M121 PRACTICE TEST PART 2 FALL 2009 DUPRE
Free Response
1. If 
,
for all x find the limit.
2. For the limit, illustrate the definition by
finding values of d that correspond to 
.
3. The displacement (in meters) of an object
moving in a straight line is given by 
,
where t is measured in seconds. Find the average velocity over the time
period [1, 1.5].
4. If 
for all x, find the limit.
5. Find the limit.
6. Use the definition of the limit to find
values of d that correspond to 
.
Round down the answer to the nearest thousandth.
7. Find a function g that agrees with f
for 
and is continuous on Â.
8. The displacement (in feet) of a certain
particle moving in a straight line is given by 
where t is measured in seconds. Find
the instantaneous velocity when 
.
9. Use the given graph of 
to find a number d such that 
whenever 
.
Round down the answer to the nearest hundredth.
10. Find a function g that agrees with f
for 
and is continuous on Â.
Multiple Choice
Identify the choice that best completes the statement or answers
the question.
____ 11. Find the limit.
Select the correct answer.
|
a. |
-1/2 |
|
b. |
3 |
|
c. |
-3 |
|
d. |
0 |
|
e. |
limit does not exist |
____ 12. Find an equation of the tangent line to the
curve 
at the point (2, 1).
Select the correct answer.
|
a. |
|
|
b. |
|
|
c. |
|
|
d. |
|
|
e. |
|
____ 13. Find the limit.
Select the correct answer.
|
a. |
-1 |
|
b. |
0 |
|
c. |
1/2 |
|
d. |
-¥ |
|
e. |
-1/2 |
____ 14. Use continuity to evaluate the limit.
Select the correct answer.
|
a. |
-17p |
|
b. |
¥ |
|
c. |
-1 |
|
d. |
0 |
|
e. |
1 |
____ 15. The slope of the tangent line to the graph of
the exponential function 
at the point (0, 1) is 
.
Estimate the slope to three decimal places.
Select the correct answer.
|
a. |
1.045 |
|
b. |
1.136 |
|
c. |
0.786 |
|
d. |
1.126 |
|
e. |
1.386 |
