# Exam 1 Review Math 160

Topics: Derivative, Function, Tangent Pages: 8 (1014 words) Published: March 11, 2013
Name: __________________________ Date: _____________

1.|Complete the table and use the result to estimate the limit. x|||||||f(x)|||||||| A)|–0.076923|
B)|0.423077|
C)|0.298077|
D)|0.548077|
E)|–0.451923|

2.|Determine the following limit. (Hint: Use the graph of the function.)| A)|6|
B)|5|
C)|1|
D)|4|
E)|does not exist|

3.|A graph of is shown and a c-value is given. For this problem, use the graph to find .| A)|0|
B)|–10|
C)|–5|
D)|15|
E)|does not exist|

4.|Use the graph of and the given c-value to find .|
A)|–1|
B)|-6|
C)|3|
D)|–7|
E)|does not exist|

5.|Use properties of limits and algebraic methods to find the limit, if it exists.| A)||
B)||
C)||
D)||
E)|does not exist|

6.|Find the limit (if it exists):|
A)|60|
B)||
C)||
D)|–15|
E)||

7.|Use properties of limits and algebraic methods to find the limit, if it exists.| A)|5|
B)|6|
C)|–6|
D)|–5|
E)|does not exist|

8.|Use the graph below to determine the one-sided limit.|||
A)|-|
B)||
C)|0|
D)|–2|
E)|2|

9.|Find the limit: .|
A)||
B)||
C)|0|
D)|–1|
E)|1|

10.|Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?| A)|continuous everywhere|
B)|, removable|
C)|, removable|
D)|, not removable|
E)|both B and C|

11.|Use analytic methods to find any point of discontinuity for the given function.| A)||
B)||
C)||
D)||
E)|continuous everywhere|

12.|Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available.| A)|discontinuous at |

B)|discontinuous at |
C)|discontinuous at |
D)|discontinuous at |
E)|continuous everywhere|

13.|Find the x-values (if any) at which is not continuous and identify whether they are removable or nonremovable.| A)|x = 9 is a removable discontinuity|
B)|x = –9 is a removable discontinuity|
C)|x = –9 is a nonremovable discontinuity|
D)|x = 9 is a nonremovable discontinuity|
E)|f(x) has no discontinuities|

14.|Describe the interval(s) on which the function is continuous.| A)| and |
B)| and |
C)| and |
D)||
E)|none of these choices|

15.|Describe the interval(s) on which the function is continuous.| A)||
B)||
C)||
D)||
E)||

16.|The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line.| A)|2|

B)|3|
C)|–1|
D)|–4|
E)|does not exist|

17.|Use the limit definition to find the slope of the tangent line to the graph of at the point .| A)||
B)||
C)||
D)||
E)||

18.|Find the derivative of the following function using the limiting process.| A)||
B)||
C)||
D)||
E)|none of the above|

19.|Find an equation of the a line that is tangent to the graph of f and parallel to the given line.| A)||
B)||
C)||
D)||
E)|both B and D|

20.|Use the graph below to determine all intervals where f is differentiable.||| A)||
B)||
C)||
D)||
E)||

21.|Find the derivative of the function.|
A)||
B)||
C)||
D)||
E)|none of the above|

22.|For the function given, find |
A)||
B)||
C)||
D)||
E)||

23.|Find the derivative of the function.|
A)||
B)||
C)||
D)||
E)||

24.|Find the derivative of the function.|
A)||
B)||
C)||
D)||
E)|none of the above|

25.|Differentiate the given function. |
A)||
B)||
C)||
D)||
E)||

26.|Find the slope of the graph of the function at the given value. when | A)||
B)||
C)||
D)||
E)||

27.|The tangent line to a curve at a point closely approximates the curve near the point. In fact, for x-values close enough to the point of tangency, the function and its tangent line are virtually indistinguishable. This problem explores this relationship. Write the equation of...