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Mastery Test: Limits and Continuity

Total questions: 25

Worksheet time: 42mins

Name
Class
Date
1.

Use the table to evaluate the limit of limx7f(x)\lim_{x\rightarrow7}f\left(x\right)

a)

4

b)

3.2

c)

3

d)

3.5

2.

Use the table to evaluate the limit of limx11f(x)\lim_{x\rightarrow11}f\left(x\right)

a)

10

b)

10.3

c)

9.6

d)

11

3.

Evaluate limx4(2x+3)\lim_{x\rightarrow-4}\left(2x+3\right)

a)

2

b)

-5

c)

6

d)

11

4.

Evaluate limx610000\lim_{x\rightarrow-6}10000

a)

-60000

b)

-6

c)

10000

d)

-10000

5.

Refer to the figure and find f(3)f\left(-3\right)

a)

0

b)

1

c)

2

d)

undefined

6.

Refer to the figure and find f(4)f\left(4\right)

a)

0

b)

1

c)

2

d)

undefined

7.

Refer to the figure and find limx0f(x)\lim_{x\rightarrow0}f\left(x\right)

a)

0

b)

1

c)

2

d)

DNE

8.

Refer to the figure and find limx2f(x)\lim_{x\rightarrow-2}f\left(x\right)

a)

0

b)

1

c)

2

d)

DNE

9.

Refer to the figure and determine if it is continuous or disconinuous at the given interval (, 3)\left(-\infty,\ 3\right)

a)

Continuous

b)

Discontinuous

10.

Refer to the figure and determine if it is continuous or disconinuous at the given interval (3, 4]\left(3,\ 4\right]

a)

Continuous

b)

Discontinuous

11.

Refer to the figure and determine if it is continuous or disconinuous at the given interval (2, )\left(2,\ \infty\right)

a)

Continuous

b)

Discontinuous

12.

Refer to the figure and determine if it is continuous or disconinuous at the point x=0x=0

a)

Continuous

b)

Discontinuous

13.

Refer to the figure and determine if it is continuous or disconinuous at the point x=4x=4

a)

Continuous

b)

Discontinuous

14.

Refer to the figure and determine if it is continuous or disconinuous at the point x=3x=-3

a)

Continuous

b)

Discontinuous

15.

Evaluate limx π312cos x\lim_{x\rightarrow\ \frac{\pi}{3}}-12\cos\ x

a)

6

b)

-6

c)

12 3-12\ \sqrt[]{3}

d)

63-6\sqrt[]{3}

16.

Evaluate the limx(11x2+21x2x325x2+x+1)\lim_{x\rightarrow-\infty}\left(\frac{11x^2+21x-2}{x^3-25x^2+x+1}\right)

a)

-\infty

b)

++\infty

c)

0

d)

DNE

17.

Evaluate the limx+(13x6+x59x2+62x325x5+14x31)\lim_{x\rightarrow+\infty}\left(\frac{13x^6+x^5-9x^2+6}{2x^3-25x^5+14x^3-1}\right)

a)

-\infty

b)

++\infty

c)

0

d)

DNE

18.

Evaluate the limx+(5x4+94x2+30x46)\lim_{x\rightarrow+\infty}\left(-\frac{5x^4+9}{4x^2+30x^4-6}\right)

a)

-\infty

b)

++\infty

c)

530\frac{5}{30}

d)

16-\frac{1}{6}

19.

Evaluate limx47x+8\lim_{x\rightarrow4}\sqrt[]{7x+8}

a)

6

b)

-6

c)

36

d)

-36

20.

Evaluate limx1(x3+2x+1)(2x1)\lim_{x\rightarrow1}\left(x^3+2x+1\right)\left(2x-1\right)

a)

4

b)

3

c)

12

d)

0

21.

Evaluate limx4(x24xx216)\lim_{x\rightarrow4}\left(\frac{x^2-4x}{x^2-16}\right)

a)

14\frac{1}{4}

b)

4

c)

13\frac{1}{3}

d)

12\frac{1}{2}

22.

Evaluate limx1(1x1)(1x+212x+1)\lim_{x\rightarrow1}\left(\frac{1}{x-1}\right)\left(\frac{1}{x+2}-\frac{1}{2x+1}\right)

a)

14\frac{1}{4}

b)

19\frac{1}{9}

c)

13\frac{1}{3}

d)

DNE

23.

Evaluate limx4(n4n2)\lim_{x\rightarrow4}\left(\frac{n-4}{\sqrt[]{n}-2}\right)

a)

DNEDNE

b)

2

c)

4

d)

18\frac{1}{8}

24.

Evaluate limx0(sinx5x)\lim_{x\rightarrow0}\left(\frac{\sin x}{5\sqrt[]{x}}\right)

a)

DNE

b)

0

c)

1

d)

15\frac{1}{5}

25.

What type of discontinuity on the graph at x0x_0 ?

a)

Removable

b)

Jump

c)

Essential

d)

None of the above