Calculus worksheet - Limits

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the graph to evaluate the limit.

1) 1)

limx -1

f(x)

A) 45

B) -45

C) -1 D)

2) 2)limx 0

f(x)

A) Does not exist B) C) 1 D) -1

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Use the graph to estimate the specified limit.

3) 3)limx (-1)-

f(x) and limx (-1)+

f(x)

A) -5; -2 B) -7; -5 C) -2; -7 D) -7; -2

4) 4)limx 0

f(x)

A) 2 B) 0 C) -2 D) Does not exist

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5) 5)limx

2-

f(x) and limx

2+

f(x)

A)2

;2

B) ; C) 3; 6 D) 6; 3

6) 6)limx 0-

f(x) and limx 0+

f(x)

A) 1; -1 B) 1; 1 C) -1; 1 D) -1; -1

Provide an appropriate response.

7) 7)Which of the following expressions is a one-sided limit?I. lim

x 0f(x)

II. limx 0-

f(x)

III. limx 0+

f(x)

A) I and II only B) II and III only C) I, II, and III D) I and III only

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8) 8)Which of the following expressions is a left-hand limit.

I. limx 0

f(x)

II. limx 0-

f(x)

III. limx 0+

f(x)

A) II and III only B) I only C) II only D) III only

9) 9)If limx 0

f(x) = L, which of the following expressions are true?

I. limx 0-

f(x) does not exist.

II. limx 0+

f(x) does not exist.

III. limx 0-

f(x) = L

IV. limx 0+

f(x) = L

A) I and IV only B) I and II only C) III and IV only D) II and III only

Use the TABLE feature of a graphing utility to find the limit.

10) limh -3

h2 - 9h2 + 3h

10)

A) 2 B) -2 C) 0 D) does not exist

11) limd 3

d3 - 27d - 3

11)

A) 27 B) 9 C) 0 D) does not exist

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