuous. If it is discontinuous, state the values of x at which the function is discontinuous.
5.) 
6.) 
7.) Find the average rate of change given the function,
f(x) = 
between
the values x = 1 and x = 4.
8.) Use the LIMIT PROCESS to find the first derivative of f(x) = 7x + 3.
9.) Find the slope of the tangent line of
at
x = 5.
Find the first derivative of the following functions in problems 10 17.
10.) f(x) = 
11.) f(x) = 
12.) f(x) = 
13,) f(x) = 
14.) f(x) = 
15.) f(x) = 
16.) f(x) = 
17.) f(x) = 
18.) f(x) =
,
find f (4). 19.)
find
f (-8).
20.) A model rocket is launched in the air from the
ground. Its height, t seconds after it is launched will be
(neglecting
air resistance) for 0 ≤ t ≤ 80.
a.) Find the velocity function.
b.) Find the time, t, when the rocket will be at its maximum height.
c.) Find the maximum height the rocket will reach.
21.)
A company manufactures cordless telephones and finds that its cost
function is 
dollars
where x is the number of telephones produced.
a.) Find the marginal cost function.
b.) Use this function to determine how much it will cost to produce the 101st telephone.