Free Printable Basic Calculus 1st Quarterly Exam

1.

Find the limit of

\lim_{x\rightarrow2^+}3x+1

a)

7

b)

6

c)

4

d)

10

2.

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

a)

3

b)

4

c)

5

d)

-1

3.

What is $\lim_{x\rightarrow0^-}\ f\left(x\right)$ ?

a)

-3

b)

The limit DOES NOT EXIST.

c)

-5

4.

$\lim_{x\rightarrow1^-}\ g\left(x\right)$

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

a)

3

b)

1

c)

5

d)

-1

e)

The limit DOES NOT EXIST

5.

Determine the value of the limit

a)

4

b)

-1

c)

1

d)

DNE

6.

Find the limit as x approaches 3 from the left

a)

4

b)

3

c)

2

d)

DNE

7.

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

a)

³/₇

b)

0

c)

∞

d)

-∞

8.

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

a)

^-2/₉

b)

0

c)

∞

d)

-∞

9.

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

a)

0

b)

DNE

c)

1/2

d)

2

10.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

11.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

12.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

13.

in what value of x does the following function is discontinuous?

a)

3

b)

-3

c)

6

d)

-6

14.

Does the following function is continuous at x=0?

a)

Continuous

b)

Discontinuous

15.

In what value of x will the following function discontinuous?

a)

-1

b)

-2

c)

-3

d)

-4

16.

One of the conditions a function must satisfy to be continuous at a number is "the value of the limit of f(x) is DNE"

a)

TRUE

b)

FALSE

17.

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

a)

TRUE

b)

FALSE

18.

At x=a there is a (a) discontinuity.

19.

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

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

20.

At which x-value is there a jump discontinuity?

a)

$x=-3$

b)

$x=-6$

c)

$x=1$

d)

$x=2$

21.

At x = 1 there is a (a) discontinuity.

22.

Determine if the graph is continuous or not. If is discontinuous determine which type. Choose 1 or 2 answers depending on the graph type.

a)

Continuous

b)

Discontinuous

c)

Jump

d)

Infinite

e)

Removable

23.

$\lim_{x\rightarrow\infty}$ $\frac{4-x^2}{x^2-1}$ is

(a)

24.

$\lim_{x\rightarrow2}$ $\frac{x^2-4}{x^2+4}$

a)

1

b)

0

c)

- $\frac{1}{2}$

d)

-1

e)

$\infty$

25.

Does the function have a jump discontinuity?

a)

Yes

b)

No

26.

This piecewise function is:

a)

Continuous

b)

Discontinuous

c)

Neither continuous nor discontinuous

d)

Both continuous and discontinuous

27.

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

a)

Continuous

b)

Removable Point Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

28.

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

a)

3

b)

1

c)

6

d)

DNE

29.

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

a)

3

b)

4

c)

5

d)

-1

30.

What is $\lim_{x\rightarrow0^+}\ f\left(x\right)$ ?

a)

-3

b)

The limit DOES NOT EXIST.

c)

-5

31.

$\lim_{x\rightarrow\infty}\frac{2x^2+1}{\left(2-x\right)\left(2+x\right)}$

(a)

32.

Find the limit of

\lim_{x\rightarrow-1^+}\left(\frac{x^2-1}{x^2+5x+4}\right)

a)

0

b)

Undefined

c)

$-\frac{2}{3}$

d)

10

33.

Find the limit of $\lim_{x\rightarrow4^-}\sqrt{x+5}$

a)

0

b)

Undefined

c)

3

d)

$-1$

34.

Determine the value of the limit

a)

4

b)

-1

c)

1

d)

DNE

35.

Find the limit as x approaches 7 from the right

a)

1

b)

0

c)

infinity

d)

DNE

36.

Find f(4)

a)

1

b)

5

c)

0

d)

DNE

37.

Find the point or points of discontinuity. If none, state continuous.

f\left(x\right)=\frac{5}{x-3}

a)

$x=3$ hole

b)

$x=-3$ VA

c)

$x=3$ VA

d)

Continuous

38.

Find the points of discontinuity and state the type.

f\left(x\right)=\frac{x+4}{x^2+10x+24}

a)

$x=-4\ and\ x=-6$ Both VA's

b)

$x=-4\$ VA; $x=-6$ Hole

c)

$x=-4$ Hole; $x=-6$ VA

d)

$x=-4\ and\ x=-6$ Both Holes

39.

Find the points of discontinuity and state the type

\frac{x^2+4x-5}{x+5}

a)

$x=1$ hole

b)

$x=-5$ VA

c)

$x=-5$ Hole

d)

$x=1$ VA ; $x=-5$ Hole

40.

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

41.

Which of the following is correct about f at x = 3?

I: the limit as x approaches 3 exists

II: f is defined at x = 3

III: f is continuous at x =3

a)

II only

b)

I and II

c)

II and III

d)

I, II, and III

42.

a)

3

b)

0

c)

1

d)

Does not exist

43.

a)

A

b)

B

c)

C

d)

D

44.

Evaluate the limit.

a)

3/2

b)

-3/2

c)

-infinity

d)

infinity

45.

a)

Does Not Exist

b)

9

c)

1

d)

0

Basic Calculus 1st Quarterly Exam

Total questions: 45

Worksheet time: 43mins

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