Free Printable Limits

1.

Evaluate

\lim_{x\rightarrow0^+}\left(\frac{1}{x^4}\right)

a)

$+\infty$

b)

$-\infty$

c)

$undefined$

d)

$0$

2.

Evaluate

\lim_{x\rightarrow0^-}\left(\frac{1}{2x^7}\right)

a)

$+\infty$

b)

$-\infty$

c)

$undefined$

d)

$0$

3.

Evaluate

\lim_{x\rightarrow5^+}\left(\frac{4}{x-5}\right)

a)

$+\infty$

b)

$-\infty$

c)

$undefined$

d)

$0$

4.

Evaluate

\lim_{x\rightarrow2^-}\left(\frac{2x}{x^2-4}\right)

a)

$+\infty$

b)

$-\infty$

c)

$undefined$

d)

$0$

5.

Use the theorems to evaluate the limit $\lim_{x\rightarrow-2}\ \frac{2}{4-x}$

a)

$\frac{1}{3}$

b)

$-\frac{1}{3}$

c)

1

d)

-1

6.

Use the theorems to evaluate the limit $\lim_{x\rightarrow-3}\ \frac{\left(2x\ +6\right)}{4x^{2\ }-36}$

a)

0

b)

does not exist

c)

$-\frac{1}{12}$

d)

-1

7.

Hint: Find the horizontal asymptote

a)

^-2/₉

b)

0

c)

∞

d)

-∞

8.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

9.

What technique would you use to find this limit?

a)

Direct Substitution only

b)

Factor & Cancel

c)

Conjugate Multiplication

d)

Rewrite with a Trig Identity

10.

Find $\lim_{x\rightarrow2^+\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

11.

Let $\lim_{x\rightarrow8}f\left(x\right)=3\ and\ \lim_{x\rightarrow8}g\left(x\right)=10.$ Find $\lim_{x\rightarrow8}\frac{f\left(x\right)}{\text{g(x)}}.$

a)

8

b)

10/3

c)

-7

d)

3/10

12.

Find $\lim_{x\rightarrow2}\frac{\text{}\frac{x}{x+2}-2}{x+4}$ .

a)

4

b)

-4

c)

$\frac{1}{4}$

d)

$-\frac{1}{4}$

13.

What is the limit?

a)

5/2

b)

-2/3

c)

Infinity

d)

17/3

14.

$\lim_{x\rightarrow4}\ \ \sqrt{\frac{x^2-7}{x}}$

a)

$\frac{\sqrt{11}}{2}$

b)

9/4

c)

3/2

d)

no limit

15.

$\lim_{x\rightarrow\infty}\ \frac{3x^2+x+2}{x^3+2x^2+1}\ =\ ...$

a)

0

b)

1,5

c)

2

d)

3

e)

$\infty$

16.

Determine the value of the limit

a)

4

b)

-1

c)

1

d)

DNE

17.

Determine the value of the limit

a)

∞

b)

-∞

c)

DNE

d)

0

18.

Determine the value of the limit

a)

∞

b)

-∞

c)

DNE

d)

0

19.

Use the given function to determine the limit

a)

-4

b)

4

c)

-9

d)

DNE

20.

Use the given function to determine the value of the limit

a)

49

b)

-6

c)

-28

d)

DNE

21.

Use the given function to determine the value of the limit

a)

DNE

b)

-12

c)

10

d)

0

22.

$The\ \lim_{x\rightarrow0}f\left(x\right)\$ fails to exist because...

a)

As the function approaches zero, left and right of zero do not match

b)

As the function approaches zero, the graph oscillates.

c)

As the function approaches zero, the graph increases without bound.

23.

$The\ \lim_{x\rightarrow0}f\left(x\right)\$ fails to exist because...

a)

As the function approaches zero, left and right of zero do not match

b)

As the function approaches zero, the graph oscillates.

c)

As the function approaches zero, the graph increases without bound.

d)

The function only approaches zero from one side.

24.

$The\ \lim_{x\rightarrow2}f\left(x\right)\$ fails to exist because...

a)

As the function approaches two, left and right of two do not match

b)

As the function approaches two, the graph oscillates.

c)

As the function approaches two, the graph increases or decreases without bound.

25.

a)

7

b)

1/4

c)

infinty

d)

-8

26.

a)

Infinity

b)

Negative Infinity

c)

2

d)

Does not exist

27.

a)

3

b)

1

c)

Infinity

d)

Does not exist

28.

a)

2 only

b)

2 and 4

c)

0 and 2 only

d)

0, 1 and 2

e)

0, 1, 2, and 4.

29.

Find the limit as x approaches 7 from the right

a)

1

b)

0

c)

infinity

d)

DNE

30.

Find f(4)

a)

1

b)

5

c)

0

d)

DNE

31.

a)

-1/4

b)

-3/10

c)

-9/5

d)

DNE

32.

a)

2

b)

-3/4

c)

-1/3

d)

1/4

33.

$\lim_{x\rightarrow3^-}f\left(x\right)=$

a)

0

b)

$\sqrt{6}$

c)

6

d)

DNE

34.

The graph of f is shown in the figure. Which of the following statements is false?

a)

b)

c)

d)

35.

The graph of f is shown in the figure. If f is defined at k, but the limit of f(x) as x approaches k DNE, then k =

a)

a

b)

b

c)

c

d)

0

36.

Select all statements that are TRUE.

a)

b)

c)

d)

37.

Find the limit. Hint: Where is the horizontal asymptote?

a)

³/₇

b)

0

c)

$\infty$

d)

$-\infty$

38.

Find the limit. Hint: Where is the horizontal asymptote?

a)

^-2/₉

b)

0

c)

$\infty$

d)

$-\infty$

39.

$\lim_{x\rightarrow\infty}\ \frac{2x-3}{4x\ +1}$

a)

0

b)

DNE

c)

1/2

d)

2

40.

$\lim_{x\rightarrow\infty}\left(2x^3+3x-1\right)=$
Hint: Think of the end behavior

a)

$\infty$

b)

$-\infty$

c)

2

d)

2/3

41.

$\lim_{x\rightarrow-\infty}\left(x^2+3x-1\right)=$
Hint: Think of the end behavior of an even and positive polynomial.

a)

$\infty$

b)

$-\infty$

c)

2

d)

3

42.

$\lim_{x\rightarrow\infty}e^x=$
Hint: Think of the end behavior

a)

$\infty$

b)

$-\infty$

c)

0

d)

DNE

43.

Determine the limit at infinity by finding the slant asymptote using long division and then looking at the end behavior of the slant asymptote.
$\lim_{x\rightarrow\infty}\left(\frac{x^2-x-12}{x+3}\right)$

a)

$\infty$

b)

$-\infty$

c)

-3

d)

4

44.

$\lim_{x\rightarrow\infty}\ \frac{\sin\ x}{x}+4$

a)

1

b)

0

c)

DNE

d)

4

45.

$\lim_{x\rightarrow-\infty}\ \frac{\cos\ x}{x}$

a)

DNE

b)

1

c)

0

d)

$-\infty$

46.

Find the limit

a)

⁶/₅

b)

0

c)

$\infty$

d)

$-\infty$

47.

$\lim_{x\rightarrow\infty}\ \frac{x^3-x^2+1}{5-3x-x^4}=...$

a)

0

b)

-1

c)

-5

d)

$\infty$

e)

$-\infty$

48.

$\lim_{x\rightarrow\infty}\ \frac{1-2x+2x^3}{x^3+x+1}=\ ...$

a)

- 4

b)

- 2

c)

1

d)

2

e)

$\infty$

49.

$\lim_{x\rightarrow\infty}\ \frac{x+7}{\sqrt{4x^2+3x}}=...$

a)

$-\infty$

b)

$\infty$

c)

$\frac{1}{2}$

d)

0

e)

$-\frac{1}{2}$

50.

$The\ \lim_{x\rightarrow0}f\left(x\right)\$ fails to exist because...

a)

As the function approaches zero, left and right of zero do not match

b)

As the function approaches zero, the graph oscillates.

c)

As the function approaches zero, the graph increases without bound.

d)

The function only approaches zero from one side.

Limits

Total questions: 50

Worksheet time: 2hrs 37mins

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