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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.

 lim⁡x→0    x2−9x2−x−6\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.

 lim⁡x→3   x2−9x2−x−6\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.


 lim⁡x→36  x−6x−36\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.

 lim⁡x→−3     ∣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.

 lim⁡x→4  x2−7x\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.

 lim⁡x→7  2x−14\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.

 lim⁡x→2  x−2x2−4\lim_{x\rightarrow2}\ \ \frac{x-2}{x^2-4}  

a)

1/4

b)

1/2

c)

-1/4

d)

no limit 

9.

 lim⁡x→−1  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.

 lim⁡x→1  x2−25x2−4x−5\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:  lim⁡x→1−   3−3x\lim_{x\rightarrow1^-}\ \ \ \sqrt{3-3x}  *Notice the symbol beside the 1**

a)

no limit

b)

0

12.

using your calculator to graph:  lim⁡x→1+   3−3x\lim_{x\rightarrow1^+}\ \ \ \sqrt{3-3x}  
**Notice the symbol beside the 1**

a)

no limit

b)

0

13.

using your calculator to graph:  lim⁡x→1   3−3x\lim_{x\rightarrow1^{ }}\ \ \ \sqrt{3-3x}  

a)

no limit

b)

0

14.

 Graph    lim⁡x→∞  x−2−xGraph\ \ \ \ \lim_{x\rightarrow\infty}\ \ \sqrt{x-2}-\sqrt{x}  

a)

no limit

b)

 ∞\infty  

c)

0

d)

 −∞-\infty  

15.

 lim⁡x→ π4  csc⁡x + 48 + tan⁡x\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.

 lim⁡x→π  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