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I reallly need help with my Calculus II Final. I need a competent calculus tutor that can be available at 1pm on 5/7.My game plan is to be talking with you prior to the examm. I’ll be joining the video chat when it opens and quickly send the final doc to you. You can look up the answers just make sure the work is complete and makes sense. I will pay good money for this and will tip well. I have been working fulltime and my lecture was during my work hours so I’m not as confident in taking this solo. Please help. I included a study guide

SUNY

ULSTER

Stone Ridge, New York

FINAL EXAMINATION

MAT 180 – Calculus II

Spring 2021

Instructor: Chaitanya Mistry

Name: __________________________________________________

DIRECTIONS: Show work for partial credit. If more

room is needed use the back of the page you are

working on and write “see back” in the answer space.

Relax and think!!!

Note: TI-89/92 calculators are not allowed.

MAT 180 – Formula Sheet – Spring 2021

1

1 cos 2 x

2

1

cos2 x 1 cos 2 x

2

1

sin x cos x sin 2 x

2

sin 2 x

sec x dx ln sec x tan x C

csc x dx ln csc x cot x C

ln u du u ln u u C

Part I: For questions 1-5, choose 4 out of 5. (Questions are worth 6 points each.)

1. Differentiate the function.

f ( x) 2sin 1 e x tan 1 3 x

1. ___________________________

2. Differentiate the function.

y cosh 2 (5x)

2. ___________________________

3. Find the area between the two curves, over the

given interval. Show a sketch of the region.

Show ALL work.

y x2 , y x ; 0 x 1

3. ___________________________

4. The region in the first quadrant bounded by the curves y x 3 and y 4 x

is rotated about the x-axis.

Set up the integral which will give the volume using:

a. Disk/washers

b. Shells

5. The region in the first quadrant bounded by the curves y x 3 and y 4 x

is rotated about the y-axis.

Set up the integral which will give the volume using:

a. Disk/washers

b. Shells

Part II: For questions 6-10, choose 4 out of 5. (Questions are worth 6 points each.)

6.

x e dx

7.

sin

8.

2 x

4

x cos3 x dx

dx

4 x2

6. __________________________

7. __________________________

8. __________________________

x3

9.

10.

x

9 x2

2

dx

5x 3

dx

2x 3

9. __________________________

10. __________________________

Part III: For questions 11-15, choose 4 out of 5. (Questions are worth 6 points each.)

11. Evaluate the limit, if it exists.

x

lim 2

x 0 x tan x

12. Find the limit, if it exists.

lim x3e 2 x

x

11. __________________________

12. __________________________

13. Evaluate the improper integral.

e

2 x

dx

13. __________________________

0

14. Evaluate the improper integral:

3

x

0 9 x2 dx

14. __________________________

Hint: The integrand is undefined at x = 3. Also, this integral does not require trig substitution.

3

15. Find the length of the curve y 1 2 x 2

over the interval 0 x 1.

b

Recall: L 1 [ f ‘( x )]2 dx

a

15. __________________________

Part IV: For questions 16-20, choose 4 out of 5. (Questions are worth 7 points each.)

16. Tell if the following converge or diverge by direct recognition:

a.

5

2

n 1

b.

5

n

n 1

c.

d.

_______________

3

2

________________

n 1

n

1

n

_________________

n

n 1

e.

_____________

n

1

n

_________________

n 1

f.

1

1

n n 1

_________________

n 1

g.

5

n 1 2

n

___________________

17. Determine whether the series converges or diverges. Justify your conclusion.

4n 2

5n 3

n 1

17. __________________________

18. Determine whether the series converges or diverges. Show all work.

n4

n

n 1 4

18. __________________________

Hint: ratio test

19. Find the radius of convergence for the power series:

n2 xn

n

n 1 2

19. __________________________

20. Derive the Maclaurin series for f ( x)

1

(1 x) 1 using the definition.

1 x

(You may not use a substitution.)

20. __________________________

Extra Credit (5 points): Do 1 of the 4 questions that you omitted and label it “Extra Credit”.

So, your exam should clearly label 3 problems “OMIT” and label 1 problem “EXTRA CREDIT”.

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