Name:    Chapter 12 Pre 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.

Determine whether the statement is true or false.

The limit of a function as x approaches c does not exist if the function approaches from the left of c and 5 from the right of c.
 a. False b. True

3.

Use the graph to determine the limit visually (if it exists). Then identify another function that
agrees with the given function at all but one point.

 a. b. c. d. e.

4.

Graphically approximate the limit (if it exists) by using a graphing utility to graph the function.

 a. d. b. e. c.

5.

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.

6.

Find the derivative of the function.

 a. b. c. d. e.

7.

Find the derivative of the function.

 a. b. c. d. e.

8.

Find the slope of the graph of at the given point.

 a. b. c. d. e.

9.

Find a formula for the slope of the graph of .
 a. b. c. d. e.

10.

Find the limit (if it exists).

 a. b. c. 3 d. –3 e. Does not exist

11.

Find the limit (if it exists).

 a. 8 b. –2 c. –8 d. 2 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. –7 b. –3 c. 7 d. 0 e. Does not exist

14.

Select the correct graph of the following function.

 a. d. b. e. c.

15.

Find the first five terms of the sequence.

 a. 1, , , , b. 1, , , , c. 1, , , , d. 1, , , , e. , , , ,

16.

Use the first six terms to predict the limit of the sequence

(assume n begins with 1).
 a. 0 b. 55 c. d. 72 e. the sequence diverges

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 four decimal places.)
 a. b. c. d. e.

18.

Use to complete the table.

 n

(Round the answer to 5 decimal places.)
 a. b. c. d. e.

19.

Rewrite

as a rational function and find .
 a. b. c. d. e.

20.

Use the limit process to find the area of the region between and the x-axis on the interval .
 a. 81 b. 126 c. 72 d. 270 e. 225