Free Printable AP Calculus AB Quiz 1 (Part 2) Review

1.

Find the limit. Hint: Where is the horizontal asymptote?

a)

³/₇

b)

0

c)

∞

d)

-∞

2.

Find the limit. Hint: Where is the horizontal asymptote?

a)

^-2/₉

b)

0

c)

∞

d)

-∞

3.

$\lim_{x\rightarrow\infty}\ \frac{2x-3}{4x\ +1}$

a)

0

b)

DNE

c)

1/2

d)

2

4.

$\lim_{x\rightarrow\infty}\left(2x^3+3x-1\right)=$
Hint: Think of the end behavior of an odd and positive polynomial.

a)

$\infty$

b)

$-\infty$

c)

2

d)

2/3

5.

$The\ \lim_{x\rightarrow0}f\left(x\right)\$ fails to exist because...

a)

As the function approaches zero, left and right of zero do not match

b)

As the function approaches zero, the graph oscillates.

c)

As the function approaches zero, the graph increases without bound.

6.

$The\ \lim_{x\rightarrow2}f\left(x\right)\$ fails to exist because...

a)

As the function approaches two, left and right of two do not match

b)

As the function approaches two, the graph oscillates.

c)

As the function approaches two, the graph increases or decreases without bound.

7.

$The\ \lim_{x\rightarrow0}f\left(x\right)\$ fails to exist because...

a)

As the function approaches zero, left and right of zero do not match

b)

As the function approaches zero, the graph oscillates.

c)

As the function approaches zero, the graph increases without bound.

8.

$\lim_{x\rightarrow-\infty}\ \frac{\cos\ x}{x}$

a)

DNE

b)

1

c)

0

d)

$-\infty$

9.

$\lim_{x\rightarrow\infty}\ \frac{x-\cos\ x}{2x}$

a)

1/2

b)

-1/2

c)

DNE

d)

0

10.

Find the value of x where the function is discontinuous.

(a)

11.

$\lim_{x\rightarrow\infty}\ \frac{x+7}{\sqrt{4x^2+3x}}=...$

a)

$-\infty$

b)

$\infty$

c)

$\frac{1}{2}$

d)

0

e)

$-\frac{1}{2}$

12.

Determine whether $f\left(x\right)=\frac{x^2+5x-6}{x-1}$ is continuous or discontinuous at $x=1.$

a)

continuous

b)

discontinuous, removable

c)

discontinuous, jump

d)

discontinuous, essential

13.

$\lim_{x\rightarrow0}\ \frac{\sin3x}{5x}$

a)

0

b)

5/3

c)

3/5

d)

DNE

14.

$\lim_{x\rightarrow-\infty}\ 2^x$

a)

$-\infty$

b)

$+\infty$

c)

0

d)

2

15.

$\lim_{x\rightarrow\infty}\ \frac{e^{5x}}{x^5}$

a)

2/5

b)

$\infty$

c)

0

d)

e/x

16.

What is the limit of h(x) as x approaches -4?

a)

$16$

b)

$4$

c)

$-4$

d)

$DNE$

17.

Check all the boxes that contain true statements.

a)

$\lim_{x\rightarrow-2^{+\ \ }}g\left(x\right)=-3$

b)

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

c)

$\lim_{x\rightarrow0^-}\ \ g\left(x\right)=1$

d)

$\lim_{x\rightarrow0}\ \ g\left(x\right)=1$

18.

$\lim_{x\rightarrow-\infty}\ \frac{4}{3x^3}=$

a)

$0$

b)

$+\infty$

c)

$-\infty$

d)

$DNE$

19.

$\lim_{x\rightarrow+\infty}\frac{5x^4-3x^3+9}{4x^4-2x^2+x-1}=\$

a)

$0$

b)

$\frac{5}{4}$

c)

$+\infty$

d)

$DNE$

20.

What is $\lim_{x\rightarrow-\infty}5x^5+7x^4-3x^2-2x-8?$

a)

$5$

b)

$0$

c)

$-\infty$

d)

$+\infty$

21.

Evaluate

a)

-7

b)

0

c)

1

d)

DNE

22.

a)

Does Not Exist

b)

9

c)

1

d)

0

23.

Which of the following best describes the continuity at x = 5?

a)

Continuous

b)

Removable discontinuity

c)

Non-removable discontinuity

24.

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

a)

Vertical Asymptote

b)

Removable Discontinuity

25.

Find the value that will make the following continuous

a)

-3

b)

-2

c)

-1

d)

c=0

26.

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

a)

2

b)

-4

c)

DNE

d)

-2

27.

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

a)

1

b)

-1

c)

5

d)

DNE

28.

lim_x→0 sin(6x) ∕ sin(2x)

a)

1/3

b)

3

c)

1

d)

DNE

29.

Find the value that will make the following continuous

a)

-3

b)

-2

c)

-1

d)

c=0

30.

What value does m have to be in order for the limit as x approaches -4 to exist in the function g(x) = (x^2+8x+m)/(x+4)

a)

18

b)

16

c)

24

d)

-12

31.

a)

6

b)

3

c)

1/6

d)

-1/6

32.

Evaluate

a)

-7

b)

0

c)

1

d)

DNE

33.

Let f be the function defined above where c is a constant. For what value of c, if any is f continuous at x=c ?

a)

6

b)

8

c)

10

d)

There is no such value c

34.

Let f be a function that is continuous on the interval (1, 10). If f(2) = -5 , f(5) = 5 and f(9) = -5, which must be true?

I. f(x) has a least 2 zeros
II. For some c, 2 < c < 9, f(c) = 3
III. The graph of f(x) has a horizontal tangent

a)

I. only

b)

I. and II.

c)

I. , II. and III.

d)

II. and III.

35.

Which of the following best describes the continuity at x = -4?

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

36.

Does the following function is continuous at x=0?

a)

Continuous

b)

Discontinuous

37.

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

a)

1

b)

-1

c)

5

d)

DNE

38.

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

a)

2

b)

-4

c)

DNE

d)

-2

39.

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

a)

Vertical Asymptote

b)

Removable Discontinuity

40.

TRUE OR FALSE? If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero (a y-value of zero) between -1 and 1.

a)

TRUE

b)

FALSE

c)

CANNOT BE DETERMINED

41.

Given the function f(x) = x³ + x - 3, which of the intervals below contains a zero?

a)

[-1,1]

b)

[0,1]

c)

[1,2]

d)

None of these intervals

42.

Given a continuous function on the interval [4,7]. Let's say that f(4) = 10 and f(7) = 20. Is there a value on the interval [4,7] where f(x) = 15?

a)

Yes - if the function is continuous, then there must be an x value on that interval that passes through 15 on its way from 10 to 20.

b)

No because there is no sign change on the interval [4,7].

c)

No because that would be just too good to be true.

d)

Yes - at x = 5.5.

43.

A function is ________ if there is a break in the function's graph.

a)

continuous

b)

open

c)

closed

d)

discontinuous

44.

There is a hole in the graph

a)

when the numerator and denominator have a common factor

b)

where the denominator equals zero

c)

if the degree of the numerator is exactly one more than the denominator

d)

if the degree of the numerator and denominator are the same.

45.

there is a vertical asymptote

a)

when the denominator equals zero

b)

when the degree of the numerator is exactly one more than the denominator

c)

when there is a common factor in the numerator and denominator

d)

when the degree of the numerator is the same as the denominator

46.

Which of the following best describes the continuity at x = 5?

a)

Maximum

b)

Minimum

c)

Vertical Asymptote

d)

Hole

47.

Find the vertical asymptotes and holes of

y = (x+3) / ((x-1)(x+3))

a)

Holes: None;

VA: x = 1, -3

b)

Holes: x = -3;

VA: x = 1

c)

Holes: x = -3, 1

VA: None

d)

Holes: x = 1

VA: x = -3

48.

Suppose t is a continuous function containing the ordered pairs shown in the table. On which interval(s) must t attain a value of -2.5? Select all that apply.

a)

(1, 2)

b)

(2, 3)

c)

(3, 4)

d)

(4, 5)

e)

(5, 6)

49.

Suppose h is a continuous function containing the ordered pairs shown in the table. On which interval must h have a zero?

a)

(12.163, 12.164)

b)

(12.164, 12.165)

c)

(12.165, 12.166)

d)

(12.166, 12.168)

50.

True or false? There is a zero on the interval [1,3].

a)

True because the function is continuous and there is a sign change on the interval [1,3]

b)

We cannot be certain since the function is not continuous on the interval [1,3]

c)

False because there is no sign change on the interval [1,3]

d)

False because the graph is not continuous on the interval [1,3]

51.

True or false: If $f\left(x\right)=\frac{\left|x+1\right|}{x+1}$ , then there is a zero on the interval [-2,0].

a)

TRUE because there is a sign change on the interval

b)

FALSE because there is no sign change on the interval

c)

TRUE because of the Intermediate Value Theorem

d)

FALSE because the function is discontinuous on the interval

AP Calculus AB Quiz 1 (Part 2) Review

Total questions: 51

Worksheet time: 1hrs 29mins

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