Deck 4: Limits and Their Properties

Question 1

Determine the following limit. (Hint: Use the graph to calculate the limit.)

A)does not exist
B)2
C)4
D)8
E)0

Answer 1

8

Question 2

Let and . Find the limit.

A)
B)
C)
D)
E)

Answer 2

Question 3

Suppose that and . Find the following limit.

A)140
B)-4
C)0
D)-24
E)-10

Answer 3

-24

Question 4

Suppose that and . Find the following limit.

A)4
B)-1
C)9
D)-20
E)5

Question 5

Find the limit.

A)
B)
C)
D)
E)

Question 6

Find the limit.

A)-5
B)50
C)-50
D)5
E)20

Question 7

Let .Determine the following limit. (Hint: Use the graph to calculate the limit.)

A)4
B)1
C)3
D)9
E)does not exist.

Question 8

Determine the following limit. (Hint: Use the graph to calculate the limit.)

A)0
B)does not exist
C)4
D)-4
E)-8

Question 9

Suppose that and . Find the following limit.

A)
B)-63
C)
D)does not exist.
E)63

Question 10

Suppose that . Find the following limit.

A)-2
B)4
C)0
D)3
E)1

Question 11

Determine the following limit. (Hint: Use the graph to calculate the limit.)

A)6
B)5
C)1
D)4
E)does not exist

Question 12

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.Find the distance traveled in 14 seconds by an object traveling at a constant velocity of 12 feet per second.

A)precalculus , 336 ft
B)precalculus , 168 ft
C)calculus , 168 ft
D)calculus , 336 ft
E)calculus , 188 ft

Question 13

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.A cyclist is riding on a path whose elevation is modeled by the function where x and are measured in miles. Find the rate of change of elevation when x = 4.5.

A)calculus , 0.21
B)calculus , 0.09
C)precalculus , 0.21
D)precalculus , 0.09
E)calculus , 0.81

Question 14

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.Find the area of the shaded region bounded by the triangle with vertices (0,0), (7,8), (15,0).

A)precalculus , 60.0
B)precalculus , 120.0
C)calculus , 180.0
D)calculus , 120.0
E)precalculus , 180.0

Question 15

Let and . Find the limit.

A)-17
B)27
C)103
D)-125
E)343

Question 16

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.A cyclist is riding on a path whose elevation is modeled by the function where x and are measured in miles. Find the rate of change of elevation when x = 4.0.

A)calculus , 1.28
B)precalculus , 1.28
C)calculus , 0.16
D)precalculus , 0.16
E)precalculus , 0.41

Question 17

Let .Determine the following limit. (Hint: Use the graph to calculate the limit.)

A)2
B)0
C)4
D)6
E)does not exist

Question 18

Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.Find the distance traveled in 17 seconds by an object moving with a velocity of feet per second.

A)precalculus , 168.0772 ft
B)calculus , 169.4497 ft
C)calculus , 168.0772 ft
D)precalculus , 169.4497 ft
E)precalculus , 170.7997 ft

Question 19

Find the limit.

A)
B)0
C)
D)
E)

Question 20

Let and . Find the limits:

A)
B)
C)
D)
E)

Question 21

Find the limit (if it exists).

A)
B)1
C)0
D)
E)Limit does not exist.

Question 22

Suppose that . Find the following limit.

A)26
B)-2
C)-13
D)-13c
E)-26

Question 23

Find constants a and b such that the function is continuous on the entire real line.

A)a = 1 , b = 0
B)a = 1 , b = 3
C)a = 1 , b = -3
D)a = -1 , b = -3
E)a = -1 , b = 3

Question 24

Use the graph to determine the following limits, and discuss the continuity of the function at .(i) (ii) (iii)

A)1 , 0 , does not exist , not continuous
B)0 , 1 , does not exist , not continuous
C)0 , 1 , 0 , continuous
D)-3 , 0 , does not exist , not continuous
E)1 , -1 , does not exist , not continuous

Question 25

Find the limit (if it exists). Note that represents the greatest integer function.

A)17
B)15
C)0
D)16
E)Limit does not exist.

Question 26

Find the limit (if it exists). where

A)10
B)0
C)27
D)9
E)Limit does not exist.

Question 27

Use the graph as shown to determine the following limits, and discuss the continuity of the function at .(i) (ii) (iii)

A)4 , 4, 4, not continuous
B)2 , 2 , 2 , not continuous
C)1 , 1 , 1 , continuous
D)2 , 2 , 2 , continuous
E)1 , 1 , 1 , not continuous

Question 28

Find the limit (if it exists).

A)
B)0
C)
D)
E)Limit does not exist.

Question 29

Find the limit (if it exists).

A)
B)0
C)
D)
E)Limit does not exist.

Question 30

Find the limit (if it exists).

A)
B)
C)does not exist
D)
E)

Question 31

Find the limit (if it exists). Note that represents the greatest integer function.

A)-11
B)10
C)does not exist
D)11
E)-10

Question 32

Find the limit (if it exists):

A)-32
B)
C)
D)8
E)

Question 33

Use the graph as shown to determine the following limits, and discuss the continuity of the function at .(i) (ii) (iii)

A)2 , 2 , 2 , not continuous
B)2 , 2 , 2 , continuous
C)3 , 3 , 3 , not continuous
D)3 , 3 , 3 , continuous
E)-3 , -3 , -3 , continuous

Question 34

Find the following limit (if it exists). Write a simpler function that agrees with the given function at all but one point.

A)does not exist
B)74
C)-74
D)-80
E)80

Question 35

Discuss the continuity of the function .

A) is continuous for all real x.
B) is discontinuous at .
C) is discontinuous at .
D) is discontinuous at .
E) is continuous at .

Question 36

Find the x-values (if any) at which is not continuous.

A) is continuous for all real x.
B) is not continuous at and both the discontinuities are nonremovable.
C) is not continuous only at and has a removable discontinuity at .
D) is not continuous only at and has a removable discontinuity at .
E) is not continuous at and has a removable discontinuity at .

Question 37

Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?

A)no points of discontinuity.
B) (not removable), (removable)
C) (removable), (not removable)
D)no points of continuity.
E) (not removable), (not removable)

Question 38

Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?

A)continuous everywhere
B) , removable
C) , removable.
D) , not removable.
E)x = 0, removable

Question 39

Find the x-values (if any) at which the function is not continuous. Which of the discontinuities are removable?

A)3 and -3, not removable.
B)continuous everywhere
C)3 and -3, removable.
D)discontinuous everywhere
E)0, removable

Question 40

Find the value of c guaranteed by the Intermediate Value Theorem. .

A)3
B)2
C)5
D)7
E)6

Question 41

Find all the vertical asymptotes (if any) of the graph of the function .

A)
B)
C)
D)
E)no vertical asymptotes.

Question 42

Find all the vertical asymptotes (if any) of the graph of the function .

A)
B)
C)
D)
E)no vertical asymptotes.

Question 43

Find the limit.

A)0
B)
C)1
D)-1
E)

Question 44

Use a graphing utility to graph the function and determine the one-sided limit .

A)
B)
C)0
D)12
E)8

Question 45

Find the value of c guaranteed by the Intermediate Value Theorem. .

A)4
B)3
C)10
D)11
E)9

Question 46

Find the limit.

A)-26
B)
C)26
D)
E)13

Question 47

Find all vertical asymptotes (if any) of the function .

A)x = 4, 3, -6
B)x = 3
C)x = -4, -3
D)x = -3
E)x = 4, 3

Question 48

Find the limit.

A)
B)
C)0
D)-1
E)1

Question 49

Find the vertical asymptotes (if any) of the function .

A)x = 4
B)x = -4
C)x = 3
D)x = -3
E)x = 12

Question 50

A 25-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of where x is the distance between the base of the ladder and the house. Find the rate r when x is 20 feet.

A)
B)
C)
D)
E)

Question 51

A 35-foot ladder is leaning against a house (see figure). If the base of the ladder is pulled away from the house at a rate of 2 feet per second, the top will move down the wall at a rate of where x is the distance between the base of the ladder and the house. Find the limit of r as .

A)
B)70
C)0
D)35
E)