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Unit 1 Test Practice: Limits & Continuity

Total questions: 130

Worksheet time: 6hrs 29mins

Name
Class
Date
1.

What is the limit?

(a)  

2.

Evaluate.

(a)  

3.

what is the limit as x approaches infinity of the function f(x)= (3x-5)/(5x2+4)

a)

infinity

b)

negative infinity

c)

0

d)

1

4.

What are the vertical asymptotes of the function f(x)=(x2-9)/(x2+6x+9)

a)

x=3

b)

x=-3

c)

x=3,-3

d)

no vertical asymptote

5.

what is the limit when x approaches infinity of the function f(x)=ex

a)

negative infinity

b)

e

c)

infinity

d)

0

6.
Name the discontinuity at x=2. 
a)
Infinite Discontinuity
b)
Removable Discontinuity
c)
Jump Discontinuity
d)
Continuous at x=2
7.
Name the discontinuity at x=2. 
a)
Infinite Discontinuity
b)
Removable Discontinuity
c)
Jump Discontinuity
d)
Continuous at x=2
8.

Find the limit.

(a)  

9.

Find the limit as x approaches 1+

a)

1

b)

-1

c)

-3

d)

DNE

10.

Select all statements that are TRUE.

a)
b)
c)
d)
e)
11.

Find the limit.

a)

0

b)

-1

c)

-5/2

d)

DNE

12.
a)
6
b)
3
c)
1/6
d)
-1/6
e)

1/3

13.

Which of the following is true?

a)

b)

c)

d)

e)

none of these

14.

Find the limit.

a)

0

b)

1

c)

-1

d)

DNE

15.

Find the limit.

a)

0

b)

-6

c)

-12

d)

12

e)

-1/6

16.

lim⁡x→0+f(x)\lim_{x\rightarrow0^+}f\left(x\right)

a)
0
b)
∞
c)
-∞
d)
1
17.
a)

4

b)

1/4

c)

0

d)

DNE

e)

-1/4

18.
a)

-7

b)

0

c)

1

d)

DNE

e)

1/7

19.
a)
Does not exist
b)
6
c)
4
d)
3
20.
a)
I only
b)
I and II only
c)
I and III only
d)

I, II, and III

21.
a)
0
b)
∞
c)
- ∞
d)
DNE
22.
What is the limit of the function as x approaches -4 from the left?
a)
2
b)
-4
c)
DNE
d)
-2
23.

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

a)

-1

b)

5

c)

0

d)

DNE

24.

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

a)

-1

b)

5

c)

0

d)

DNE

25.

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

a)

-1

b)

5

c)

0

d)

DNE

26.

 Find  lim⁡x→4 f(x)\lim_{x\rightarrow4\ }f\left(x\right)  

a)

2

b)

0

c)

-4

d)

DNE

27.

Find the limit

(a)  

28.

Find the limit

(a)  

29.

Find the limit

(a)  

30.

Given the graph of f(x)f\left(x\right) , which of the following are true? Select all that are true

a)

lim⁡x→af(x)=lim⁡x→ bf(x)\lim_{x\rightarrow a}f\left(x\right)=\lim_{x\to\ b}f\left(x\right)

b)

lim⁡x→af(x)=2\lim_{x\to a}f\left(x\right)=2

c)

lim⁡x→ b+f(x)=2\lim_{x\to\ b^+}f\left(x\right)=2

d)

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

e)

lim⁡x→ bf(x)\lim_{x\to\ b}f\left(x\right) does not exist

31.

True or False:

The f(x)f\left(x\right) is continuous at x=ax=a

a)
True
b)
False
32.



(a)  

33.
Which of the following best describes the continuity at x = 1?
a)
Continuous
b)
Removable Point Discontinuity
c)
Non-removable Infinite Discontinuity
d)
Non-removable Jump Discontinuity
34.

Consider the graph of f(x). What is the lim⁡x→2− f(x)?\lim_{x\rightarrow2^-}\ f\left(x\right)?  

a)

−∞-\infty  

b)

3

c)

2

d)

∞\infty  

35.

Determine whether the function f(x) is continuous or discontinuous at x=2.x=2.  

a)

continuous

b)

discontinuous, essential

c)

discontinuous, removable

d)

discontinuous, jump

36.

Which among these statements is true about g(x)=1−x2g\left(x\right)=\sqrt[]{1-x^2}  ?

a)

g(x) is continuous at all points in the interval [-1, 1]

b)

lim⁡x→−1 1−x2\lim_{x\rightarrow-1}\ \sqrt[]{1-x^2}  exists

c)

g(x) has a removable discontinuity at x=-1

d)

lim⁡x→0 1−x2 = g(0)\lim_{x\rightarrow0}\ \sqrt[]{1-x^2\ }=\ g\left(0\right)  

37.

What is the limit?

(a)  

38.
What is the limit?
a)
DNE
b)

1/12

c)
6
d)
12
e)

-6

39.
a)
0
b)
-2/9
c)
Infinity
d)
-5/6
40.

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

a)

1

b)

-1

c)

-3

d)

DNE

e)

0

41.

lim⁡x→0 tan⁡(12x)3x\lim_{x\rightarrow0}\ \frac{\tan\left(12x\right)}{3x}  

(a)  

42.

lim⁡x→0 sin⁡(4x)16x\lim_{x\rightarrow0}\ \frac{\sin\left(4x\right)}{16x}  

a)

1/16

b)

4

c)

1/4

d)

0

43.

Is f(x) continuous at x= -2?

a)

Yes, f(x) is continuous at x= -2

b)

No, there is a jump discontinuity at x=-2

c)

No, there is a hole at x= -2

d)

No, there is a vertical asymptote at x= -2

44.

Identify the type of discontinuity and the x-value where it occurs:

f(x)=x2−3x−10x2+x−30f\left(x\right)=\frac{x^2-3x-10}{x^2+x-30}  

a)

f(x) is continuous

b)

vertical asymptotes at x=5, −6x=5,\ -6  

c)

hole at x=−5x=-5  vertical asymptote at x=6x=6  

d)

hole at x=5x=5  , vertical asymptote at x=−6x=-6  

45.

Which of the following conditions must be met in order for a function to be continuous at a point x=c?

a)

f(c) is defined

b)

lim⁡x→c f(x)\lim_{x\rightarrow c}\ f\left(x\right)  exists

c)

lim⁡x→c f(x) = f(c)\lim_{x\rightarrow c}\ f\left(x\right)\ =\ f\left(c\right)  

46.

Evaluate the limit:

lim⁡x→92x−6x−9\lim_{x\to9}\frac{2\sqrt{x}-6}{x-9}

a)

13\frac{1}{3}

b)

2

c)

9

d)

DNE

47.

Evaluate the limit:

lim⁡s→75−4+3s7−s\lim_{s\to7}\frac{5-\sqrt{4+3s}}{7-s}

a)

57\frac{5}{7}

b)

0

c)

310\frac{3}{10}

d)

3

48.

Evaluate the limit

lim⁡x→2(3x2−4x+5)\lim_{x\to2}\left(3x^2-4x+5\right)

a)

0

b)

3

c)

9

d)

∞\infty

49.

Evaluate the limit:

lim⁡y→−45y+4y−5\lim_{y\rightarrow-4}\sqrt{\frac{5y+4}{y-5}}

a)

−45-\frac{4}{5}

b)

43\frac{4}{3}

c)

5\sqrt{5}

d)

5

50.

Evaluate the limit:

lim⁡x→−2(8−3x)\lim_{x\to-2}\left(8-3x\right)

a)

-2

b)

0

c)

5

d)

14

e)

2

51.

Is the function  f(x)=x2−2x+1f\left(x\right)=x^2-2x+1 , continuous at x=0?

a)

yes

b)

no

52.

Which of the following best describes h(x) at x = 1?

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

53.

At what x-value does this function have an infinite discontinuity?

a)

−2-2

b)

22

c)

−4-4

d)

00

54.

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

a)

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

b)

lim⁡x→3f(x)\lim_{x\rightarrow3}f\left(x\right) exists

c)

lim⁡x→4f(x)\lim_{x\rightarrow4}f\left(x\right) exists

d)

lim⁡x→5f(x)\lim_{x\rightarrow5}f\left(x\right) exists

e)

The function f is continuous at x=3

55.

Consider the graph of f(x). What is the lim⁡x→2− f(x)?\lim_{x\rightarrow2^-}\ f\left(x\right)?  

a)

−∞-\infty  

b)

3

c)

2

d)

∞\infty  

e)

DNE

56.

Consider the graph of f(x). What is the lim⁡x→4 f(x)?\lim_{x\rightarrow4}\ f\left(x\right)?  

a)

2

b)

1

c)

3

d)

DNE

57.

Which of the following best describes h(x) at x = 0?

a)
Continuous
b)
Removable Point Discontinuity
c)
Non-removable Infinite Discontinuity
d)
Non-removable Jump Discontinuity
58.

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

a)

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

b)

f is continuous at x=a

c)

lim⁡x→af(x)=1\lim_{x\rightarrow a}f\left(x\right)=1

d)

lim⁡x→af(x)=2\lim_{x\rightarrow a}f\left(x\right)=2

e)

lim⁡x→af(x)\lim_{x\rightarrow a}f\left(x\right) does not exist

59.

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

a)

lim⁡x→1−f(x)\lim_{x\rightarrow1^-}f\left(x\right)

b)

lim⁡x→1f(x)\lim_{x\rightarrow1}f\left(x\right)

c)

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

d)

lim⁡x→3f(x)\lim_{x\rightarrow3}f\left(x\right)

e)

lim⁡x→5f(x)\lim_{x\rightarrow5}f\left(x\right)

60.

Does the following function is continuous at x=0?

a)

Continuous

b)

Discontinuous

61.

Find the value for that makes f(x) continuous.

a)

0

b)

1

c)

1.5

d)

2

e)

No such value exists

62.

lim⁡x→π sin⁡x\lim_{x\rightarrowπ}\ \sin x  

a)

1

b)

0

c)

-1

d)

Does not exist

63.

lim⁡x→0 5(1−cos⁡x)x\lim_{x\rightarrow0}\ \frac{5\left(1-\cos x\right)}{x}  

a)

0

b)

5

c)

10

d)

Does not exist

64.

lim⁡x→6f(x)=\lim_{x\rightarrow6}f\left(x\right)=  
If the limit does not exist, write "DNE."



(a)  

65.

The table above gives values of a function  ff  at selected values of  x.x.  Which of the following conclusions is supported by the data in the table?

a)

lim⁡x→3f(x)=0\lim_{x\rightarrow3}f\left(x\right)=0  

b)

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

c)

lim⁡x→3f(x) =10\lim_{x\rightarrow3}f\left(x\right)\ =10  

d)

lim⁡x→3f(x)\lim_{x\rightarrow3}f\left(x\right)  does not exist

66.

The table above gives values of a function ff at selected values of x.x. Which of the following conclusions is supported by the data in the table?

a)

lim⁡x→2f(x)=−1\lim_{x\rightarrow2}f\left(x\right)=-1

b)

lim⁡x→2f(x)=6\lim_{x\rightarrow2}f\left(x\right)=6

c)

lim⁡x→2−f(x) =−1\lim_{x\rightarrow2^-}f\left(x\right)\ =-1 and lim⁡x→2+f(x)=6\lim_{x\rightarrow2^+}f\left(x\right)=6

d)

lim⁡x→2−f(x)=6\lim_{x\rightarrow2^-}f\left(x\right)=6 and lim⁡x→2+f(x)=−1\lim_{x\rightarrow2^+}f\left(x\right)=-1

67.

The table above gives values of a function ff at selected values of x.x. Which of the following conclusions is supported by the data in the table?

a)

lim⁡x→11f(x)=32\lim_{x\rightarrow11}f\left(x\right)=32

b)

lim⁡x→11f(x)=∞\lim_{x\rightarrow11}f\left(x\right)=\infty

c)

lim⁡x→32f(x) =11\lim_{x\rightarrow32}f\left(x\right)\ =11

d)

lim⁡x→32f(x)=∞\lim_{x\rightarrow32}f\left(x\right)=\infty

68.

The table above gives values of a function ff at selected values of x.x. Which of the following conclusions is supported by the data in the table?

a)

lim⁡x→4f(x)=6\lim_{x\rightarrow4}f\left(x\right)=6

b)

lim⁡x→4f(x)=7\lim_{x\rightarrow4}f\left(x\right)=7

c)

lim⁡x→4−f(x) =6\lim_{x\rightarrow4^-}f\left(x\right)\ =6 and lim⁡x→4+f(x)=7\lim_{x\rightarrow4^+}f\left(x\right)=7

d)

lim⁡x→4−f(x)=7\lim_{x\rightarrow4^-}f\left(x\right)=7 and lim⁡x→4+f(x)=6\lim_{x\rightarrow4^+}f\left(x\right)=6

69.

What is the limit of f(x) as x approaches c?

(a)  

70.

lim⁡x→−4f(x)=\lim_{x\rightarrow-4}f\left(x\right)=  
If the limit does not exist, write "DNE."



(a)  

71.

lim⁡x→0 tan⁡xx\lim_{x\rightarrow0}\ \frac{\tan x}{x}  

a)

0

b)

1

c)

-1

d)

DNE

72.

lim⁡x→0 cos⁡xx\lim_{x\rightarrow0}\ \frac{\cos x}{x}  

a)

0

b)

1

c)

-1

d)

DNE

73.

lim⁡x→0 sin⁡xx\lim_{x\rightarrow0}\ \frac{\sin x}{x}  

a)

0

b)

1

c)

-1

d)

DNE

74.

lim⁡x→πtan⁡ x\lim_{x\rightarrow\pi}\tan\ x  

a)

0

b)

1

c)

-1

d)

DNE

75.
a)

A

b)

B

c)

C

d)

D

e)

E

76.
a)

A

b)

B

c)

C

d)

D

e)

E

77.
a)

A

b)

B

c)

C

d)

D

e)

E

78.
a)

A

b)

B

c)

C

d)

D

e)

E

79.
a)

A

b)

B

c)

C

d)

D

e)

E

80.

Evaluate the limit.

a)

DNEDNE

b)

−1-1

c)

44

d)

−4-4

81.

Evaluate the limit.

a)

−1-1

b)

16\frac{1}{6}

c)

77

d)

DNEDNE

82.

Evaluate the limit.

a)

23\frac{2}{3}

b)

00

c)

DNEDNE

d)

33

83.

Evaluate the limit.

a)

1010

b)

−7-7

c)

DNEDNE

d)

−110-\frac{1}{10}

84.

Evaluate the limit.

a)

114\frac{1}{14}

b)

12\frac{1}{2}

c)

DNEDNE

d)

23\frac{2}{3}

85.

Find lim⁡x→023x+4+2\lim_{x\rightarrow0}\frac{\text{2}}{\sqrt{3x+4}+2}  .

a)

DNE

b)

1

c)

2

d)

12\frac{1}{2}  

86.

Find lim⁡x→01+x−1x\lim_{x\rightarrow0}\frac{\sqrt{1+x}-1}{\text{x}} . 

a)

12\frac{1}{2}  

b)

14\frac{1}{4}  

c)

DNE

d)

0

87.

Find lim⁡x→4x2+3x−28x−4\lim_{x\rightarrow4}\frac{x^2+3x-28}{x-4} . 

a)

11

b)

0

c)

DNE

d)

3

88.

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}  

89.

Find lim⁡x→21x−12x−2\lim_{x\rightarrow2}\frac{\frac{1}{x}-\frac{1}{2}}{x-2} . 

a)

DNE

b)

14\frac{1}{4}  

c)

12\frac{1}{2}  

d)

−14-\frac{1}{4}  

90.
a)

I only

b)

II only

c)

I, II, III

d)

None

91.
Find the value that makes the function continuous
a)
c=1/3
b)
c=3
c)
c=-3
d)
c=-1/3
92.

Use the graph above to solve: lim⁡x→−3g(f(x))\lim_{x\rightarrow-3}g\left(f\left(x\right)\right)  

a)

-7

b)

-2

c)

-6

d)

DNE

93.

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 ,  lim⁡x→ch(x)=4\lim_{x\rightarrow c}h\left(x\right)=4  then find  lim⁡x→c[f(x)2 4−g(x)]\lim_{x\rightarrow c}\left[\frac{f\left(x\right)^{2\ }}{4-g\left(x\right)}\right]  

a)

3/2 

b)

8/3

c)

2/3

d)

9/2

94.

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 ,  lim⁡x→ch(x)=4\lim_{x\rightarrow c}h\left(x\right)=4  then find  lim⁡x→c[h(x)⋅(f(x)+6)]\lim_{x\rightarrow c}\left[h\left(x\right)\cdot\left(f\left(x\right)+6\right)\right]  

a)

36

b)

16

c)

-18

d)

-20

95.

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 ,  lim⁡x→ch(x)=4\lim_{x\rightarrow c}h\left(x\right)=4  then find  lim⁡x→c(2f(x)+3h(x)h(x)−g(x))\lim_{x\rightarrow c}\left(\frac{2f\left(x\right)+3h\left(x\right)}{h\left(x\right)-g\left(x\right)}\right)  

a)

3

b)

2

c)

1

d)

0

96.

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 ,  lim⁡x→ch(x)=4\lim_{x\rightarrow c}h\left(x\right)=4  then find  lim⁡x→c[7−g(x)]2\lim_{x\rightarrow c}\left[7-g\left(x\right)\right]^2  

a)

81

b)

25

c)

9

d)

45

97.

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 ,  lim⁡x→ch(x)=4\lim_{x\rightarrow c}h\left(x\right)=4  then find  lim⁡x→c[f(x)⋅5g(x)]\lim_{x\rightarrow c}\left[f\left(x\right)\cdot5g\left(x\right)\right]  

a)

-30

b)

-40

c)

60

d)

-80

98.

What is the domain in interval notation of f(x)f\left(x\right) ? 

f(x)=x+2 , g(x)=x2f\left(x\right)=\sqrt{x+2}\ ,\ g\left(x\right)=x^2  

a)

(−∞,−2]\left(-\infty,-2\right]  

b)

[−2,∞)\left[-2,\infty\right)  

c)

(−∞,−2)∪(−2,∞)\left(-\infty,-2\right)\cup\left(-2,\infty\right)  

d)

(−∞,∞)\left(-\infty,\infty\right)  

e)

(−2,2)\left(-2,2\right)  

99.

What is the domain in interval notation of g(x)g\left(x\right) ? 

f(x)=x+2 , g(x)=x2f\left(x\right)=\sqrt{x+2}\ ,\ g\left(x\right)=x^2  

a)

(−∞,−2]\left(-\infty,-2\right]  

b)

[−2,∞)\left[-2,\infty\right)  

c)

(−∞,−2)∪(−2,∞)\left(-\infty,-2\right)\cup\left(-2,\infty\right)  

d)

(−∞,∞)\left(-\infty,\infty\right)  

e)

(−2,2)\left(-2,2\right)  

100.

What's the domain of

f(x)=−2x+5f\left(x\right)=-2x+5  

a)

(−∞, ∞)\left(-\infty,\ \infty\right)  

b)

(−∞, 5)\left(-\infty,\ 5\right)  

c)

(−∞, 5]\left(-\infty,\ 5\right]  

d)

[5, ∞)\left[5,\ \infty\right)  

101.

Find the domain of the function:  f(x)=x2x+4f(x)=\frac{x}{2x+4}  

a)

(−∞, 2)∪(2, ∞)\left(-\infty,\ 2\right)\cup\left(2,\ \infty\right)  

b)

(−∞, 4)∪(4, ∞)\left(-\infty,\ 4\right)\cup\left(4,\ \infty\right)  

c)

(−∞, −2)∪(−2, ∞)\left(-\infty,\ -2\right)\cup\left(-2,\ \infty\right)  

d)

(−∞, ∞)\left(-\infty,\ \infty\right)  

102.

Find the domain of the function

f(x)=2x−7f\left(x\right)=\frac{2}{\sqrt{x-7}}  

a)

(7, ∞)\left(7,\ \infty\right)  

b)

[7, ∞)\left[7,\ \infty\right)  

c)

(−∞, 7)\left(-\infty,\ 7\right)  

d)

(−∞, 7]\left(-\infty,\ 7\right]  

103.

Find the domain of each function.


f(x)=8x+40f\left(x\right)=\sqrt{8x+40}  

a)

[−5,∞]\left[-5,\infty\right]  

b)

(−5,∞)\left(-5,\infty\right)  

c)

[−5,∞)\left[-5,\infty\right)  

d)

[5,∞)\left[5,\infty\right)  

104.

Find the domain of each function.


f(x)=x − 5x2−6xf\left(x\right)=\frac{x\ -\ 5}{x^2-6x}  

a)

(−∞,0)∪(6,∞)\left(-\infty,0\right)\cup\left(6,\infty\right)  

b)

(−∞,0)∪(0,∞)\left(-\infty,0\right)∪\left(0,\infty\right)  

c)

(−∞,0)∪(0, 6)∪(6,∞)\left(-\infty,0\right)∪\left(0,\ 6\right)\cup\left(6,\infty\right)  

d)

(−∞,6)∪(6,∞)\left(-\infty,6\right)∪\left(6,\infty\right)  

105.

Find the domain of each function.


f(x)=x2+5x−6x2+10x+24f\left(x\right)=\frac{x^2+5x-6}{x^2+10x+24}  

a)

(−∞,−6)∪(−6, 1)∪(1,∞)\left(-\infty,-6\right)∪\left(-6,\ 1\right)\cup\left(1,\infty\right)  

b)

(−∞,−6)∪(−6, −4)∪(−4,∞)\left(-\infty,-6\right)∪\left(-6,\ -4\right)\cup\left(-4,\infty\right)  

c)

(−∞,4)∪(4, 6)∪(6,∞)\left(-\infty,4\right)∪\left(4,\ 6\right)\cup\left(6,\infty\right)  

d)

(−∞,−6)∪(−4,∞)\left(-\infty,-6\right)∪\left(-4,\infty\right)  

106.

Domain of  f(x)=11−xf\left(x\right)=\frac{1}{\sqrt{1-x}}  is

a)

(−∞,1)\left(-\infty,1\right)  

b)

(1,∞)\left(1,\infty\right)  

c)

R−{1}R-\left\{1\right\}  

d)

none of these

107.

Evaluate the limit.

a)

2π3\frac{2\pi}{3}

b)

32\frac{\sqrt{3}}{2}

c)

−12-\frac{1}{2}

d)

DNE

108.
a)
Does Not Exist
b)
9
c)
1
d)
0
109.

The graphs of f and g are given. Use the graph to evaluate the limit: lim⁡x→−1[f(x)+g(x)]\lim_{x\rightarrow-1}\left[f\left(x\right)+g\left(x\right)\right]  

a)

3

b)

1

c)

2

d)

-2

110.

The graphs of f and g are given. Use the graph to evaluate the limit: lim⁡x→3[f(x)g(x)]\lim_{x\rightarrow3}\left[f\left(x\right)g\left(x\right)\right]  

a)

0

b)

1

c)

10

d)

-1

111.

lim⁡x→−4   17 = ....\lim_{x\rightarrow-4}\ \ \ 17\ =\ ....  

a)

17

b)

−68-68  

c)

−4-4  

d)

−17-17  

e)

0

112.

lim⁡x→2(2x2−x−13x2−x−2)=\lim_{x\rightarrow2}\left(\frac{2x^2-x-1}{3x^2-x-2}\right)=      ....

a)

23\frac{2}{3}  

b)

34\frac{3}{4}  

c)

58\frac{5}{8}  

d)

85\frac{8}{5}  

e)

25\frac{2}{5}  

113.

What is the limits of the function when x approching a?

a)

Undefined

b)

2

c)

Does not exist

d)

3

114.
a)
0/0
b)
DNE
c)
-1/4
d)
1/4
115.



(a)  

116.
a)
13
b)
7
c)
6
d)
-3
117.
a)
9
b)
-1
c)
1/4
d)
0
118.
a)
2
b)
-3/4
c)
-1/3
d)
1/4
119.

What is the limit?

a)

2

b)

-2

c)

1/2

d)

-1/2

120.
a)
2
b)
0
c)
Does not exist
d)
4
121.
What is the limit?
a)
3
b)
-3
c)

1/3

d)

-1/3

e)

0

122.

Let f be the function defined above where c is a constant. For what value of c, if any is f continuous at x=c ?

a)

6

b)

8

c)

10

d)

There is no such value c

123.

lim⁡x→∞ 3x2−5x+82x−7\lim_{x\rightarrow\infty}\ \frac{3x^2-5x+8}{2x-7}  

a)

0

b)

∞\infty  

c)

3/2

d)

−∞-\infty  

124.

Find the following limit Analytically

a)

A

b)

B

c)

C

d)

D

125.

Which of the following limits can be found by direct substitution?

(check all that apply)

a)

lim⁡x→5(4x+9)\lim_{x\rightarrow5}\left(4x+9\right)

b)

lim⁡x→12x2−144x−12\lim_{x\rightarrow12}\frac{x^2-144}{x-12}

c)

lim⁡x→π3cos⁡(x)\lim_{x\rightarrow\frac{\pi}{3}}\cos\left(x\right)

d)

lim⁡x→7x+18−5x−7\lim_{x\rightarrow7}\frac{\sqrt{x+18}-5}{x-7}

126.

The table above gives values of a function ff at selected values of x.x. Which of the following conclusions is supported by the data in the table?

a)

lim⁡x→11f(x)=32\lim_{x\rightarrow11}f\left(x\right)=32

b)

lim⁡x→11f(x)=∞\lim_{x\rightarrow11}f\left(x\right)=\infty

c)

lim⁡x→32f(x) =11\lim_{x\rightarrow32}f\left(x\right)\ =11

d)

lim⁡x→32f(x)=∞\lim_{x\rightarrow32}f\left(x\right)=\infty

127.

The table above gives values of a function ff at selected values of x.x. Which of the following conclusions is supported by the data in the table?

a)

lim⁡x→2f(x)=−1\lim_{x\rightarrow2}f\left(x\right)=-1

b)

lim⁡x→2f(x)=6\lim_{x\rightarrow2}f\left(x\right)=6

c)

lim⁡x→2−f(x) =−1\lim_{x\rightarrow2^-}f\left(x\right)\ =-1 and lim⁡x→2+f(x)=6\lim_{x\rightarrow2^+}f\left(x\right)=6

d)

lim⁡x→2−f(x)=6\lim_{x\rightarrow2^-}f\left(x\right)=6 and lim⁡x→2+f(x)=−1\lim_{x\rightarrow2^+}f\left(x\right)=-1

128.

Using the table to find

lim⁡x→4f(x)\lim_{x\rightarrow4}f\left(x\right)  

a)

-1

b)

0

c)

1

d)

DNE

129.

Find the value of b for which g(x) is continuous at x=3.

(a)  

130.
a)
0
b)
-1
c)
+∞
d)
-∞

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