Free Printable Limits and Continuity

1.

The graph of the function f is shown. Which of the following statements is FALSE?

a)

$\lim_{x\rightarrow2}f\left(x\right)$ exists

b)

$\lim_{x\rightarrow3}f\left(x\right)$ exists

c)

$\lim_{x\rightarrow4}f\left(x\right)$ exists

d)

$\lim_{x\rightarrow5}f\left(x\right)$ exists

e)

The function f is continuous at x=3

2.

The graph of the function f is shown. At what value of x does f have a jump discontinuity?

a)

1

b)

3

c)

7

d)

10

3.

The graph of a function f is shown in the figure above. Which of the following statements is true?

a)

$f\left(a\right)=2$

b)

f is continuous at x=a

c)

$\lim_{x\rightarrow a}f\left(x\right)=1$

d)

$\lim_{x\rightarrow a}f\left(x\right)=2$

e)

$\lim_{x\rightarrow a}f\left(x\right)$ does not exist

4.

$\lim_{x\rightarrow0}\frac{2x^6+6x^3}{4x^5+3x^3}$ is

a)

0

b)

1/2

c)

1

d)

2

e)

DNE

5.

$\lim_{x\rightarrow-3}\frac{x^2-9}{x^2-2x-15}$ is

a)

0

b)

3/5

c)

3/4

d)

1

e)

DNE

6.

$\lim_{x\rightarrow2}\frac{x^2+x-6}{x^2-4}$ is

a)

-1/4

b)

0

c)

1

d)

5/4

e)

DNE

7.

$\lim_{x\rightarrow0}\frac{5x^4+8x^2}{3x^4-16x^2}$ is

a)

-1/2

b)

0

c)

1

d)

5/3

e)

DNE

8.

Let f be the function given by

f\left(x\right)=\frac{\left(x-2\right)^2\left(x+3\right)}{\left(x-2\right)\left(x+1\right)}

. For which of the following values of x is f not continuous?

a)

-3 and -1

b)

-3, -1, and 2

c)

-1

d)

-1 and 2

e)

2

9.

The graph of a function f is shown Which of the following limits does not exist?

a)

$\lim_{x\rightarrow1^-}f\left(x\right)$

b)

$\lim_{x\rightarrow1}f\left(x\right)$

c)

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

d)

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

e)

$\lim_{x\rightarrow5}f\left(x\right)$

10.

$\lim_{x\rightarrow3^-}\frac{\left|x-3\right|}{x-3}$ is

a)

-3

b)

-1

c)

1

d)

3

e)

DNE

Limits and Continuity

Total questions: 10

Worksheet time: 5mins

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