Free Printable AP Calculus Unit 1

1.

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

a)

2

b)

-4

c)

DNE

d)

-2

2.

What three conditions must exist for a function to be continuous?

a)

ƒ(c) must exist

b)

the limit as x → c must exist

c)

the limit as x →c must equal ƒ(c)

d)

all functions are continuous

3.

What is the limit?

a)

Infinity

b)

20

c)

DNE

d)

12

4.

a)

Does not exist

b)

-2

c)

0

d)

-1

5.

a)

Does not exist

b)

2

c)

0

d)

1

6.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

7.

Find the vertical asymptote(s) (if any) of the graph of the function.

a)

x=2

b)

x=-2

c)

None

d)

X=2, x=-2

8.

a)

-7

b)

0

c)

1

d)

DNE

9.

a)

A

b)

B

c)

C

d)

D

10.

a)

Does not exist

b)

1

c)

-1

d)

0

11.

a)

1/5

b)

1

c)

5

d)

Does not exist

12.

a)

Does not exist

b)

6

c)

4

d)

3

13.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

14.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , and $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\sqrt{3h\left(x\right)-2g\left(x\right)}$ .

a)

16

b)

4

c)

8

d)

12

15.

If $\lim_{x\rightarrow c}f\left(x\right)=3$ , $\lim_{x\rightarrow c}g\left(x\right)=-2$ , $\lim_{x\rightarrow c}h\left(x\right)=4$ then find $\lim_{x\rightarrow c}\left[f\left(x\right)\cdot5g\left(x\right)\right]$

a)

-30

b)

-40

c)

60

d)

-80

16.

a)

2

b)

-2

c)

1/2

d)

-1/2

17.

a)

13

b)

7

c)

6

d)

-3

18.

a)

1

b)

Does not exist

c)

0

d)

-1

19.

Choose the best answer

a)

A

b)

B

c)

C

d)

D

e)

E

20.

Choose the best answer

a)

A

b)

B

c)

C

d)

D

e)

E

21.

Select all statements that are TRUE.

a)

b)

c)

d)

22.

Find the value of α that makes f(x) continuous at x=2.

a)

0

b)

1

c)

2

d)

No such value exists

23.

Find the value of c that makes the function continuous

a)

c=1/3

b)

c=3

c)

c=-3

d)

c=-1/3

24.

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

a)

TRUE

b)

FALSE

c)

CANNOT BE DETERMINED

25.

TRUE OR FALSE? If f(x) = |x+1|/(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

26.

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

27.

Find the limit

a)

infinity

b)

0

c)

-1

d)

-infinity

28.

5 points

a)

A

b)

B

c)

C

d)

D

e)

E

29.

Evaluate

\lim_{x\rightarrow0}\ \frac{\sin\left(x\right)}{8x}

.

(a)

30.

a)

4

b)

1/4

c)

0

d)

infinity

31.

a)

1

b)

-1

c)

-∞

d)

$\frac{\sqrt{2}}{2}$

e)

$-\frac{\sqrt{2}}{2}$

32.

a)

∞

b)

-3

c)

0

d)

1

33.

a)

-∞

b)

∞

c)

1

d)

-1

34.

Find the limit at infinity

a)

0

b)

1

c)

infinity

d)

DNE

35.

a)

0

b)

3

c)

1

d)

Does not exist

36.

$4^x\le m\left(x\right)\le x^4$ on $\left(0,5\right)$

$\lim_{x\rightarrow2}m\left(x\right)=$

If the limit does not exist, type DNE.

(a)

37.

$3\sin\left(\left(\frac{\pi}{2}x\right)\le m\left(x\right)\le3e^{\left(x-3\right)}\right)$ on $\left(0,5\right)$

$\lim_{x\rightarrow3}m\left(x\right)=$

If the limit does not exist, type DNE.

a)

-3

b)

3

c)

can not be determine

d)

DNE

38.

$\lim_{x\rightarrow0}\left(\frac{\sin\left(3x\right)}{8x}\right)=$

If the limit does not exist, type DNE.

(a)

39.

$4^x\le m\left(x\right)\le x^4$ on $\left(0,5\right)$

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

If the limit does not exist, type DNE.

(a)

40.

Is f(x) continuous at x= -2?

a)

Yes, f(x) is continuous at x= -2

b)

No, there is a jump discontinuity at x=-2

c)

No, there is a hole at x= -2

d)

No, there is a vertical asymptote at x= -2

41.

$\lim_{x\rightarrow0}\ x^2\sin\left(\frac{1}{x^3}\right)$ 5 points

a)

$\infty$

b)

DNE

c)

1

d)

0

42.

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

a)

TRUE

b)

FALSE

c)

CANNOT BE DETERMINED

43.

Find the value that makes the function continuous

a)

c=1/3

b)

c=3

c)

c=-3

d)

c=-1/3

44.

a)

0/0

b)

DNE

c)

-1/4

d)

1/4

45.

Tentukan Nilai dari $\lim_{x\rightarrow0}\ \frac{1-\cos\ 2x}{x\tan2x}$ adalah . . .

a)

-2

b)

-1

c)

0

d)

1

e)

2

46.

$\lim_{x\rightarrow0}\ \frac{\sin\ \frac{1}{3}x}{x}$

a)

-3

b)

$-\frac{1}{3}$

c)

$0$

d)

$\frac{1}{3}$

e)

3

47.

a)

12

b)

4

c)

3

d)

1

e)

0

48.

a)

6

b)

3

c)

2

d)

1

e)

0

49.

Evaluate f(-3)=

(a)

50.

a)

0

b)

1

c)

-1

d)

DNE

AP Calculus Unit 1

Total questions: 50

Worksheet time: 2hrs 44mins

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