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Unformatted text preview: Exam 1 Math 408D Name
Spring 2009 TA Discussion Time: TTH You must Show sufﬁcient work in order to receive full credit for a problem.
Do your work on the paper provided. Write your name on this sheet and
turn it in with your work. Please write legibly and label the problems clearly.
Circle your answers when appropriate. No calculators allowed. 1. Evaluate each limit or explain clearly why it does not exist. 1
(a) (14 points) lim n2 sin <—) n—wo 7L (b) (14 points) lim (1:2 > m—>0+ I," 1
2. (14 points) Evaluate /0 Walt or show that it diverges. 0" H2 k+3
3. (14 points) Find the sum of the series Z ( )
k:1 3k or show that it diverges. 4. Determine whether each of the series below converges absolutely, con—
verges conditionally, or diverges. State what tests you use and verify that
the hypotheses are satisﬁed. °° 2 ‘ k:
(a) (14 points) E $— 1621 (b) (14 points) fix—W“ <$>k k:0
5. (16 points) Find the radius and interval of convergence of the power series
below. Justify all your conclusions. 0° (3)’“($ 2V“
; k+\/E Bonus (5 points): Assume that Z ak and Z bk are positive termed series
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 Fall '09
 ALTHARODIN

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