Deck 2: Limits

Question 1

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = + 2t, [ 2, 9]

A)
B) 13

C) 11
D)

Answer 1

13

Question 2

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = 4 + 8 - 5, [ -8, -2]

A)
B) -
C) -768
D) 256

Answer 2

256

Question 3

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = , [2, 8]

A) 2
B) 7
C) -
D)

Answer 3

Question 4

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = , [4, 7]

A) 2
B) 7
C) -
D)

Question 5

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = 4 ,

A)
B) 2
C) 7
D) -

Question 6

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = -3 - t, [5, 6]

A) -2
B)
C) -
D) -34

Question 7

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = sin ( 3t),

A)
B)
C) -
D)

Question 8

Find the average velocity of an object which follows the position function s(t) over the given interval.

-s(t) = 3 + tan t,

A) 0
B)
C) -
D) -

Question 9

Use the table to find the instantaneous velocity of y at the specified value of x.

-x = 1.

A) 1
B) 0.5
C) 1.5
D) 2

Question 10

Use the table to find the instantaneous velocity of y at the specified value of x.

-x = 1.

A) 2
B) 1
C) 0.5
D) 1.5

Question 11

Use the table to find the instantaneous velocity of y at the specified value of x.

-x = 1.

A) 2
B) 6
C) 8
D) 4

Question 12

Use the table to find the instantaneous velocity of y at the specified value of x.

-x = 2.

A) 4
B) 0
C) 8
D) -8

Question 13

Use the table to find the instantaneous velocity of y at the specified value of x.

-x = 1.

A) -0.5
B) 0
C) 1
D) 0.5

Question 14

Find the slope of the curve for the given value of x.

-y = x² + 5x, x = 4

A) slope is -39
B) slope is -
C) slope is
D) slope is 13

Question 15

Find the slope of the curve for the given value of x.

-y = x² + 11x - 15, x = 1

A) slope is 13
B)slope is -
C) slope is
D) slope is -39

Question 16

Find the slope of the curve for the given value of x.

-y = - 8x, x = 1

A) slope is -3
B) slope is -5
C) slope is 1
D) slope is 3

Question 17

Find the slope of the curve for the given value of x.

-y = - 2 + 4, x = 3

A) slope is 15
B) slope is -15
C) slope is 0
D) slope is 1

Question 18

Find the slope of the curve for the given value of x.

-y = 4 - , x = -1

A) slope is -3
B) slope is -1
C) slope is 0
D) slope is 3

Question 19

Solve the problem.

-

A) I
B) III
C) II
D) none

Question 20

Solve the problem.

-

A) I
B) III
C) II
D) none

Question 21

Solve the problem.

-

A) I and II only
B) II and III only
C) I and IV only
D) III and IV only

Question 22

Solve the problem.

-What conditions, when present, are sufficient to conclude that a function f(x) has a limit as x approaches some value of a?

A) The limit of f(x) as x-a from the left exists, the limit of f(x) as x-a from the right exists, and these two limits are the same.

B) f(a) exists, the limit of f(x) as x-a from the left exists, and the limit of f(x) as x-a from the right exists.

C) The limit of f(x) as x-a from the left exists, the limit of f(x) as x-a from the right exists, and at least one of these limits is the same as f(a).

D) Either the limit of f(x) as x-a from the left exists or the limit of f(x) as x-a from the right exists

Question 23

Use the graph to evaluate the limit.

-

A) $\infty$
B) -1
C)
D) -

Question 24

Use the graph to evaluate the limit.

-

A) 0
B) 2
C) -2
D) does not exist

Question 25

Use the graph to evaluate the limit.

-

A) -1
B) does not exist
C) 1
D) 0

Question 26

Use the graph to evaluate the limit.

-

A) 6
B) -1
C) 0
D) does not exist

Question 27

Use the graph to evaluate the limit.

-

A) -1
B) $\infty$
C) does not exist
D) 1

Question 28

Use the graph to evaluate the limit.

-

A) 1
B) $\infty$
C) does not exist
D) -1

Question 29

Use the graph to evaluate the limit.

-

A) 0
B) does not exist
C) 2
D) -2

Question 30

Use the graph to evaluate the limit.

-

A) 1
B) does not exist
C) -2
D) 0

Question 31

Use the graph to evaluate the limit.

-

A) -2
B) does not exist
C) 2
D) -1

Question 32

Use the graph to evaluate the limit.

-

A) -2; -7
B) -5; -2
C) -7; -5
D) -7; -2

Question 33

Use the table of values of f to estimate the limit.

-Let f(x) = x² + 8x - 2, find f(x).

A)
B) 11ee9522_33a8_2bd9_bdb6_ab0544314364_TB9662_11
C)
D)

Question 34

Use the table of values of f to estimate the limit.

-Let f(x) = , find f(x).

A)
B)
C)
D)

Question 35

Use the table of values of f to estimate the limit.

-Let f(x) = x² - 5, find f(x).

A)
B)
C)
D)

Question 36

Use the table of values of f to estimate the limit.

-Let f(x) = , find f(x).

A)
B)
C)
D)

Question 37

Use the table of values of f to estimate the limit.

-Let f(x) = , find f(x).

A)
B)
C)
D)

Question 38

Use the table of values of f to estimate the limit.

-Let f(x) = , find f(x).

_

A)limit = 4
B) limit does not exist
C) limit = 3.5
D) limit = 0

Question 39

Use the table of values of f to estimate the limit.

-Let f( $\theta$ ) = , find f( $\theta$ ).

A) limit = 5
B) limit = 8.7758256
C) limit = 0
D) limit does not exist

Question 40

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response.

-It can be shown that the inequalities hold for all values of x close to zero. What, if anything, does this tell you about Explain.

Question 41

Choose the one alternative that best completes the statement or answers the question.

-Write the formal notation for the principle "the limit of a quotient is the quotient of the limits" and include a statement of any restrictions on the principle.

A)

B)
C)

D)

Question 42

Choose the one alternative that best completes the statement or answers the question.

-Provide a short sentence that summarizes the general limit principle given by the formal notation

A) The limit of a sum or a difference is the sum or the difference of the limits.
B) The sum or the difference of two functions is the sum of two limits.
C) The sum or the difference of two functions is continuous.
D) The limit of a sum or a difference is the sum or the difference of the functions.

Question 43

Choose the one alternative that best completes the statement or answers the question.

-The statement "the limit of a constant times a function is the constant times the limit" follows from a combination of two fundamental limit principles. What are they?

A) The limit of a constant is the constant, and the limit of a product is the product of the limits.
B) function is a constant times a limit, and the limit of a constant is the constant.
C) The limit of a product is the product of the limits, and a constant is continuous.
D) The limit of a product is the product of the limits, and the limit of a quotient is the quotient of the limits.

Question 44

Find the limit.

-

A)
B) 5
C)
D) 17

Question 45

Find the limit.

- ( 7x-4)

A) 10
B) -10
C) 18
D) -18

Question 46

Find the limit.

- (10-4x)

A) -10
B) 10
C) 30
D) -30

Question 47

Give an appropriate answer.

-

A) -9
B) 5
C) 3
D) -3

Question 48

Give an appropriate answer.

-

A) 56
B) -8
C)-15
D) -9

Question 49

Give an appropriate answer.

-

A) -3
B) -10
C) -
D) -

Question 50

Give an appropriate answer.

-

A) -1
B) 16
C) 4
D) 2.0000

Question 51

Give an appropriate answer.

-

A) -2
B) 4
C) 34
D) 8

Question 52

Give an appropriate answer.

-

A) 5
B) 4
C) 10
D) 1024

Question 53

Give an appropriate answer.

-

A) -
B) -
C) -
D) -8

Question 54

Find the limit.

-

A) 0
B) 15
C) 29
D) does not exist

Question 55

Find the limit.

-

A) 41
B) -167
C) -7
D) -103

Question 56

Find the limit.

-

A) does not exist
B) 0
C) 1
D) -

Question 57

Find the limit.

-

A) 0
B) Does not exist
C) -4
D) 4

Question 58

Find the limit.

-

A) -
B) -
C) 0
D) Does not exist

Question 59

Find the limit.

-

A) 128
B) -1024
C) 32
D) -256

Question 60

Find the limit.

-

A) 144
B) 12
C) does not exist
D) ±12

Question 61

Find the limit.

-

A) -136
B) 2
C) 136
D) -2

Question 62

Find the limit.

-

A) Does not exist
B) 1/2
C) 1
D) 2

Question 63

Find the limit.

-

A) 1/4
B) 1/2
C) 0
D) Does not exist

Question 64

Determine the limit by sketching an appropriate graph.

- f(x), where f(x)=

A) -20
B) -4
C) 21
D) -3

Question 65

Determine the limit by sketching an appropriate graph.

- f(x), where f(x) =

A) -3
B) 11
C) -4
D) -30

Question 66

Determine the limit by sketching an appropriate graph.

- f(x), where f(x) =

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

Question 67

Determine the limit by sketching an appropriate graph.

-

A) Does not exist
B) 1
C) 0
D) 4

Question 68

Determine the limit by sketching an appropriate graph.

-

A) -1
B) -0
C) 7
D) Does not exist

Question 69

Find the limit, if it exists.

-

A) 0
B) 5
C) Does not exist
D) -1

Question 70

Find the limit, if it exists.

-

A) 2
B) 0
C) Does not exist
D) 4

Question 71

Find the limit, if it exists.

-

A) Does not exist
B) 18
C) 1
D) 9

Question 72

Find the limit, if it exists.

-

A) Does not exist
B) -3
C) 11
D) 154

Question 73

Find the limit, if it exists.

-

A) 8
B) 4
C) 0
D) Does not exist

Question 74

Find the limit, if it exists.

-

A)
B) -
C) Does not exist
D) 0

Question 75

Find the limit, if it exists.

-

A) -
B) Does not exist
C) 0
D) -

Question 76

Find the limit, if it exists.

-

A)
B) Does not exist
C)
D) -

Question 77

Find the limit, if it exists.

-

A)3x² + 3xh + h²
B) Does not exist
C) 0
D) 3x²

Question 78

Find the limit, if it exists.

-

A) -1
B) Does not exist
C) 0
D) 1

Question 79

Provide an appropriate response.

-

A) 1
B) 0.0007
C) 0
D) does not exist

Question 80

Provide an appropriate response.

-

A) 0.0007
B) 1
C) does not exist
D) 0