Name:    Chapter 12 Post Test

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Select the correct graph for the following function using a graphing utility.

 a. d. b. e. c.

2.

Use the given information to evaluate the limit.

 a. –66 b. 11 c. –65 d. –64 e. –6

3.

Find the limit by direct substitution.

 a. = b. = c. = d. = e. =

4.

Find the limit by direct substitution. Round your answer to two decimal places.

 a. = 8103.08 b. = 2.72 c. = d. = 20.09 e. = –20.09

5.

Complete the table and use the result to estimate numerically.
 x –7.1 –7.01 –7.001 –7 –6.999 –6.99 –6.9 f(x) ?
 a. b. –11 c. 11 d. ¥ e. limit does not exist

6.

Use the graph to find

 a. limit does not exist b. 3 c. ¥ d. e. 0

7.

Use the limit process to find the slope of the graph of the function at the specified point. Use a graphing utility to confirm your result.

 a. b. c. d. e.

8.

Find a formula for the slope of the graph of at the point . Then use it to find the slope at the given point.

 a. , b. , c. , d. , e. ,

9.

Select a graph of the function and the tangent line at the point .

 a. d. b. e. c.

10.

Find the derivative of the function.

 a. b. c. d. e. 9

11.

Find the limit (if it exists).

 a. 12 b. 7 c. –7 d. 5 e. Does not exist

12.

Find the limit (if it exists).

 a. b. c. – d. – e. Does not exist

13.

Find the limit (if it exists).

 a. b. – c. d. – e. Does not exist

14.

Find the first five terms of the sequence.

 a. , , , , b. , , , , c. , , , , d. , , , , e. , , , ,

15.

Complete the table and numerically estimate the limit as x approaches infinity for the following function.

 x f(x)

 a. x                                                                                 f(x)              –1.6458     –0.2956       –0.0300      –0.0030 b. x                                                                               f(x)     –0.0300    –0.0030                –1.6458     –0.2956 c. x                                                                                 f(x)      –0.2956    –0.0300      –0.0030               –1.6458 d. x                                                                              f(x)    –0.0030             –1.6458    –0.2956       –0.0300 e. x                                                                                  f(x)      –1.6458    –0.2956     –0.0300    –0.0030

16.

Find .

 a. b. c. d. e.

17.

Complete the table using the function , over the specified interval to approximate the area of the region bounded by the graph of , the x-axis, and the vertical lines and using the indicated number of rectangles. Then find the exact area as .

 n 4 8 20 50 100 Approximate area

(Round the answer to two decimal places.)
 a. b. c. d. e.

18.

Use the limit process to find the area of the region between the graph of the function and the
x-axis over the specified interval.

 a. square units b. square units c. square units d. square units e. square units

19.

Use the limit process to find the area of the region between the graph of the function and the
x-axis over the specified interval.

 a. square units b. square units c. square units d. 6 square units e. square units

20.

Use the limit process to find the area of the region between and the x-axis on the interval .
 a. 228 b. 108 c. 180 d. 408 e. 188