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Math 104 Final Exam Fall 2017, Exams of Calculus

University of Pennsylvania (UPenn)Calculus

The final exam for Math 104 at the University of Pennsylvania in Fall 2017. The exam consists of 15 questions and covers topics such as finding volumes of solids, evaluating integrals, finding limits of sequences, and determining the convergence of series. The exam instructions state that no calculators are allowed, but students may use one standard sized 8.5”X11” sheet with notes handwritten on both sides. The exam also emphasizes the importance of showing work and complying with the University of Pennsylvania's Code of Academic Integrity.

Typology: Exams

2016/2017

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University of Pennsylvania
Math 104 Final Exam
Fall 2017
First and Last Name ____________________________________(PRINT) Penn ID_________________
Professor (circle one): Ghini-Bettiol Sergel Block Gressman Rimmer
Recitation number _____________________________
There are fifteen questions on this examination. No calculators are allowed, but you may use one
standard sized 8.5”X11” sheet with notes handwritten on both sides. Show your work in the space
provided, and then transfer your answers carefully to this sheet.
It is important to show your work because we will be going back over it – you might gain additional
partial credit for substantial progress toward the solution of a problem, or you might lose credit for an
unsubstantiated correct answer.
Please put away and silence (don’t set to vibrate) all electronic devices (computers, tablets, cell phones,
mp3 players), use of these are forbidden during the examination period. Good luck!
My signature below certifies that I have complied with the University of Pennsylvania's Code of
Academic Integrity in completing this examination. In particular, all the work on this test is my own.
_________________________________________
Signature
1. (A) (B) (C) (D) (E) (F) 9. (A) (B) (C) (D) (E) (F)
2. (A) (B) (C) (D) (E) (F) 10. (A) (B) (C) (D) (E) (F)
3. (A) (B) (C) (D) (E) (F) 11. (A) (B) (C) (D) (E) (F)
4. (A) (B) (C) (D) (E) (F) 12. (A) (B) (C) (D) (E) (F)
5. (A) (B) (C) (D) (E) (F) 13. (A) (B) (C) (D) (E) (F)
6. (A) (B) (C) (D) (E) (F) 14. (A) (B) (C) (D) (E) (F)
7. (A) (B) (C) (D) (E) (F) 15. (A) (B) (C) (D) (E) (F)
8. (A) (B) (C) (D) (E) (F)
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Download Math 104 Final Exam Fall 2017 and more Exams Calculus in PDF only on Docsity!

University of Pennsylvania

Math 104 Final Exam

Fall 2017

First and Last Name ____________________________________(PRINT) Penn ID_________________

Professor (circle one): Ghini-Bettiol Sergel Block Gressman Rimmer

Recitation number _____________________________

There are fifteen questions on this examination. No calculators are allowed, but you may use one

standard sized 8.5”X11” sheet with notes handwritten on both sides. Show your work in the space

provided, and then transfer your answers carefully to this sheet.

It is important to show your work because we will be going back over it – you might gain additional

partial credit for substantial progress toward the solution of a problem, or you might lose credit for an

unsubstantiated correct answer.

Please put away and silence (don’t set to vibrate) all electronic devices (computers, tablets, cell phones,

mp3 players), use of these are forbidden during the examination period. Good luck!

My signature below certifies that I have complied with the University of Pennsylvania's Code of

Academic Integrity in completing this examination. In particular, all the work on this test is my own.

Signature

1. (A) (B) (C) (D) (E) (F) 9. (A) (B) (C) (D) (E) (F)

2. (A) (B) (C) (D) (E) (F) 10. (A) (B) (C) (D) (E) (F)

3. (A) (B) (C) (D) (E) (F) 11. (A) (B) (C) (D) (E) (F)

4. (A) (B) (C) (D) (E) (F) 12. (A) (B) (C) (D) (E) (F)

5. (A) (B) (C) (D) (E) (F) 13. (A) (B) (C) (D) (E) (F)

6. (A) (B) (C) (D) (E) (F) 14. (A) (B) (C) (D) (E) (F)

7. (A) (B) (C) (D) (E) (F) 15. (A) (B) (C) (D) (E) (F)

8. (A) (B) (C) (D) (E) (F)

1. Find the volume of the solid generated by revolving the region bounded

above by y  sin x and bounded below y  0 for 0  x  about the line x.

(a)

2

 (b)

2

2  (c)

2

4  (d)

2

(e)

2

(f) None of these

4

2

1

  1. Let +. Find the arclength for 1 2.

16 2

x

y x

x

  

(a)

(b)

(c)

(d)

(e)

(f) None of these

  1. Evaluate

(^2 )

2

1

1

.

x x

dx

x x

 

(a) 0 (b) 1 (c)

1 ln

(d) 2 (e)

2 ln

(f) None of these

  1. Evaluate

 

3

3/

2

0

.

25

dx

 x

(a) 0 (b)

(c)

(d)

(e)

(f) None of these

 

  1. Let y x be the solution to the initial value problem

   

2

sin with 0

dy

x y x x y

dx

   

What is y  2  (^) ?

(a) ^ ^ (b)  2  (c)  4  (d) 0 (e) 2  (f) 4 

  1. Let

 

2 2 /

r b

Cr e r

f r

r

Find so that is a probability density function pdf

for the random variable , is a constant.

This is used to model the distance between the nucleus and the electron

in a hydrogen atom. With 0,

C

r b

b  it is called the Bohr length.

Find the mean of this pdf.

(a)

3

, mean

b

C   b (b) 2

C , mean b

b

  (c)

2

C , mean b

b

(d) 3

, mean

C b

b

  (e)

2

2

, mean

C b

b

  (f)

3

, mean

C b

b

  1. Find the limit of the sequence

ln 3 ln

n

a  n  n   n 

(a) 0 (b) 1 (c) ln 3  (d) 3 (e)  (f) the limit does not exist

  1. Determine whether the following series convergent absolutely ,

converge conditionally , or diverge. For full credit be sure

to explain your reasoning and tell what test was used.

A

C D

   

2

2 2

1 2 1

3

n n n

n

n n

n

 

 

 

 

(a) both A (b) one A, the other C (c) one A, the other D

(d) both C (e) one C , the otherD (f) both D

  1. Find the interval of convergence of the power series

 

3

2

2 5

.

n n

n

x

n

(a)

11 9

2 2

     

(b) (^) 

11 9

2 2

  

(c) (^)  

11 9

2 2

 

(d) (^) 

(^9 )

2 2

(e) (^)  

9 11

2 2

, (^) (f)

(^9 )

2 2

   

  (^)    

3

0

  1. Let be the unique function that satisfies 0 0 and

1

sin for all. Find the Taylor Series of centered at 0.

F x F

F x x x F x x

x

 (^)  

(a)

 

 

6 3

0

1

2 1!

n n

n

x

n

 

 (^) (d)

 

 

6 2

0

1

2 1!

n n

n

x

n

 

(b)

   

 

6 2

0

1 6 3

2 1!

n n

n

n x

n

 

 

 (e)

   

 

6 2

0

1 6 2

2 1!

n n

n

n x

n

 

 

(c)

 

  

6 3

0

1

6 3 2 1!

n n

n

x

n n

 

 

 (f)

 

  

2 3

0

1

6 3 2 1!

n n

n

x

n n

 

 

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