MAT 195 – Spring Quarter 2002
TEST 2
NAME_______________________________________________________
Show work and write clearly.
1. The displacement (in meters) of an object moving in a straight line is given by s  1 
t
 2t 2 ,
4
where t is measured in seconds.
a. Find the average velocity over the following time periods:
(i) [1, 2]
(ii) [1, 1.5]
(iii) [1, 1.1]
b. Estimate the instantaneous velocity (to 4 decimal places) when t = 1. Explain.
2. Referring to the graphs below, find each limit, if it exists. If the limit does not exist, explain why.
a. lim
f ( x)
g ( x)
b. lim [ f ( x)  g ( x)]
c. lim
g ( x)
f ( x)
d. lim [ x  g ( x)]
e. lim [ f ( x)  g ( x)]
f. lim[ x  f ( x)]
x0
x  1
x  1
x 1
x2
x 1
g. lim
x 1
g ( x)
f ( x)
1 x  1

3. f (x)  0 x  1
1 x  1

a. Evaluate the following limits, if they exist. If the limit does not exist, explain why.
i. lim f ( x)
ii. lim f ( x)
x 1
iii. lim f ( x)
x 1
x 1
b. What is the domain of f(x).
c. Where is f(x) discontinuous? What is the type of discontinuity? Explain.
4. Find a value for the constant k, if possible, that will make f continuous.
7 x  2
x 1
f ( x)   2
x 1
kx
5. Find the limits, algebraically, if they exist. If the limit does not exist, explain.
3 x
t 3  t 2  5t  3
a. lim
b. lim 2
3
t 1
x

4
x  2x  8
t  3t  2
c. lim
x 1
e. lim
y 9
x4  1
x 1
4 y
2
y
d. lim
x 5
x 3  3x  1
x 3
x9
f. lim
x9

5. Find the vertical and horizontal asymptotes for f ( x)  a 1  x 1

1
, where a > 0.