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Radius - Calculus - Exam, Exams of Calculus

Main points of this exam are: Radius, Sum, Finite Series, Fraction, Decimal, Interval of Convergence, Series, Determine, Series Converge, Specifying

Typology: Exams

2012/2013

Uploaded on 03/20/2013

moti
moti 🇮🇳

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NAME_______________________________________
I_________II_________III_________IV_________V_________ TOTAL ___________
March 11 Mathematics 106c Mr. Haines
2005 Calculus II
Examination #2
(5) I. What is the sum of this finite series? (Write your answer as a fraction, not a decimal.)
5
11 1 1
1...
525125 5
  
++ + ++
  
  
(24) II Give the interval of convergence and radius of convergence for these series:
A. 2345
1 (5) (5) (5) (5) (5) ...
xx x x x++ + + + +.
pf3
pf4
pf5

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NAME_______________________________________

I_________II_________III_________IV_________V_________ TOTAL ___________

March 11 Mathematics 106c Mr. Haines 2005 Calculus II Examination #

(5) I. What is the sum of this finite series? (Write your answer as a fraction, not a decimal.)

1 1 1 1 5 1 ... 5 25 125 5

+ ^ ^ + ^ ^ + ^ ^ + +^ 

(24) II Give the interval of convergence and radius of convergence for these series:

A. 1 + (5 ) x + (5 ) x^2 + (5 ) x 3 + (5 ) x^4 + (5 ) x^5 + ....

II (cont’d)

B. 1 7

n n n

∞ x

C.

n n

x n

∞

III (cont’d)

C.

2 1 3

n^1

n n

∞

D.

5 n 1 7 1

n n

∞

E.

1

( 1) n n n

∞

(24) IV. Give the Taylor Series for these functions

A. f ( ) x = x^4 + 7 x^3 − 5 x + 1 near x = 0.

B. f ( ) x = ln(1 + x )near x = 0.

C. f ( ) x = xex near x = 0.