Homework_Set_9

Homework_Set_9 - for series using | a n | + a n ; see...

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Math 1a B. Simon Fall 2005 HOMEWORK SET 9 DUE AT 1:00 PM ON TUESDAY, NOVEMBER 29, 2005 Note 1: Due one day later than usual Note 2: LAST HOMEWORK! Note 3: Problems are worth 20 points each. Note 4: Total is 120 points! This homework counts slightly more than others. (1) Suppose f is a continuous function on [0 , ) so that sup x i x 0 | f ( y ) | dy < Prove that I 0 f ( y ) dy exists. ( Hint : Look at our proof of the analogous fact
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Unformatted text preview: for series using | a n | + a n ; see Theorem 10.15 in Apostol.) (2) Apostol, page 111, problems 10 and 13 (3) Apostol, page 365, problem 3, parts (e), (h), (i), (j) (4) Apostol, page 365, problem 5, parts (a), (b), (d), (f) (5) Apostol, page 371, problem 1, parts (d), (e), (f), (g), (h) (6) Write cos(5 x ) as a polynomial in cos( x ). 1...
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