Free Printable Unit 1: Limits and Continiutiy

1.

a)

0

b)

2

c)

3

d)

4

2.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

3.

Find the limit as x approaches 3 from the left

a)

4

b)

3

c)

2

d)

DNE

4.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

5.

4

a)

2

b)

-2

c)

1/2

d)

-1/2

6.

a)

-3

b)

1

c)

2

d)

infinity

7.

a)

3

b)

1

c)

infinity

d)

negative infinity

8.

Find $\lim_{x\rightarrow2^-\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

9.

Find $\lim_{x\rightarrow2^+\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

10.

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

a)

-1

b)

5

c)

0

d)

DNE

11.

Find $f\left(2\right)$

a)

-1

b)

5

c)

0

d)

DNE

12.

Find $\lim_{x\rightarrow-1^-\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

13.

Find $\lim_{x\rightarrow-1^+\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

14.

Find $\lim_{x\rightarrow-1\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

15.

Find $f\left(-1\right)$

a)

4

b)

0

c)

-1

d)

DNE

16.

Find $\lim_{x\rightarrow-4^-\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

17.

Find $\lim_{x\rightarrow-4^+\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

18.

Find $\lim_{x\rightarrow-4\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

19.

Find $f\left(-4\right)$

a)

-2

b)

3

c)

-4

d)

DNE

20.

Find $f\left(4\right)$

a)

2

b)

4

c)

-4

d)

DNE

21.

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

a)

2

b)

0

c)

-4

d)

DNE

22.

Find $\lim_{x\rightarrow4^+\ }f\left(x\right)$

a)

-2

b)

2

c)

-4

d)

DNE

23.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , and $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\sqrt{3h\left(x\right)-2g\left(x\right)}$ .

a)

16

b)

4

c)

8

d)

12

24.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[f\left(x\right)\cdot5g\left(x\right)\right]$

a)

-30

b)

-40

c)

60

d)

-80

25.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[7-g\left(x\right)\right]^2$

a)

81

b)

25

c)

9

d)

45

26.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left(\frac{2f\left(x\right)+3h\left(x\right)}{h\left(x\right)-g\left(x\right)}\right)$

a)

3

b)

2

c)

1

d)

0

27.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[h\left(x\right)\cdot\left(f\left(x\right)+6\right)\right]$

a)

36

b)

16

c)

-18

d)

-20

28.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[\frac{f\left(x\right)^{2\ }}{4-g\left(x\right)}\right]$

a)

3/2

b)

8/3

c)

2/3

d)

9/2

29.

Use the graph above to solve: $\lim_{x\rightarrow-1}g\left(f\left(x\right)\right)$

a)

-7

b)

-2

c)

-6

d)

DNE

30.

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

a)

-7

b)

-2

c)

-6

d)

DNE

31.

$\lim_{x\ \rightarrow\ 12}\left(3\ x-7\right)=L$

Submit $L$

(a)

32.

$\lim_{x\ \rightarrow\ 19}\left(2\ x^{\ 2}-36\ x-5\right)=L$

Submit $L$

(a)

33.

$\lim_{x\ \rightarrow\ -\ 6}\left(3\ x^{\ 3}+19\ x^{\ 2}+4\ x-20\right)=L$

Submit $L$

(a)

34.

$\lim_{x\ \rightarrow\ 8}\left(\ \frac{x^{\ 3}+512}{x+8}\ \right)=L$

Submit $L$

(a)

35.

Which of the following limits cannot be found using direct substitution?

( Check all that apply )

a)

$\lim_{x\ \rightarrow\ 9}\ \left(\ 2\ x^{\ 3}-15\ x^{\ 2\ }-28\ x\ +16\ \right)$

b)

$\lim_{x\rightarrow\ 17}\ \left(\frac{x^{\ 2}-289}{x-17}\right)$

c)

$\lim_{x\ \rightarrow\ 5}\ \left(\ \frac{x\ ^2-4\ x-45}{x^{\ 2}+3\ x-10}\ \right)$

d)

$\lim_{x\ \rightarrow\ 4}\ \left(\ \frac{x\ ^2+3\ x-28}{x^{\ 2}-7\ x+12}\ \right)$

e)

$\lim_{x\ \rightarrow\ 7}\ \sqrt{5\ x+1}$

36.

Polynomial function $P\left(x\right)$

$\lim_{x\ \rightarrow\ c}\ P\left(x\right)=P\left(c\right)$

a)

Always

b)

Sometimes

c)

Never

37.

$\lim_{x\ \rightarrow\ 26}\sqrt{13\ x-14}=L$

Submit $L$

(a)

38.

$\lim_{x\ \rightarrow\ \frac{\pi}{6}}\cos\left(x\right)=\frac{\sqrt{A}}{B}$

Submit $A,B$

(a)

39.

Rational function $R\left(x\right)$

$\lim_{x\ \rightarrow\ c}\ R\left(x\right)=R\left(c\right)$

a)

Always

b)

Sometimes

c)

Never

40.

Which of the following limits cannot be found using direct substitution?

( Check all that apply )

a)

$\lim_{x\ \rightarrow\ 5}\ \left(\ \frac{\frac{1}{x+4}-\frac{1}{9}}{x-5}\ \right)$

b)

$\lim_{x\rightarrow\ 6}\ \left(\frac{x^{\ 3}+216}{x+6}\right)$

c)

$\lim_{x\ \rightarrow\ 11}\ \left(\ \frac{\sqrt{x+12}-\sqrt{23}}{x-11}\ \right)$

d)

$\lim_{x\ \rightarrow\ 4}\ \left(\ \frac{x\ ^5-1024}{x-4}\ \right)$

e)

$\lim_{x\ \rightarrow\ 33}\ \left(\ \frac{\sqrt{x-8}-41}{x-20}\ \right)$

41.

$\lim_{x\rightarrow-3}\left(2x^2+x-5\right)=$

If the limit does not exist, write "DNE."

(a)

42.

$\lim_{x\rightarrow5}\sqrt{3x-11}=$

If the limit does not exist, write "DNE."

(a)

43.

$\lim_{x\rightarrow0}\left(-5\right)=$

If the limit does not exist, write "DNE."

(a)

44.

$\lim_{x\rightarrow-1}\ \frac{x^2-3x+9}{x}=$

If the limit does not exist, write "DNE."

(a)

45.

$\lim_{x\rightarrow2}\ \frac{x^2+3x}{x-2}=$
If the limit does not exist, write "DNE."

(a)

46.

$\lim_{x\rightarrow-3}\ \frac{2x^2+7x+3}{x+3}=$
If the limit does not exist, write "DNE."

(a)

47.

$\lim_{x\rightarrow7}\ \frac{-x^2+13x-42}{x-7}=$

If the limit does not exist, write "DNE."

(a)

48.

$\lim_{x\rightarrow0}\ \frac{\sin\left(4x\right)}{3x}=$

If the limit does not exist, write "DNE."

(a)

49.

$\lim_{x\rightarrow0}\ \frac{1-\cos\left(4x\right)}{2x}=$

If the limit does not exist, write "DNE."

(a)

50.

$\lim_{x\rightarrow0}\ \frac{\sin^2\left(5x\right)}{4x^2}=$

If the limit does not exist, write "DNE."

(a)

51.

If $f$ is the function defined by $f\left(x\right)=\frac{x^2-9}{x^2+2x-15},$ then $\lim_{x\rightarrow3}f\left(x\right)$ is

a)

$0$

b)

$\frac{9}{15}$

c)

$\frac{3}{4}$

d)

nonexistent

52.

$\lim_{x\rightarrow3}\ \frac{x-3}{x^3-9x}$ is

a)

$0$

b)

$\frac{1}{18}$

c)

$1$

d)

nonexistent

53.

It is known that $\lim_{x\rightarrow0}\ \frac{\sin\left(2x\right)}{2x}=1.$ What is $\lim_{x\rightarrow0}\ \frac{\cos\left(5x\right)}{8x\cot\left(2x\right)}?$

a)

$0$

b)

$\frac{1}{8}$

c)

$\frac{1}{4}$

d)

nonexistent

54.

It is known that $\lim_{x\rightarrow0}\ \frac{\sin\left(2x\right)}{2x}=1.$ What is $\lim_{x\rightarrow0}\ \frac{\tan\left(2x\right)}{6x\sec\left(3x\right)}?$

a)

$0$

b)

$\frac{1}{6}$

c)

$\frac{1}{3}$

d)

nonexistent

55.

If $f$ is the function defined by $f\left(x\right)=\frac{x^2-4}{x^2+x-6},$ then $\lim_{x\rightarrow2}f\left(x\right)$ is

a)

$0$

b)

$\frac{2}{3}$

c)

$\frac{4}{5}$

d)

nonexistent

56.

$\lim_{x\rightarrow-4}\ \ \ 17\ =\ ....$

a)

17

b)

$-68$

c)

$-4$

d)

$-17$

e)

0

57.

$\lim_{x\rightarrow-5}\ \ \ \frac{x+5}{2}\ =\ ....$

a)

0

b)

5

c)

$\infty$

d)

$\frac{5}{2}$

e)

$\frac{2}{5}$

58.

$f\left(x\right)\ =\ \frac{4x-5}{5x-1}$

What law is appropriate to use to get the limit of the function above?

a)

Quotient law

b)

Sum law

c)

Root law

d)

Identity function law

59.

$\lim_{x\rightarrow y}\ 5\left(4x^2\right)$

What law is appropriate to use to get the limit of the function above?

a)

Constant Multiple Law

b)

Sum law

c)

Root law

d)

Identity function law

60.

Find the $\lim_{t\rightarrow2}\ t^2-5t$

a)

-6

b)

-10

c)

8

d)

14

61.

$\lim_{z\rightarrow-2}\ z^3+2$

What law is appropriate to use to get the limit of the function above?

a)

Constant Multiple Law

b)

Sum law

c)

Root law

d)

Identity function law

62.

Find the $\lim_{x\rightarrow2}\ f\left(x\right)\times g\left(x\right)$ if $f\left(x\right)\ =\ x^2+3;\ g\left(x\right)=\ 2$

a)

2

b)

14

c)

11

d)

12

63.

$\lim_{x\rightarrow3}\ \left(3x\right)^4$

What law is appropriate to use to get the limit of the function above?

a)

Difference Law

b)

Sum law

c)

Root law

d)

Power law

64.

$\lim_{x\rightarrow3}\ \sqrt{3x+4}$

What law is appropriate to use to get the limit of the function above?

a)

Identity Law

b)

Difference Law

c)

Root law

d)

Quotient Law

65.

If $f\left(x\right)\ =\ 4x\ and\ g\left(x\right)=2x$ , find $\lim_{x\rightarrow-2}f\left(x\right)\ -\ g\left(x\right)$ .

a)

-4

b)

8

c)

16

d)

0

66.

$\lim_{x\rightarrow25}$ $\frac{\sqrt{x}-5}{x-25}$

a)

$2$

b)

$-\frac{1}{3}$

c)

$\frac{1}{10}$

d)

$\frac{8}{17}$

67.

$\lim_{x\rightarrow16}$ $\frac{x-16}{\sqrt{x}-4}$

a)

$14$

b)

$13$

c)

$1$

d)

$8$

68.

$\lim_{x\rightarrow2}$ $\frac{\sqrt{x-1}-1}{x-2}$

a)

$-\frac{1}{4}$

b)

$-\frac{9}{8}$

c)

$-\frac{7}{5}$

d)

$\frac{1}{2}$

69.

$\lim_{x\rightarrow2}$ $-\frac{x-2}{x^2-5x+6}$

a)

$-5$

b)

$-6$

c)

$1$

d)

$-3$

70.

$\lim_{x\rightarrow5}$ $\frac{x^2-4x-5}{x-5}$

a)

$-2$

b)

$5$

c)

$15$

d)

$6$

71.

$\frac{x^2-1}{x+1}$ $\lim_{x\rightarrow-1}$

a)

$-2$

b)

$-11$

c)

$0$

d)

$6$

72.

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

a)

$13$

b)

$12$

c)

$6$

d)

$-2$

73.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

74.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

75.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

76.

Identify the type of location of the discontinuity/discontinuities.

a)

Infinite at x = 4

b)

The function is continuous

c)

Removable at x = 4

d)

Jump at x = 4

77.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

78.

Where is the infinite discontinuity (Vertical Asymptote)?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

79.

Where is the removable discontinuity (hole)?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

80.

Evaluate the limit: $\lim_{x\rightarrow0}\ \frac{5x^2-20x}{x}$

a)

1/20

b)

20

c)

-20

d)

-1/20

81.

Find $\lim_{x\rightarrow2^-\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

82.

Find $\lim_{x\rightarrow2^+\ }f\left(x\right)$

a)

-1

b)

5

c)

0

d)

DNE

83.

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

a)

-1

b)

5

c)

0

d)

DNE

84.

Find $f\left(2\right)$

a)

-1

b)

5

c)

0

d)

undefined

85.

Find $\lim_{x\rightarrow-1^-\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

86.

Find $\lim_{x\rightarrow-1^+\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

87.

Find $\lim_{x\rightarrow-1\ }f\left(x\right)$

a)

4

b)

0

c)

-1

d)

DNE

88.

Find $\lim_{x\rightarrow-4^-\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

89.

Find $\lim_{x\rightarrow-4^+\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

90.

Find $\lim_{x\rightarrow-4\ }f\left(x\right)$

a)

-2

b)

3

c)

-4

d)

DNE

91.

Find $f\left(-4\right)$

a)

-2

b)

3

c)

-4

d)

undefined

92.

Find $f\left(4\right)$

a)

2

b)

4

c)

-4

d)

undefined

93.

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

a)

2

b)

0

c)

-4

d)

DNE

94.

The graph of the function, f(x) is shown in the graph. What is $\lim_{x\rightarrow-1}f\left(x\right)?$

a)

1

b)

2

c)

5

d)

dne

95.

The graph of the function, f(x) is shown in the graph. What is $\lim_{x\rightarrow2}f\left(x\right)?$

a)

1

b)

2

c)

5

d)

dne

96.

The graph of the function, f(x) is shown in the graph. What is $\lim_{x\rightarrow2+}f\left(x\right)?$

a)

1

b)

2

c)

5

d)

dne

97.

The graph of the function, f(x) is shown. What is $\lim_{x\rightarrow2+}f\left(x\right)?$

a)

1

b)

3

c)

4

d)

dne

98.

The graph of the function, f(x) is shown. What is $\lim_{x\rightarrow2-}f\left(x\right)?$

a)

1

b)

3

c)

4

d)

dne

99.

The graph of the function, f(x) is shown. What is $f\left(2\right)?$

a)

1

b)

3

c)

4

d)

dne

100.

The graph of the function, f(x) is shown above. What is $\lim_{x\rightarrow2+}f\left(x\right)?$

a)

3

b)

2

c)

1

d)

dne

e)

4

101.

The graph of the function, f(x) is shown above. What is $\lim_{x\rightarrow2-}f\left(x\right)?$

a)

3

b)

2

c)

1

d)

dne

e)

4

102.

The graph of the function, f(x) is shown above. What is $\lim_{x\rightarrow2}f\left(x\right)?$

a)

3

b)

2

c)

1

d)

dne

e)

4

103.

Give the interval of continuity for the graph provided.

a)

(-∞, 2)U(2,6]

b)

(-∞, 2]U(2,6]

c)

(-∞, 2)U[2,6]

d)

(-∞, 2)U(2,6)

104.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

105.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

106.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

107.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

108.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

109.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

110.

Determine the type(s) and location(s) of all discontinuitie(s)

a)

jump at x = 1

b)

removable and x = 1

c)

infinite at x = 1

d)

jump at x = -3

111.

a)

0

b)

2

c)

3

d)

4

112.

a)

0

b)

1

c)

2

d)

DNE

113.

Use interval notion to describe those intervals on which the function is positive.
y=-x(x+2)(x-1)

a)

(-2,0),(1,∞)

b)

(-2,0),(0,1)

c)

(-∞,-2),(0,1)

d)

(0,1),(1,∞)

114.

a)

-4

b)

-1

c)

0

d)

DNE

115.

a)

0

b)

1

c)

2

d)

DNE

116.

a)

2

b)

4

c)

32

d)

DNE

117.

Let f be a continuous function for which f(-2)=1 and f(5)=-3. The Intermediate Value Theorem guarantees that

a)

f(c)=2 for at least one c between -3 and 1

b)

f(c)=0 for at least one c between -2 and 5

c)

f(c)=0 for at least one c between -3 and 1

d)

f(c)=2 for at least one c between -2 and 5

118.

a)

I only

b)

II only

c)

I, II, III

d)

None

119.

a)

b)

f is continuous for all real numbers x

c)

d)

The domain of f ix (-∞,3)(3,∞)

120.

what type of discontinuity is represented in the graph

a)

continuous

b)

finite jump discontinuity

c)

infinite discontinuity

d)

removable discontinuity

121.

if

1.) f(a) is defined or undefined

2.) limit of f(x) as x approaches to a - is not equal to f(x) as x approaches to a+

then what kind of discontinuity is this?

a)

finite jump discontinuity

b)

infinite discontinuity

c)

removable discontinuity

122.

$f\ \left(a\right)\ =\ \lim_{x\rightarrow a}f\ \left(x\right)$ what kind of discontinuity if
f (a) is undefined
the limit exists
and

a)

continuous

b)

finite jump discontinuity

c)

infinite discontinuity

d)

removable discontinuity

123.

$\lim_{x\rightarrow0}\ \frac{\left(x+9\right)\ -\ 9}{x}$

what is the limit?

a)

1

b)

2

c)

0

d)

-1

124.

$\lim_{x\rightarrow-\infty}\left(\frac{3x^5+4x^3-15x^2+7}{8x^5-6x^4+20x\ -11}\right)$

(a)

125.

$\lim_{x\rightarrow\infty}\left(\frac{12x^3+17x-1}{13x+1}\right)$

a)

$\infty$

b)

$-\infty$

c)

$\frac{5}{3}$

d)

$0$

126.

$\lim_{x\rightarrow-\infty}\left(\frac{5x}{x^5-3}\right)$

(a)

127.

$\lim_{x\rightarrow-\infty}\left(\frac{5x^2-17}{-3x+10}\right)$

a)

$\infty$

b)

$-\infty$

c)

$\frac{5}{3}$

d)

$0$

128.

$\lim_{x\rightarrow\infty}\left(\frac{x^4-11x^2+7}{5x^4-3x^3-11x^2\ +71}\right)$

(a)

129.

$\lim_{x\rightarrow-\infty}\left(-5+\frac{4}{x^3}\right)$

(a)

130.

$\lim_{x\rightarrow-7^+}\left(\frac{5}{x+7}\right)$

a)

$\infty$

b)

$-\infty$

c)

DNE

d)

$\frac{5}{7}$

131.

$\lim_{x\rightarrow7^-}\left(\frac{x^2-9}{x^2-4x-21}\right)$

a)

$\infty$

b)

$-\infty$

c)

DNE

d)

$1$

132.

$\lim_{x\rightarrow-5}\left(\frac{x-1}{x^2+4x-5}\right)$

a)

$\infty$

b)

$-\infty$

c)

DNE

d)

$1$

133.

$\lim_{x\rightarrow-3}\left(\frac{-4}{\left(x+3\right)^2}\right)$

a)

$\infty$

b)

$-\infty$

c)

DNE

d)

$1$

134.

If a function f has a domain

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

, then it is _______________.

a)

increasing

b)

extraneous

c)

continuous

d)

undefined

135.

For the function

f\left(x\right)=\lfloor x\rfloor

, determine an interval where f is continuous.

a)

[0.5, 1.5]

b)

[-1, 1]

c)

[-2, 0]

d)

[1, 1.5]

136.

Suppose t is a continuous function containing the ordered pairs shown in the table. On which interval(s) must t attain a value of -2.5? Select all that apply.

a)

(1, 2)

b)

(2, 3)

c)

(3, 4)

d)

(4, 5)

e)

(5, 6)

137.

Suppose f is a continuous function containing the ordered pairs shown in the table. On which interval(s) must f attain a value of 5.9? Select all that apply.

a)

(-3, -2)

b)

(-2, -1)

c)

(0, 1)

d)

(1, 2)

e)

(2, 3)

138.

Suppose h is a continuous function containing the ordered pairs shown in the table. On which interval must h have a zero?

a)

(12.163, 12.164)

b)

(12.164, 12.165)

c)

(12.165, 12.166)

d)

(12.166, 12.168)

139.

Assume f(x) is continuous over the interval [-2, 3]. The function f has at least how many zeros?

a)

1

b)

2

c)

3

d)

4

140.

Determine the interval(s) for which the function is continuous. Select all that apply.

a)

(p, 0)

b)

[0, q]

c)

[q, r]

d)

(r, s)

e)

(q, s)

141.

Use the Intermediate Value Theorem to find an interval between two consecutive integers that contains a zero of the function

h\left(x\right)=2x-x^2-\ln x

a)

[-1, 0]

b)

[0, 1]

c)

[1, 2]

d)

(-1, 1)

142.

Consider the function

f\left(x\right)=\frac{1}{x-3}-5

. Can you conclude that there must be a zero between f(2) and f(3.1)?

a)

Yes, because f(2) is negative and f(3.1) is positive.

b)

No, because f(2) is negative and f(3.1) is also negative.

c)

Yes, because f(2) is positive and f(3.1) is negative.

d)

No, because there is a discontinuity at x = 3.

e)

No, because f(2) is positive and f(3.1) is also positive.

143.

A hot apple pie is left on a window sill to cool. Suppose its temperature (degrees F) after x minutes is given by

f\left(x\right)=90e^{-0.61x}+70

. Give an interval in which its temperature will first be under

100\degree F

a)

(0, 0.5)

b)

(0.5, 1)

c)

(1, 1.5)

d)

(1.5, 2)

Unit 1: Limits and Continiutiy

Total questions: 143

Worksheet time: 5hrs 16mins

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