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please help with the following questions for calculus II


MATH-1326-THQ 1, 2016-08-24 15:07

 


 

(Printed First Name)

 


 

(Printed Last Name)

 


 



 



 

XXX0000

 

Net ID

 


 

(First Letter of Last Name)

 


 



 



 

001 ? 502

 

Section

 


 

Take Home Quiz 1

 

Penalty

 


 

Instructions

 

1. Fill in the requested information on the line above.

 

2. This handout is due at the beginning of lecture on

 

Tuesday (08-30-2016). One point penalty per minute

 

late. Submit right away, don?t wait for the end of

 

class! THQ with missing name will receive 10 points

 

penalty.

 

3. This handout must be printed out and. You may print

 

it single sided or double sided. Failing to print costs

 

10 points.

 

4. This handout must be stapled. Failing to staple costs

 

10 points.

 

5. Your work must be hand written on this handout.

 

6. You must show all work. You may receive zero or

 

reduced points for insufficient work.

 

7. Your work must be neatly organized and written. You

 

may receive zero or reduced points for sloppy work.

 

8. Only a subset of these questions will be graded. You

 

will not be told which questions will be graded in advance.

 


 

Due Date: Tuesday, 08-30-2016

 


 

Page 2 of 7

 

Problem 1 For functions,

 

f (x) =

 


 

?

 

x

 

+ 5x and g(x) = x + 3

 

x?2

 


 

find,

 

1. (f + g)(x)

 


 

2. (f + g)(2)

 


 

3. (f ? g)(x)

 


 

4. (f ? g)(1)

 


 

5. (f g)(x)

 


 

6. (f g)(2)

 


 

 

 

f

 

7.

 

(x)

 

g

 


 

 

 

f

 

(2)

 

8.

 

g

 


 

 

 

g

 

9.

 

(x)

 

f

 


 

 

 

g

 

(1)

 

10.

 

f

 


 

11. (f ? g) (x)

 


 

12. (f ? g) (3)

 


 

13. (g ? f ) (x)

 


 

14. (g ? f ) (3)

 


 

MATH-1326-THQ 1, 2016-08-24 15:07

 


 

Page 3 of 7

 

Problem 2 For functions,

 

f (x) = e(2x+3) and g(x) = ln (3x + 5)

 

1. (f + g)(x)

 


 

2. (f + g)(0)

 


 

3. (f ? g)(x)

 


 

4. (f ? g)(0)

 


 

5. (f g)(x)

 


 

6. (f g)(1)

 


 

 

 

f

 

7.

 

(x)

 

g

 


 

 

 

f

 

8.

 

(0)

 

g

 


 

 

 

g

 

9.

 

(x)

 

f

 


 

 

 

g

 

10.

 

(0)

 

f

 


 

11. (f ? g) (x)

 


 

12. (f ? g) (1)

 


 

13. (g ? f ) (x)

 


 

14. (g ? f ) (1)

 


 

MATH-1326-THQ 1, 2016-08-24 15:07

 


 

Page 4 of 7

 


 

MATH-1326-THQ 1, 2016-08-24 15:07

 


 

Problem 3 Use the properties of logarithms to expand each of the following function.

 



 

(a)f (x) = ln 9x7 (x ? 2)6

 


 



 



 

2

 

(b)f (x) = ln 3x(3x ? 4)2 e6x

 


 



 

(c)f (x) = ln

 


 



 

(d)f (x) = ln

 


 

x2 (3x ? 5)

 

3(2x + 1)e7x

 


 



 


 

?

 



 

5x3 2x + 3

 

(4x + 3)5 e?3x

 


 

Page 5 of 7

 

Problem 4 Evaluate the limit for each of the following functions, if exist.

 

3x2 ? 5

 

x?1 x2 ? 3x ? 4

 


 

(a) lim

 


 

?

 

(b) lim

 


 

x?4

 


 

x?3

 

2x ? 8

 


 

x2 ? 5x + 4

 

x?4

 

x2 ? 20

 


 

(c) lim

 


 

MATH-1326-THQ 1, 2016-08-24 15:07

 


 

Page 6 of 7

 

Problem 5 Evaluate the limit for each of the following functions, if exist.

 

(a) lim

 


 

x?6

 


 

2x ? 12

 

x2 ? 4x ? 12

 


 

?

 

(b) lim

 


 

x?3

 

? 81

 


 

x?9 x2

 


 

x2 + 3x + 2

 

x??2

 

x2 ? 4

 


 

(c) lim

 


 

MATH-1326-THQ 1, 2016-08-24 15:07

 


 

Page 7 of 7

 

Problem 6 Evaluate the limit for each of the following functions, if exist.

 

x4 ? 3x2 + 3

 

x?? 4x3 + 2x + 1

 


 

(a) lim

 


 

2x3 ? 3x2 + 13

 

x?? 5x + 7x2 ? 9x3

 


 

(b) lim

 


 

12x3 ? 2x + 3

 

x??

 

7x ? 9x6

 


 

(c) lim

 


 

MATH-1326-THQ 1, 2016-08-24 15:07

 


 

 







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