Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Math 201-203-RE: Fall 2009 Final Exam Solutions, Exams of Calculus

Alagappa UniversityCalculus

The solutions to the math 201-203-re final exam held in fall 2009. It includes answers to various math problems involving integration, differentiation, logarithms, and series. The problems are labeled with numbers (1 to 17) and include both calculus and algebraic questions.

Typology: Exams

2012/2013

Uploaded on 02/27/2013

aliya
aliya ๐Ÿ‡ฎ๐Ÿ‡ณ

4.4

(12)

86 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Math 201-203-RE - Final Exam Fall 2009 Page 1 of 2
ANSWERS
(1 a) xฯ€+1
ฯ€+1 โˆ’ln |secx|+ฯ€x
ln ฯ€โˆ’x+C; (1 b) 1
2x2+ ln |x2+xโˆ’2|+C; (1 c) 175
4= 43.75
(1 d) 2 (โˆšx+ 4) โˆ’8 ln (โˆšx+ 4) + C= 2โˆšxโˆ’8 ln (โˆšx+ 4) + C
(1 e) โˆ’x2cos x+ 2xsin x+ 2 cos x+C; (1 f ) ln |x| โˆ’ 3
xโˆ’2 ln |x+ 4|+C
(2 a) factor then F39 or complete square then F26: ln ๎˜Œ
๎˜Œ
๎˜Œx+ 2 + โˆšx2+ 4xโˆ’5๎˜Œ
๎˜Œ
๎˜Œ+C
(2 b) substitution then F12: โˆ’1
12 ln ๎˜Œ
๎˜Œ
๎˜Œ
๎˜Œ
x2โˆ’1
x2+ 5๎˜Œ
๎˜Œ
๎˜Œ
๎˜Œ
+C
(3)
x
y
g(x) = x2
โˆ’2x
f(x) = 4xโˆ’x2+ 8
0
โˆ’12 4
12
โˆ’1
b
b
b
b
Area = 125
3โ‰ˆ41.67 square units
(4 a) point of equilibrium: (2,44)
(4 b)
p(x)
x
p=x2+ 16x+ 8
p= 48 โˆ’x2
P.S.
C.S.
44
8
48
2 6.90
b
b
b
b
(4 c) P.S.=37.33
(5) 6.6705 ; (6 a) y=1
5x5+1
4e2x+1
2x+15
4; (6 b) y=xln xโˆ’x+ 6
7(a) y=3
q3
4xโˆ’3 ln(x) + C; (7 b) y=Cโˆšx2+ 1 ; (8 a) about 25 persons ; (8 b) about 5.4 weeks
pf2

Partial preview of the text

Download Math 201-203-RE: Fall 2009 Final Exam Solutions and more Exams Calculus in PDF only on Docsity!

Math 201-203-RE - Final Exam Fall 2009 Page 1 of 2

ANSWERS

(1 a)

xฯ€+ ฯ€+

โˆ’ ln |secx| +

ฯ€x ln ฯ€

โˆ’ x + C ; (1 b)

1 2

x

2

  • ln |x

2

  • x โˆ’ 2 | + C ; (1 c)

175 4

(1 d) 2 (

x + 4) โˆ’ 8 ln (

x + 4) + C = 2

x โˆ’ 8 ln (

x + 4) + C

(1 e) โˆ’x

2 cos x + 2x sin x + 2 cos x + C ; (1 f) ln |x| โˆ’

3 x โˆ’^ 2 ln^ |x^ + 4|^ +^ C

(2 a) factor then F39 or complete square then F26: ln

โˆฃx^ + 2 +^

x^2 + 4x โˆ’ 5

โˆฃ +^ C

(2 b) substitution then F12: โˆ’

1 12

ln

x

2 โˆ’ 1

x^2 + 5

+ C

x

y

g(x) = x

2 โˆ’ 2 x

f (x) = 4x โˆ’ x^2 + 8

โˆ’ 1 0 2 4

12

โˆ’ 1

b

b

b

b

Area =

125 3

โ‰ˆ 41 .67 square units

(4 a) point of equilibrium: (2, 44)

(4 b)

p(x)

x

p = x

2

  • 16x + 8

p = 48 โˆ’ x^2

P.S.

C.S. 44

8

48

0 2 6.

b

b

b

b

(4 c) P.S.=37. 33

(5) 6.6705 ; (6 a) y =

1 5

x^5 +

1 4

e^2 x^ +

1 2

x +

15 4

; (6 b) y = x ln x โˆ’ x + 6

7(a) y =

3

3 4

x โˆ’ 3 ln(x) + C ; (7 b) y = C

x^2 + 1 ; (8 a) about 25 persons ; (8 b) about 5.4 weeks

Math 201-203-RE - Final Exam Fall 2009 Page 2 of 2

(9 a) โˆ’

1 6 ; (9 b)^ โˆ’โˆž^ ; (10 a)^ โˆ’โˆž^ , divergent ; (10 b) converges to^ โˆ’^

3 2

(11 a) a 5 =

25 5

, a 6 =

29 6

, a 7 =

33 7

, a 8 =

37 8

; (11 b) an =

4 n + 5

n

; (11 c) converges to 4

(12) the first 6 terms are: 1 , 3 , 5 , 7 , 9 , 11 ; an = 2n โˆ’ 1 ; (13) an = (โˆ’1)

n+1 n!

5 n

(14 a) ยฑ

5 3

, divergent ; (14 b) converges to 1 ; (15) $2188. 10

(16 a) divergent by n.T.T. ; (16 b) convergent by geometric test to

9 2 ; (17) $1975.^90