Free Printable [PRACTICE] Limits

1.

What does the degree of a polynomial function tell you?

a)

how hot it is

b)

the most number of x-intercepts it can have

c)

the most number of y-intercepts it can have

d)

the most number of terms it has

e)

the most number of solutions it can have

2.

a)

6

b)

-5

c)

3

d)

150

e)

195

3.

a)

16

b)

46

c)

10

d)

6

4.

a)

-infinity

b)

infinity

c)

6

d)

3

5.

$\lim_{x\rightarrow4}\left(\frac{\left(x+3\right)\left(x-4\right)}{\left(x-4\right)}\right)=$

a)

0

b)

1

c)

3

d)

7

e)

Does not exist

6.

$\lim_{x\rightarrow3}\left(\frac{\left(x-1\right)\left(x+3\right)}{\left(x-3\right)}\right)=$

a)

2

b)

-2

c)

12

d)

0

e)

Does not exist

7.

$\lim_{x\rightarrow0}\left(\frac{x\left(x+2\right)}{\left(x+2\right)}\right)=$

a)

1

b)

2

c)

1/2

d)

0

e)

Does not exist

8.

a)

0

b)

-1

c)

infinity

d)

-infinity

9.

a)

A

b)

B

c)

C

d)

D

10.

a)

0

b)

∞

c)

- ∞

d)

DNE

11.

a)

Does not exist

b)

-7/5

c)

-5/9

d)

-1/2

12.

a)

Infinity

b)

20

c)

DNE

d)

12

13.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

14.

Which of the following statements is/are ALWAYS TRUE for Polynomial Functions?

a)

Domain is the Set of All Real Numbers

b)

Range is the Set of All Real Numbers

c)

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

15.

Which of the following will result to DNE?

a)

$\lim_{x\rightarrow a^-}f\left(x\right)\ne\lim_{x\rightarrow a^+}f\left(x\right)$

b)

$\lim_{x\rightarrow a^-}f\left(x\right)=\lim_{x\rightarrow a^+}f\left(x\right)$

c)

$\lim_{x\rightarrow a^-}f\left(x\right)=\infty;\ \lim_{x\rightarrow a^+}f\left(x\right)=\infty$

d)

$\lim_{x\rightarrow a^-}f\left(x\right)=\infty;\ \lim_{x\rightarrow a^+}f\left(x\right)=-\infty$

e)

$\lim_{x\rightarrow a^-}f\left(x\right)=-\infty;\ \lim_{x\rightarrow a^+}f\left(x\right)=-\infty$

16.

$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.

17.

$\lim_{x\rightarrow4}\frac{\left(x+3\right)\left(x-4\right)}{\left(x-4\right)}=$

a)

0

b)

1

c)

3

d)

7

e)

Does not exist

18.

$\lim_{x\rightarrow3}\frac{\left(x-1\right)\left(x+3\right)}{\left(x-3\right)}=$

a)

2

b)

-2

c)

12

d)

0

e)

Does not exist

19.

$\lim_{x\rightarrow0}\frac{x\left(x+2\right)}{\left(x+2\right)}=$

a)

1

b)

2

c)

1/2

d)

0

e)

Does not exist

20.

$\lim_{x\rightarrow1}\left(\frac{\left(x-1\right)\left(x+3\right)}{\left(x-3\right)}\right)=$

a)

4

b)

-4

c)

8

d)

0

e)

Does not exist

21.

$\lim_{x\rightarrow-2}\left(\frac{x\left(x+2\right)}{\left(x+2\right)}\right)=$

a)

1

b)

2

c)

-2

d)

0

e)

Does not exist

22.

$\lim_{x\rightarrow3}\left(\frac{\left(2x-1\right)\left(x-3\right)}{\left(x-3\right)}\right)=$

a)

1

b)

2

c)

5

d)

0

e)

Does not exist

23.

$\lim_{x\rightarrow-3}\left(\frac{\left(2x-1\right)\left(x+3\right)}{\left(x-3\right)}\right)=$

a)

1

b)

-7

c)

5

d)

0

e)

Does not exist

24.

$\lim_{x\rightarrow-2}\left(\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}\right)=$

a)

-1

b)

-3

c)

3

d)

0

e)

Does not exist

25.

$\lim_{x\rightarrow-1}\left(\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}\right)=$

a)

-1

b)

-2

c)

3

d)

0

e)

Does not exist

26.

$\lim_{x\rightarrow1}\left(\frac{\left(x-1\right)\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}\right)=$

a)

-1

b)

1/3

c)

3

d)

0

e)

Does not exist

27.

$\lim_{x\rightarrow0}\left(\frac{4x}{x\left(x-2\right)}\right)=$

a)

-2

b)

-4

c)

4

d)

0

e)

Does not exist

28.

All rational function is continuous anywhere.

a)

True

b)

False

29.

a)

0/0

b)

DNE

c)

-1/4

d)

1/4

30.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow-9^-}g\left(x\right)$ ?

a)

-10

b)

-9

c)

0

d)

1

e)

DNE

31.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow1}g\left(x\right)$ ?

a)

-1

b)

0

c)

1

d)

2

e)

DNE

32.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow-9^+}g\left(x\right)$ ?

a)

-10

b)

-9

c)

0

d)

1

e)

DNE

33.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow-9}g\left(x\right)$ ?

a)

-10

b)

-9

c)

0

d)

1

e)

DNE

34.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow-3^-}g\left(x\right)$ ?

a)

-3

b)

-2

c)

0

d)

2

e)

DNE

35.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow-3}g\left(x\right)$ ?

a)

-3

b)

-2

c)

0

d)

2

e)

DNE

36.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow0^-}g\left(x\right)$ ?

a)

-5

b)

-4

c)

0

d)

4

e)

DNE

37.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow9^-}g\left(x\right)$ ?

a)

-4

b)

-1

c)

0

d)

3

e)

DNE

38.

Given the graph of $g\left(x\right)$ , what is $\lim_{x\rightarrow13^+}g\left(x\right)$ ?

a)

0

b)

8

c)

10

d)

15

e)

DNE

39.

a)

1/5

b)

1

c)

5

d)

Does not exist

40.

$\lim_{x\rightarrow0}\ \frac{\tan x}{x}$

a)

0

b)

1

c)

-1

d)

DNE

41.

$\lim_{x\rightarrow0}\ \frac{\sin\ \frac{1}{3}x}{x}$

a)

-3

b)

$-\frac{1}{3}$

c)

$0$

d)

$\frac{1}{3}$

e)

3

42.

$\lim_{x\rightarrow0}\ \frac{7\ \sin\ x\ \cos\ x}{2x}$

a)

$-\frac{7}{2}x$

b)

$-\ 3,5$

c)

$\frac{7}{2}$

d)

7

e)

2

43.

a)

12

b)

4

c)

3

d)

1

e)

0

44.

a)

6

b)

3

c)

2

d)

1

e)

0

45.

$\lim_{x\rightarrow0}\ -\frac{4\sin\ 3x}{5}$

a)

$-\frac{43}{5}$

b)

$-\frac{12}{5}$

c)

$\frac{12}{5}$

d)

$\frac{1}{5}$

e)

1

46.

$\lim_{x\rightarrow0}\ \frac{\sin\left(-x\right)}{3x}$

a)

-3

b)

$-\frac{1}{3}$

c)

$0$

d)

$\frac{1}{3}$

e)

3

47.

Given the graph of $f\left(x\right)$ , what is $\lim_{x\rightarrow-5}f\left(x\right)$ ?

a)

-5

b)

-2

c)

-1

d)

0

e)

1

48.

Given the graph of $f\left(x\right)$ , what is $\lim_{x\rightarrow-2^+}f\left(x\right)$ ?

a)

-5

b)

-2

c)

-1

d)

0

e)

DNE

49.

In finding $\lim_{x\rightarrow2^+}f\left(x\right)$ , which sub-function should be observed?

a)

red

b)

blue

c)

orange

d)

green

e)

violet

50.

Given the graph of $f\left(x\right)$ , what is $\lim_{x\rightarrow5^-}f\left(x\right)$ ?

a)

0

b)

5

c)

6

d)

$-\infty$

e)

$\infty$

[PRACTICE] Limits

Total questions: 50

Worksheet time: 50mins

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