Deck 2: Limits and Continuity

Question 1

Estimate the slope of at .

A)
B)
C)
D)

Answer 1

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

Question 3

Estimate the slope of at .

A)
B)
C)
D)

Answer 3

Question 4

Estimate the slope of at .

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

Question 5

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 6

Complete the tables appropriately and use the numerical evidence to conjecture the value of . x 2.9
2)99
2)999
2)9999
X 3.1
3)01
3)001
3)0001

A) 0
B) 3
C) -3
D) -81

Question 7

Estimate the slope of at .

A) 6
B) 28
C) 16
D) 56

Question 8

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

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

Question 9

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

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

Question 10

Use graphical and numerical evidence to estimate the limit.

A) 0
B)
C)
D)

Question 11

Sketch the graph of . What is ?

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

Question 12

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 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

Use graphical and numerical evidence to estimate the limit.

A)
B)
C)
D)

Question 15

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

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

Question 16

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

A) 3.552
B) 3.604
C) 1.902
D) 0.634

Question 17

Complete the tables appropriately and use the numerical evidence to conjecture the value of . x 1.9
1)99
1)999
1)9999
X 2.1
2)01
2)001
2)0001

A) 0
B) 5
C) -10
D) 2

Question 18

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

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

Question 19

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 20

Sketch the graph of . What is ?

A)
B)
C)
D) does not exist

Question 21

Evaluate the limit, if it exists.

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

Question 22

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 23

Evaluate the indicated limit, if it exists.

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

Question 24

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 25

Sketch the graph of a function with the given properties.

Question 26

Evaluate the limit, if it exists. Assume that

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

Question 27

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 28

A ski rental shop charges $7.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $56.00 for all day. If equals the total charge for the ski equipment for t hours, determine the limit , if it exists.

A) $45.50
B) $42.00
C) $49.00
D) The limit does not exist.

Question 29

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 30

Evaluate where .

A)
B)
C)
D) does not exist

Question 31

Sketch the graph of a function with the given properties.

Question 32

Use graphical and numerical evidence to estimate the limit.

A)
B) 0
C)
D)

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 at .
D) The limit does not exist; the function is decreasing without bound at .

Question 34

Evaluate the limit, if it exists.

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

Question 35

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 36

Evaluate the limit, if it exists.

A)
B)
C)
D)

Question 37

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 5 from the right.
D) The limit does not exist; the function is not defined for .

Question 38

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 39

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 40

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 41

Find all discontinuities.

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

Question 42

Find all discontinuities.

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

Question 43

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 44

Find all discontinuities.

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

Question 45

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 46

Evaluate the limit, if it exists.

A)
B)
C)
D) does not exist

Question 47

Determine the intervals where f is continuous.

A)
B)
C)
D)

Question 48

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 49

Determine the intervals where f is continuous.

A)
B)
C)
D)

Question 50

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 51

Given , and , find .

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

Question 52

Determine the intervals where f is continuous.

A)
B)
C)
D)

Question 53

Find all discontinuities.

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

Question 54

Evaluate where .

A)
B)
C)
D) does not exist

Question 55

Given and , find .

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

Question 56

Determine where f is continuous.

A) x ≠ 0
B) x > 0
C)
D) continuous on all reals

Question 57

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

Question 58

Evaluate the limit, if it exists. Assume that

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

Question 59

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 60

Given and , find .

A)
B)
C)
D)

Question 61

Use the graph to identify all discontinuities of f.

Question 62

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 63

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

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

Question 64

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

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

Question 65

Use the graph to identify all discontinuities of f.

Question 66

Use the graph to identify all discontinuities of f.

Question 67

Use the graph to identify all discontinuities f.

Question 68

Use the Intermediate Value Theorem to determine if f has a zero in the interval [2, 7].

Question 69

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

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

Question 70

Determine the limit (answer as appropriate, with a number, or does not exist).

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

Question 71

Determine the limit (answer as appropriate, with a number, or does not exist).

A)
B)
C)
D) does not exist

Question 72

Use the Intermediate Value Theorem to determine if f has a zero in the interval [1,7].

Question 73

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

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

Question 74

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

A)
B)
C) 25
D) The limit does not exist.

Question 75

Determine the limit (answer as appropriate, with a number, or does not exist).

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

Question 76

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 77

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 78

Determine the limit (answer as appropriate, with a number, or does not exist).

A) 3
B)
C)
D)
E) does not exist

Question 79

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 80

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

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