Deck 2: Limits and Continuity

Question 1

For the function graphed below, identify or state that the limit does not exist.

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

Answer 1

C

Question 2

For the function graphed below, identify or state that the limit does not exist.

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

Answer 2

A

Question 3

Estimate the slope of at .

A)
B)
C)
D)

Answer 3

D

Question 4

Complete the tables appropriately and use the numerical evidence to conjecture the value of .

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

Question 5

For the function graphed below, identify or state that the limit does not exist.

A) 1
B) 2
C) 3
D) does not exist

Question 6

For the function graphed below, identify or state that the limit does not exist.

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

Question 7

Estimate the slope of at .

A) 6
B) 3
C) 18
D) 9

Question 8

Estimate the slope of at .

A)
B)
C)
D)

Question 9

Estimate the length of the curve on the interval using four line segments. Round the answer to 3 decimal places.

A) 16.492
B) 8.000
C) 16.638
D) 16.000

Question 10

Complete the tables appropriately and use the numerical evidence to conjecture the value of .

A) 0
B) 5
C) -20
D) 12

Question 11

For the function graphed below, identify or state that the limit does not exist.

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

Question 12

Estimate the length of the curve on the interval using three line segments. Round the answer to 3 decimal places.

A) 3.464
B) 3.518
C) 1.732
D) 0.577

Question 13

For the function graphed below, identify or state that the limit does not exist.

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

Question 14

Estimate the slope of at .

A)
B)
C)
D)

Question 15

For the function graphed below, identify or state that the limit does not exist.

A) 0
B) 1
C) 3
D) does not exist

Question 16

Sketch the graph of . What is ?

A)
B)
C)
D) does not exist

Question 17

Estimate the slope of at .

A) -2.00
B) 0.00
C) 1.00
D) 1.41

Question 18

Estimate the slope of at .

A)
B)
C)
D)

Question 19

For the function graphed below, identify or state that the limit does not exist.

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

Question 20

Sketch the graph of . What is ?

A)
B) 0
C) 5
D) does not exist

Question 21

Find the limit or explain why it does not exist.

A)
B)
C)
D) The limit does not exist; the function is not defined for .

Question 22

Use graphical and numerical evidence to determine if exists. If so, state the limit.

A) the limit exists and is at
B) the limit exists and is 0 at
C) does not exist; the right and left limits at are different
D) does not exist; the function is increasing without bound at

Question 23

Use graphical and numerical evidence to determine if exists. If so, state the limit.

A) The limit exists and is at .
B) The limit exists and is at .
C) The limit does not exist; the function is increasing without bound from the left and decreasing without bound from the right at .
D) The limit does not exist; the function is decreasing without bound from the left and decreasing without bound from the right at .

Question 24

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 25

Find the limit or explain why it does not exist.

A)
B)
C)
D) The limit does not exist; the function is not defined for .

Question 26

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 27

Evaluate the limit, if it exists.

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

Question 28

Use graphical and numerical evidence to estimate the limit.

A)
B) 0
C)
D)

Question 29

Sketch the graph of a function with the given properties.

Question 30

Sketch the graph of a function with the given properties.

Question 31

Evaluate the limit, if it exists. Assume that

A) 0
B) 10
C)
D) The limit does not exist.

Question 32

Use graphical and numerical evidence to determine if exists. If so, state the limit.

A) The limit exists and is at .
B) The limit exists and is at .
C) The limit does not exist; the function is increasing without bound at .
D) The limit does not exist; the function is decreasing without bound at .

Question 33

Use graphical and numerical evidence to determine if exists. If so, state the limit.

A) The limit exists and is at .
B) The limit exists and is at .
C) The limit does not exist; the function is increasing without bound from the right at and is undefined for .
D) The limit does not exist; the function is decreasing without bound from the right at and is undefined for .

Question 34

Evaluate the limit, if it exists.

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

Question 35

Use graphical and numerical evidence to estimate the limit.

A)
B)
C)
D)

Question 36

Use graphical and numerical evidence to estimate the limit.

A) 0
B)
C)
D)

Question 37

Evaluate the limit, if it exists.

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

Question 38

Find the limit or explain why it does not exist.

A)
B)
C) The limit does not exist; the function increases without bound as x approaches 6 from the right.
D) The limit does not exist; the function is not defined for .

Question 39

A ski rental shop charges $6.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $48.00 for all day. If equals the total charge for the ski equipment for t hours, determine the limit , if it exists.

A) $15.00
B) $12.00
C) $18.00
D) The limit does not exist.

Question 40

Evaluate the limit, if it exists.

A)
B)
C)
D)

Question 41

Complete the table appropriately and use the numerical evidence to conjecture the value of .

A) 0
B) 1
C) 3.5
D)

Question 42

For the position function f(t) (feet) find the instantaneous velocity at time seconds.

A) feet per second
B) feet per second
C) feet per second
D) feet per second

Question 43

Evaluate the limit, if it exists.

A) 0
B) 8
C) 9
D) The limit does not exist.

Question 44

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 45

Given , and , find .

A)
B)
C)
D) The limit does not exist.

Question 46

Find all discontinuities. For each discontinuity that is removable, define a new function that removes the discontinuity.

Question 47

Find all discontinuities.

A) discontinuous at
B) discontinuous at
C) discontinuous at
D) continuous for all x

Question 48

Given and , find .

A)
B)
C)
D) The limit does not exist.

Question 49

Find all discontinuities.

A) discontinuous at
B) discontinuous at
C) discontinuous at
D) continuous for all x

Question 50

Given and , find .

A)
B)
C)
D)

Question 51

Evaluate where .

A)
B)
C)
D) does not exist

Question 52

Find all discontinuities.

A) discontinuous at
B) discontinuous at
C) discontinuous at
D) continuous for all x

Question 53

Given that find the limit or explain why it does not exist.

A)
B)
C)
D) The limit does not exist; the function is not defined at .

Question 54

Evaluate where .

A)
B)
C)
D) does not exist

Question 55

Determine where is continuous.

A)
B)
C)
D)

Question 56

Evaluate the limit, if it exists. Assume that

A) 0
B)
C)
D) The limit does not exist.

Question 57

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 58

Suppose that a state's tax code states that tax liability is % on the first of taxable earnings and % on the remainder. Find the constants a and b in the tax function T(x) such that and exists.

A) and
B) and
C) and
D) and

Question 59

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 60

For the position function f(t) (feet) find the instantaneous velocity at time seconds.

A) feet per second
B) feet per second
C) feet per second
D) feet per second

Question 61

Determine if f is continuous at from the right.

A) but is continuous from the right
B) so is continuous from the right
C) so is not continuous from the right
D) but is not continuous from the right

Question 62

Determine the intervals where f is continuous.

A)
B)
C)
D)

Question 63

Determine the values of a and b that make f(x) continuous. Use .

A)
B)
C)
D) No values of a and b will make f(x) continuous.

Question 64

Suppose that a state's tax code states that tax liability is % on the first of taxable earnings and % on the remainder. Find the constants a and b in the tax function T(x) that make the function T(x) continuous.

A) and
B) and
C) and
D) and

Question 65

Determine the limit. Answer with a number, , or that the limit does not exist.

A)
B)
C) 0
D) 16
E) The limit does not exist.

Question 66

Determine the intervals where f is continuous.

A)
B)
C)
D)

Question 67

Determine if f is continuous at from the right.

A) , but is continuous from the right
B) , so is continuous from the right
C) , so is not continuous from the right
D) , but is not continuous from the right

Question 68

Explain why the function fails to be continuous at by indicating which of the conditions in the definition of continuity are not met.

A) exists but does not exist
B) exists but does not exist
C) neither nor exist
D) exists and exists but

Question 69

Determine the values of a and b that make f(x) continuous.

A)
B)
C)
D) No values of a and b will make f(x) continuous.

Question 70

Use the graph to identify all discontinuities f.

Question 71

Determine the intervals where f is continuous.

A)
B)
C)
D)

Question 72

Use the graph to identify all discontinuities of f.

Question 73

Determine the intervals on which is continuous.

A)
B)
C)
D)

Question 74

Use the Intermediate Value Theorem to determine if f has a zero in the interval [3,8].

Question 75

Use the graph to identify all discontinuities of f.

Question 76

Use the graph to identify all discontinuities of f.

Question 77

Determine the intervals on which is continuous.

A)
B)
C)
D)

Question 78

Determine the intervals where f is continuous.

A)
B)
C)
D)

Question 79

Use the Intermediate Value Theorem to determine if f has a zero in the interval [3, 9].

Question 80

Find all discontinuities.

A) discontinuous at
B) discontinuous at
C) discontinuous at
D) continuous for all x