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Unformatted text preview: Exam 3, Day 2
Fall 2009 Name: 8. (10 pts.) Assume that b and c are ﬁxed, positive, constants and consider the series
∞ n=2 (cn + 1)2
bn ln n (a) Apply the root or ratio test to this series. Write your answer in the form ρ = something.
(b) For what values of b and c is this series convergent?
9. (10 pts.) Suppose that f (x) is a function with the following properties:
f (0) = 1
f ′ (0) = 4
f ′′ (x) = 4x − f (x)
Compute the fourth order approximation of f (x) centered at 0.
Bonus: Guess a simple formula for the function f (x). Convince me that your guess is correct. 1 ...
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This note was uploaded on 10/11/2011 for the course MATH 175 taught by Professor Staff during the Fall '08 term at Boise State.
- Fall '08