Multi Choice Problems

Find the slope of the tangent line to the graph of f at the given point.

f(x) = at ( 36, 6)

	A.
	B. 12
	C. 3
	D.

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

	A. 16
	B. does not exist
	C. -16
	D. 0

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

(2x² + 2x + 3)²

	A. -9
	B. 9
	C. does not exist
	D. 1

Complete the table for the function and find the indicated limit.

	A. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = -1
	B. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0
	C. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 0.1
	D. -0.0300, -0.0200, -0.0100, 0.0100, 0.0200, 0.0300 limit = 1

Use the definition of continuity to determine whether f is continuous at a.

f(x) = 5x⁴ – 9x³+ x – 7a = 7

	A. Not continuous
	B. Continuous

Find the slope of the tangent line to the graph of f at the given point.

f(x) = x²+ 5x at (4, 36)

	A. 13
	B. 21
	C. 9
	D. 3

Use the definition of continuity to determine whether f is continuous at a.

f(x) = a = 4

	A. Not continuous
	B. Continuous

Graph the function. Then use your graph to find the indicated limit. f(x) = 7e^x , f(x)

	A. 0
	B. 7
	C. 1
	D. -7

The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or function value does not exist.

a. f(x)
b. f(1)

	A. a.  f(x) = 1 b. f(1) = 0
	B. a. f(x) does not exist b. f(1) = 2
	C. a. f(x) = 2 b. f(1) = 2
	D. a. f(x) = 2 b. f(1) = 1

Choose the table which contains the best values of x for finding the requested limit of the given function.

	A.
	B.
	C.
	D.

Choose the table which contains the best values of x for finding the requested limit of the given function.

(x²+ 8x – 2)

	A.
	B.
	C.
	D.

Determine for what numbers, if any, the given function is discontinuous.

f(x) =

	A. 5
	B. None
	C. 0
	D. -5, 5

Complete the table for the function and find the indicated limit.

	A. -1.22843; -1.20298; -1.20030; -1.19970; -1.19699; -1.16858 limit = -1.20
	B. -2.18529; -2.10895; -2.10090; -2.09910; -2.09096; -2.00574 limit = -2.10
	C. -4.09476; -4.00995; -4.00100; -3.99900; -3.98995; -3.89526 limit = -4.0
	D. 4.09476; 4.00995; 4.00100; 3.99900; 3.98995; 3.89526 limit = 4.0

The function f(x) = x³describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. If x is changing, find the average rate of change of the volume with respect to x as x changes from 1 inches to 1.1 inches.

	A. 2.33 cubic inches per inch
	B. -3.31 cubic inches per inch
	C. 23.31 cubic inches per inch
	D. 3.31 cubic inches per inch

The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limit or function value does not exist.

a. f(x)
b. f(3)

	A. a. f(x) = 3 b. f(3) = 5
	B. a. f(x) = 5 b. f(3) = 5
	C. a. f(x) = 4 b. f(3) does not exist
	D. a. f(x) does not exist b. f(3) = 5

Use the definition of continuity to determine whether f is continuous at a.

f(x) = 
a = -5

	A. Not continuous
	B. Continuous

Use the graph and the viewing rectangle shown below the graph to find the indicated limit.

( x² – 2)

[-6, 6, 1] by [-6, 6, 1]

	A. (x2 – 2) = -6
	B. (x2 – 2) = 2
	C. (x2 – 2) = -2
	D. (x2 – 2) = 6

Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limit properties can be applied.

5

	A. -5
	B. 0
	C. 5
	D. 2

Find the derivative of f at x. That is, find f ‘(x). f(x) = 7x + 8; x = 5

	A. 40
	B. 8
	C. 35
	D. 7

Graph the function. Then use your graph to find the indicated limit.

f(x) = , f(x)

	A. 6
	B. -2
	C. -6
	D. 2