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Limits 4

Total questions: 75

Worksheet time: 3hrs 45mins

Name
Class
Date
1.

 lim⁡x→−2−f(x)\lim_{x\rightarrow-2^-}f\left(x\right)  

a)

DNE

b)

-2

c)

3

d)

-4

2.

 lim⁡x→−2f(x)\lim_{x\rightarrow-2^{ }}f\left(x\right)  

a)

DNE

b)

-2

c)

3

d)

-4

3.

 lim⁡x→2−f(x)\lim_{x\rightarrow2^-}f\left(x\right)  

a)

DNE

b)

 ∞\infty  

c)

 −∞-\infty  

d)

2

4.

 lim⁡x→2f(x)\lim_{x\rightarrow2^{ }}f\left(x\right)  

a)

DNE

b)

 ∞\infty  

c)

 −∞-\infty  

d)

2

5.

 lim⁡x→−37x+22\lim_{x\rightarrow-3}\sqrt{7x+22}  

a)

 43\sqrt{43}  

b)

1

c)

DNE

d)

3

6.

 lim⁡x→2x2−3x+9\lim_{x\rightarrow2}x^2-3x+9  

a)

7

b)

DNE

c)

2

d)

9

7.

 lim⁡x→−618\lim_{x\rightarrow-6}18  

a)

DNE

b)

-6

c)

18

d)

Not enough information

8.

 lim⁡x→π4xtan⁡x\lim_{x\rightarrow\frac{\pi}{4}}x\tan x  

a)

 22\frac{\sqrt{2}}{2}  

b)

DNE

c)

 12\frac{1}{2}  

d)

 π4\frac{\pi}{4}  

9.

 lim⁡x→∞4x2+6x−92x2−18\lim_{x\rightarrow\infty}\frac{4x^2+6x-9}{2x^2-18}  

a)

DNE

b)

 ∞\infty  

c)

2

d)

0

10.

 lim⁡x→∞x−3x3+9\lim_{x\rightarrow\infty}\frac{x-3}{x^3+9}  

a)

DNE

b)

0

c)

 ∞\infty  

d)

6

11.

 lim⁡x→22x−8x2−16\lim_{x\rightarrow2}\frac{2x-8}{x^2-16}  

a)

DNE

b)

 ∞\infty  

c)

2

d)

 13\frac{1}{3}  

12.

 lim⁡x→1(3x+5)\lim_{x\rightarrow1}\left(3^x+5\right)  

a)

DNE

b)

1

c)

8

d)

 ∞\infty  

13.

 lim⁡x→5(x2−7x+10x−5)\lim_{x\rightarrow5}\left(\frac{x^2-7x+10}{x-5}\right)  

a)

5

b)

3

c)

-5

d)

Does not exist

e)

 00\frac{0}{0}  

14.
a)
3
b)
0
c)
1
d)
Does not exist
15.

Find lim⁡x→2xx+2−2x+4\lim_{x\rightarrow2}\frac{\text{}\frac{x}{x+2}-2}{x+4} . 

a)

4

b)

-4

c)

 14\frac{1}{4}  

d)

 −14-\frac{1}{4}  

16.

Determine the limit.
 lim⁡x→∞(x14+x−12x+3)\lim_{x\rightarrow\infty}\left(\frac{x^{14}+x-12}{x+3}\right)  

a)

 ∞\infty  

b)

 −∞-\infty  

c)

-3

d)

4

17.
a)
0
b)
1
c)
2
d)
DNE
18.
a)
0/0
b)
DNE
c)
-1/4
d)
1/4
19.

 Find  lim⁡x→2 f(x)\lim_{x\rightarrow2\ }f\left(x\right)  

a)

-1

b)

5

c)

0

d)

DNE

20.

If  lim⁡x→cf(x)=3\lim_{x\rightarrow c}f\left(x\right)=3 ,  lim⁡x→cg(x)=−2\lim_{x\rightarrow c}g\left(x\right)=-2  , and  lim⁡x→ch(x)=4\lim_{x\rightarrow c}h\left(x\right)=4  then find  lim⁡x→c3h(x)−2g(x)\lim_{x\rightarrow c}\sqrt{3h\left(x\right)-2g\left(x\right)} . 

a)

16

b)

4

c)

8

d)

12

21.
a)
Does not exist
b)
2
c)
0
d)
1
22.
What is the limit?
a)
DNE
b)
Infinity
c)
6
d)
12
23.
What is the limit of the function as x approaches -4 from the left?
a)
2
b)
-4
c)
DNE
d)
-2
24.
a)
Infinity
b)
20
c)
DNE
d)
12
25.

 lim⁡x→−5   x+52 = ....\lim_{x\rightarrow-5}\ \ \ \frac{x+5}{2}\ =\ ....  

a)

0

b)

5

c)

 ∞\infty  

d)

 52\frac{5}{2}  

e)

 25\frac{2}{5}  

26.

Find the limit as x approaches 7 from the right

a)

1

b)

0

c)

infinity

d)

DNE

27.

Select all statements that are TRUE.

a)
b)
c)
d)
28.

Find the limit

a)

9/12

b)

0

c)

∞

d)

-∞

29.

Find the limit

a)

7/9

b)

0

c)

∞

d)

-∞

30.

Determine the limit.

a)

−∞-\infty

b)

∞\infty

c)

0

d)

-1

31.

What is the limit of  f(x)=45 +23 (.1)xf\left(x\right)=45\ +23\ \left(.1\right)^x  as  x approaches infinity?

a)

23

b)

45

c)

68

d)

0

32.

 f(x)=(3x5−2x+47x5−3x−2 )f\left(x\right)=\left(\frac{3x^5-2x+4}{7x^5-3x-2}\ \right)  

What is the limit of f(x) as x appoaches infinity?

a)

 ∞\infty  

b)

 −∞-\infty  

c)

 37\frac{3}{7}  

d)

 00  

33.

 f(x)=(52x−4x+12)5f\left(x\right)=\left(\frac{5}{2x}-4x+12\right)^5  

What combination of limit properties are require to evaluate the limit?

a)

Sum, difference, quotient, power

b)

Sum, difference, product, root

c)

sum, difference, product, power

d)

Sum, difference, quotient, root

34.

 f(x)=(x2−x−2)(x−2)f\left(x\right)=\frac{\left(x^2-x-2\right)}{\left(x-2\right)}  

What value must be defined for f(2) to remove the discontinuity of this function at x = 2?

a)

3

b)

-3

c)

0

d)

2

35.

 f(x)=(x2+8x+16)(x+4)f\left(x\right)=\frac{\left(x^2+8x+16\right)}{\left(x+4\right)}  

What value must be defined for f(-4) to remove the discontinuity of this function at x = -4?

a)

8

b)

-8

c)

0

d)

2

36.
Find the limit as x approaches 3 from the left
a)
4
b)
3
c)
2
d)
DNE
37.
What is the limit of the function as x approaches 1 from the left?
a)
DNE
b)
1
c)
4
d)
-2
38.
a)
Does not exist
b)
0
c)
-1
d)
1
39.

The table above gives values of the function at selected values of . What is lim⁡x→11f(x)?\lim_{x\rightarrow11}f\left(x\right)?  

a)

11

b)

32

c)

32.03

d)

dne

40.

What is the limit of  lim⁡x→−1(x2+1)\lim_{x\rightarrow-1}\left(x^2+1\right)  ?

a)

1

b)

2

c)

3

d)

4

41.

 Find  lim⁡x→−1 f(x)\lim_{x\rightarrow-1\ }f\left(x\right)  

a)

4

b)

0

c)

-1

d)

DNE

42.
What is the limit?
a)
DNE
b)
Infinity
c)
6
d)
12
43.
a)
Does not exist
b)
-7/5
c)
-5/9
d)
-1/2
44.
a)
Does Not Exist
b)
9
c)
1
d)
0
45.
a)
Does not exist
b)
2
c)
0
d)
1
46.
a)
2
b)
0
c)
Does not exist
d)
4
47.

 lim⁡x→∞ 1−2x+2x3x3+x+1= ...\lim_{x\rightarrow\infty}\ \frac{1-2x+2x^3}{x^3+x+1}=\ ...  

a)

- 4

b)

- 2

c)

1

d)

2

e)

 ∞\infty  

48.

Find the limit

a)

6/5

b)

0

c)

∞\infty

d)

−∞-\infty

49.
a)
0/0
b)
DNE
c)
-1/4
d)
1/4
50.
a)
0/0
b)
DNE
c)
-1/4
d)
1/4
51.
a)
0
b)
0/0
c)
1/4
d)
DNE
52.

Evaluate

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

a)

+∞+\infty  

b)

−∞-\infty  

c)

undefinedundefined  

d)

00  

53.

Evaluate

lim⁡x→0−(12x7)\lim_{x\rightarrow0^-}\left(\frac{1}{2x^7}\right)  

a)

+∞+\infty  

b)

−∞-\infty  

c)

undefinedundefined  

d)

00  

54.

Evaluate

lim⁡x→0+(1x4)\lim_{x\rightarrow0^+}\left(\frac{1}{x^4}\right)  

a)

+∞+\infty  

b)

−∞-\infty  

c)

undefinedundefined  

d)

00  

55.

Use the theorems to evaluate the limit  lim⁡x→−2 24−x\lim_{x\rightarrow-2}\ \frac{2}{4-x}  

a)

13\frac{1}{3}  

b)

−13-\frac{1}{3}  

c)

1

d)

-1

56.

Use the theorems to evaluate the limit lim⁡x→−3 (2x +6)4x2 −36\lim_{x\rightarrow-3}\ \frac{\left(2x\ +6\right)}{4x^{2\ }-36}  

a)

0

b)

does not exist

c)

−112-\frac{1}{12}  

d)

-1

57.

Let lim⁡x→8f(x)=3 and lim⁡x→8g(x)=10.\lim_{x\rightarrow8}f\left(x\right)=3\ and\ \lim_{x\rightarrow8}g\left(x\right)=10.  Find  lim⁡x→8f(x)g(x).\lim_{x\rightarrow8}\frac{f\left(x\right)}{\text{g(x)}}.  

a)

8

b)

10/3

c)

-7

d)

3/10

58.

Find lim⁡x→2xx+2−2x+4\lim_{x\rightarrow2}\frac{\text{}\frac{x}{x+2}-2}{x+4} . 

a)

4

b)

-4

c)

14\frac{1}{4}  

d)

−14-\frac{1}{4}  

59.

lim⁡x→4  x2−7x\lim_{x\rightarrow4}\ \ \sqrt{\frac{x^2-7}{x}}  

a)

112\frac{\sqrt{11}}{2}  

b)

9/4

c)

3/2

d)

no limit

60.

lim⁡x→∞ 3x2+x+2x3+2x2+1 = ...\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  

61.

Determine the value of the limit

a)

4

b)

-1

c)

1

d)

DNE

62.

Use the given function to determine the value of the limit

a)

DNE

b)

-12

c)

10

d)

0

63.

The lim⁡x→0f(x) 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.

64.

The lim⁡x→2f(x) 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.

65.
a)
Infinity
b)
Negative Infinity
c)
2
d)
Does not exist
66.

Find the limit as x approaches 7 from the right

a)

1

b)

0

c)

infinity

d)

DNE

67.
a)
2
b)
-3/4
c)
-1/3
d)
1/4
68.

lim⁡x→3−f(x)=\lim_{x\rightarrow3^-}f\left(x\right)=  

a)

0

b)

6\sqrt{6}  

c)

6

d)

DNE

69.

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

a)
b)
c)
d)
70.

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

a)

3/7

b)

0

c)

∞\infty

d)

−∞-\infty

71.

lim⁡x→∞ 2x−34x +1\lim_{x\rightarrow\infty}\ \frac{2x-3}{4x\ +1}  

a)

0

b)

DNE

c)

1/2

d)

2

72.

lim⁡x→∞(2x3+3x−1)=\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

73.

lim⁡x→∞ex=\lim_{x\rightarrow\infty}e^x=  
Hint:  Think of the end behavior

a)

∞\infty  

b)

−∞-\infty  

c)

0

d)

DNE

74.

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→∞(x2−x−12x+3)\lim_{x\rightarrow\infty}\left(\frac{x^2-x-12}{x+3}\right)  

a)

∞\infty  

b)

−∞-\infty  

c)

-3

d)

4

75.

lim⁡x→∞ sin⁡ xx+4\lim_{x\rightarrow\infty}\ \frac{\sin\ x}{x}+4  

a)

1

b)

0

c)

DNE

d)

4

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