wayground logo

Free Printable Worksheets

NEW

Font size

S
M
L
XL
Worksheets

Limits

Total questions: 16

Worksheet time: 1hrs 15mins

Name
Class
Date
1.

Define a limit

a)

The value of a function at a certain x-value

b)

The value of x when a function hits a certain point

c)

The value a function approaches when x approaches a certain value

2.

 limx0    x29x2x6\lim_{x\rightarrow0\ \ }\ \ \frac{x^2-9}{x^2-x-6}  

a)

No Limit because it is undefined

b)

3/2

c)

-3/2

d)

2/3

3.

 limx3   x29x2x6\lim_{x\rightarrow3}\ \ \ \frac{x^2-9}{x^2-x-6}  

a)

no limit because it is undefined

b)

3/2

c)

6/5

d)

5/6

4.


 limx36  x6x36\lim_{x\rightarrow36}\ \ \frac{\sqrt{x}-6}{x-36}  

a)

1/12

b)

-1/12

c)

no limit because it is undefined

d)

0

5.

 limx3     5x+1  \lim_{x\rightarrow-3}\ \ \ \ \ \left|5x+1\right|\ \   

a)

no limit because the one sided limits are not equal

b)

14

c)

-14

d)

0

6.

 limx4  x27x\lim_{x\rightarrow4}\ \ \sqrt{\frac{x^2-7}{x}}  

a)

 112\frac{\sqrt{11}}{2}  

b)

9/4

c)

3/2

d)

no limit

7.

 limx7  2x14\lim_{x\rightarrow7}\ \ \sqrt{2x-14}  by looking at the graph

a)

no limit because there is no left hand limit

b)

0

c)

 28\sqrt{28}  

d)

1

8.

 limx2  x2x24\lim_{x\rightarrow2}\ \ \frac{x-2}{x^2-4}  

a)

1/4

b)

1/2

c)

-1/4

d)

no limit 

9.

 limx1  3xx+1\lim_{x\rightarrow-1}\ \ \frac{3x}{x+1}  by making a chart.  Include values of -1.001 and -.999

a)

300

b)

-300

c)

no limit because the one sided limits are not equal

d)

0

10.

 limx1  x225x24x5\lim_{x\rightarrow1}\ \ \frac{x^2-25}{x^2-4x-5}  

a)

no limit 

b)

-3

c)

-2

d)

3

11.

using your calculator to graph:  limx1   33x\lim_{x\rightarrow1^-}\ \ \ \sqrt{3-3x}  *Notice the symbol beside the 1**

a)

no limit

b)

0

12.

using your calculator to graph:  limx1+   33x\lim_{x\rightarrow1^+}\ \ \ \sqrt{3-3x}  
**Notice the symbol beside the 1**

a)

no limit

b)

0

13.

using your calculator to graph:  limx1   33x\lim_{x\rightarrow1^{ }}\ \ \ \sqrt{3-3x}  

a)

no limit

b)

0

14.

 Graph    limx  x2xGraph\ \ \ \ \lim_{x\rightarrow\infty}\ \ \sqrt{x-2}-\sqrt{x}  

a)

no limit

b)

 \infty  

c)

0

d)

 -\infty  

15.

 limx π4  cscx + 48 + tanx\lim_{x\rightarrow\ \frac{\pi}{4}}\ \ \frac{\csc x\ +\ 4}{8\ +\ \tan x}  

a)

 429\frac{4\sqrt{2}}{9}  

b)

 4+29\frac{4+\sqrt{2}}{9}  

c)

no limit 

d)

4/9

16.

 limxπ  sin(x  2π3)\lim_{x\rightarrow\pi}\ \ \sin\left(x\ -\ \frac{2\pi}{3}\right)  

a)

 22\frac{\sqrt{2}}{2}  

b)

 32\frac{-\sqrt{3}}{2}  

c)

 32\frac{\sqrt{3}}{2}  

d)

1/2