Deck 1: Limits and Continuity

Question 1

Find the limit.

A) 0
B) -1
C) 1
D) $\infty$
E) Does not exist

Answer 1

Does not exist

Question 2

Find .

Answer 2

Question 3

Answer true or false. The value of k that makes f continuous for is 7

Answer 3

True

Question 4

Find .

Question 5

Find the limit.

A) 1
B) 6
C) 0
D) + $\infty$
E) - $\infty$

Question 6

Find the limit.

A) 0
B)
C)
D) + $\infty$
E) - $\infty$

Question 7

Find .

Question 8

Find .

Question 9

Find the limit

A) 0
B) -1
C) 1
D) + $\infty$
E) - $\infty$

Question 10

Answer true or false. The Squeeze Theorem can be used to show utilizing and .

Question 11

Answer true or false. The value of k that makes f continuous for is 2

Question 12

Answer true or false. The Intermediate-Value Theorem can be used to show that the equation x⁵ = cos x has at least one solution on the interval [-5 $\pi$ /6, 5 $\pi$ /6].

Question 13

Find the limit.

A) 0
B)
C)
D) 1
E) + $\infty$

Question 14

Find the limit.

A) 0
B) -1
C) 1
D) + $\infty$
E) - $\infty$

Question 15

Find the limit.

A) 0
B) 1
C) -1
D) + $\infty$
E) - $\infty$

Question 16

Find the limit

A) 0
B) 1
C)
D) + $\infty$
E) - $\infty$

Question 17

Find all points of discontinuity, if any, for

A) 0
B)

C) 2 $\pi$
D)

E) None exist

Question 18

Find the limit.

A) 9
B)
C) 0
D) + $\infty$
E) - $\infty$

Question 19

Answer true or false. The fact that and that guarantees that by the Squeeze Theorem.

Question 20

Find the limit

A) 0
B) 1
C) 3
D) + $\infty$
E) - $\infty$

Question 21

Find .

Question 22

Find a value for the constant k so that will be continuous at t = 0.

Question 23

Find .

Question 24

Find .

Question 25

Find .

Question 26

Find .

Question 27

Find a value for the constant k so that will be continuous at t = 0.

Question 28

Find .

Question 29

Find .

Question 30

Find a value for the constant k so that will be continuous at t = 0.

Question 31

Find .

Question 32

Find .

Question 33

Find a value for the constant k so that will be continuous at $\theta$ = 0.

Question 34

Find .

Question 35

Find .

Question 36

Find .

Question 37

Find .

Question 38

Find a value for the constant k so that will be continuous at t = 0.

Question 39

Find a value for the constant k so that will be continuous at $\theta$ = 0.

Question 40

On the interval of [-4, 4], where is f not continuous?

A) -2
B) 0 and 2
C) -3 and 1
D) 3
E) Nowhere

Question 41

Answer true or false. The Intermediate-Value Theorem can be used to approximate the locations of all discontinuities for .

Question 42

Show that is not a continuous function.

Question 43

Answer true or false. The function is continuous everywhere.

Question 44

Answer true or false. The function has a removable discontinuity at x = 5.

Question 45

Answer true or false. f(x) = x⁴ - 2x² + 11 = 0 has at least one solution on the interval [0, 9].

Question 46

Answer true or false. f(x) = x² - 6x + 5 = 0 has at least one solution on the interval [0, 2].

Question 47

Find the x-coordinates for all points of discontinuity for .

A) 6 and 2
B) 6
C) -2 and -6
D) -2
E) 2

Question 48

Answer true or false. f(x) = tan (x⁴ - 1) has no point of discontinuity.

Question 49

Find any points of discontinuity for .

Question 50

Find the x-coordinates for all points of discontinuity for .

A) 5
B) 7
C) -5
D) 0 and 7
E) None exists.

Question 51

A point of discontinuity of is at

A)
B)
C)
D)
E)

Question 52

Find the value of k, if possible, that will make the function continuous.

A) -2
B) 6
C) -6
D) 2
E) None exists.

Question 53

Define so that it will be continuous everywhere.

Question 54

Answer true or false. f(x) = x⁵ - 5x⁴ + 9 has no point of discontinuity.

Question 55

Redefine so that it will be continuous everywhere.

Question 56

Use the fact that is a solution of x⁴ - 2 = 0 to approximate with an error of at most 0.005.

A) 1.169
B) 1.179
C) 1.189
D) 1.199
E) 1.209

Question 57

Answer true or false. f(x) = |x² - 4| has points of discontinuity at x = -2 and x = 2.

Question 58

Find the x-coordinates for all points of discontinuity for .

A) 0
B) -2 and 2
C) -2
D) 2
E) 5

Question 59

Answer true or false. If f and g are each continuous at c, may be discontinuous at c.

Question 60

Find any points of discontinuity for .

Question 61

Assign a value to the constant k which will make g continuous.

Question 62

Find the values of x (if any) at which f is not continuous. f(x) = (x + 8)⁷.

Question 63

Determine the interval for which is a continuous function.

Question 64

Show that is not continuous at x = -6 but is continuous from the right at x = -6.

Question 65

Determine if the discontinuity at x = 0 in the function is removable.

Question 66

Given , determine if h is continuous from the right at 0.

Question 67

Determine if the discontinuity at x = 9 in the function is removable.

Question 68

Prove that is continuous on [0,+ $\infty$ ).

Question 69

Find the point of discontinuity in and state whether it is removable.

Question 70

Determine if the discontinuity at x = 2 in the function is removable.

Question 71

Show that cannot be made continuous for any assigned value of the constant k.

Question 72

Given , determine if h is continuous at -6.

Question 73

Find the discontinuities in and state whether each is removable or nonremovable.

Question 74

Given , determine if g is continuous at x = .

Question 75

Assign a value to the constant k which will make f continuous.

Question 76

Show that the equation f(x) = x² + 3x - 4 has at least one solution in the interval [-5,0].

Question 77

Given , determine if h is continuous at 0.

Question 78

Show that the equation f(x) = x³ + 8x + 3 has at least one solution in the interval [-2,2].

Question 79

Assign a value to the constant k which will make g continuous.

Question 80

Given , is g continuous at x = 10.