Free Printable Limits Review

1.

a)

-1/4

b)

8

c)

DNE

d)

∞

2.

a)

∞

b)

DNE

c)

3

d)

1

3.

$\lim_{x\rightarrow-1^-}f\left(x\right)=$

a)

3

b)

1

c)

Does Not Exist

d)

-1

4.

$\lim_{x\rightarrow-1^+}f\left(x\right)=$

a)

3

b)

1

c)

Does Not Exist

d)

-1

5.

$\lim_{x\rightarrow-1}f\left(x\right)=$

a)

3

b)

1

c)

Does Not Exist

d)

-1

6.

$\lim_{x\rightarrow1}f\left(x\right)=$

a)

-5

b)

1

c)

Does Not Exist

d)

-2

7.

$\lim_{x\rightarrow-2^+}f\left(x\right)=$

a)

4

b)

3

c)

Does Not Exist

d)

1

8.

$\lim_{x\rightarrow-2^-}f\left(x\right)=$

a)

4

b)

3

c)

Does Not Exist

d)

1

9.

$\lim_{x\rightarrow-3}f\left(x\right)=$

a)

0

b)

1

c)

Does Not Exist

d)

-1

10.

$\lim_{x\rightarrow0}f\left(x\right)=$

a)

2

b)

1

c)

Does Not Exist

d)

0

11.

Where is the graph discontinuous?

a)

x = 0 only

b)

x = 3 only

c)

x = 0 and x = 3

d)

The graph is always continuous.

12.

Where are there removable discontinuities?

a)

x = 0 only

b)

x = 3 only

c)

x = 0 and x = 3

d)

There are no removable discontinuities.

13.

Where is the graph discontinuous?

a)

x = -2 and x = 1 only

b)

x = -2 only

c)

x = -3, -2 and 1 only

d)

x = 1 only

14.

Which discontinuities are removable?

a)

x = -2 and x = 1 only

b)

x = -2 only

c)

x = -3, -2 and 1 only

d)

x = 1 only

15.

Find the limit as x approaches 3 from the left

a)

4

b)

3

c)

2

d)

DNE

16.

Find the limit of the function as x approaches 2⁺.

a)

1

b)

-1

c)

5

d)

DNE

17.

What is the limit of the function as x approaches -4 from the left?

a)

2

b)

-4

c)

DNE

d)

-2

18.

What is the limit of the function as x approaches 1 from the left?

a)

DNE

b)

1

c)

4

d)

-2

19.

What is the limit of the function as x approaches 1 from the right?

a)

DNE

b)

1

c)

4

d)

-2

20.

Find the limit of the function as x approaches 4 from the right.

a)

-1

b)

2

c)

-2

d)

DNE

21.

What is the limit as x approaches -1

a)

0

b)

Infinity

c)

-Infinity

d)

What are you talking about?!?!?

22.

Find the limit as x approaches 0-

a)

0

b)

∞

c)

-∞

d)

1

23.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

24.

a)

1/2

b)

0

c)

Positive Infinity

d)

Negative Infinity

25.

Find the limit as x approaches -3

a)

0

b)

1

c)

-6

d)

DNE

26.

Find the Limit

a)

0

b)

3

c)

1

d)

DNE

27.

Find the limit as x approaches -1

a)

-1

b)

1

c)

0

d)

DNE

28.

List the horizontal and vertical asymptotes of the function.

a)

x = 3

b)

x = -3

c)

y = -2

d)

y = 2

29.

Find the value of f so that f(x) is continuous at x = -1

a)

3

b)

-3

c)

1

d)

-1

30.

Find where the function is continuous

a)

(-∞,-1)(-1,2)(2,∞)

b)

(-∞,2)(2,∞)

c)

(-∞,∞)

d)

(-∞,2)(2,0)(0,∞)

31.

The function is continuous on $\left[-2,\ 3\right]$ .

a)

True

b)

False

32.

The graph is continuous at

x=4

.

a)

True

b)

False

33.

The function is continuous on $\left[-2,\ 5\right]$ .

a)

True

b)

False

34.

The function is continuous on the interval $\left(-\infty,\ \infty\right)$ .

a)

True

b)

False

35.

On the interval [-7, 7] where is the function f not continuous?

a)

-2, 2

b)

2

c)

-2

d)

nowhere

36.

Over which interval is the function continuous?

a)

[-6, -1]

b)

[-1, 1]

c)

[1, 6]

d)

None of the Above

37.

Which one of these open intervals is the function discontinuous?

a)

(-5,-4)

b)

(-4,-2)

c)

(-2,0)

d)

(0,1)

38.

A function is continuous on a number if and only if f(c) = lim f(x) as x approaches a number c.

a)

TRUE

b)

FALSE

39.

One of the conditions a function must satisfy to be continuous at x=c is "f(c) must exist"

a)

TRUE

b)

FALSE

40.

Which of the following best describes the continuity at x = 1?

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

41.

Find the value of b for which g(x) is continuous at x=3.

(a)

42.

Is the above function differentiable at x = 0? Why?

a)

No. The $\lim_{x\rightarrow0}\ x^{\frac{2}{3}}=0$ does not exist.

b)

Yes. The $\lim_{h\rightarrow0}\frac{\left(\left(x+h\right)^{\frac{2}{3}}-\left(x\right)^{\frac{2}{3}}\right)}{h}$ exists.

c)

Yes. The $\lim_{h\rightarrow0}\frac{\left(\left(x+h\right)^{\frac{2}{3}}-\left(x\right)^{\frac{2}{3}}\right)}{h}$ from the left and the right.

d)

No. The undefineddoesn't exist since the left and right hand limits are not the same.

43.

Is the above function differentiable at

x = 0? Why?

a)

Yes. The derivative would be equal to zero since there is a vertical tangent.

b)

No. The derivative would not exist at x = 0 since there is a vertical tangent.

c)

No. The derivative does not exist since $\lim_{x\rightarrow0}\ x^{\frac{1}{3}}$ does not exist.

d)

Yes since $\lim_{h\rightarrow0}\ \frac{\left(x+h\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{h}$ exists.

44.

If $f\left(x\right)$ has a derivative at x = a, then f is continuous at x = a.

a)

True

b)

False

45.

A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a...

a)

corner, cusp, horizontal tangent, discontinuity

b)

corner, cusp, vertical tangent, continuity

c)

corner, cusp, vertical tangent, discontinuity

d)

corner, curve, vertical tangent, continuity

46.

a)

I only

b)

II only

c)

I and II only

d)

I and III only

e)

I, II and III

47.

Given that $\lim_{x\rightarrow2}f\left(x\right)=7\ and\ \lim_{x\rightarrow2}\ g\left(x\right)=9,$ find $\lim_{x\rightarrow2}\frac{f\left(x\right)}{\text{g(x)}}.$

a)

-2

b)

7/9

c)

16

d)

9/7

48.

Find $\lim_{x\rightarrow0}\frac{x^2-4x+8}{x-2}$ .

a)

0

b)

4

c)

-4

d)

d.n.e.

49.

What is the $\lim_{x\rightarrow-5}\ \frac{x^2-25}{x+5}$ ?

a)

d.n.e.

b)

5

c)

10

d)

-10

50.

Consider the graph of f(x). What is the $\lim_{x\rightarrow4}\ f\left(x\right)?$

a)

2

b)

1

c)

3

d)

d.n.e.

Limits Review

Total questions: 50

Worksheet time: 57mins

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