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### ma6021HandOut3

Course: MATH 6021, Summer 2009
School: Georgia Tech
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Word Count: 104

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6021 Math Let a and b be two strictly positive real numbers. 2ab a+b ab . 1) Show that a+b 2 2) Define a0 = a and b0 = b and put an+1 = 2an bn an + b n and bn+1 = Summer 2007 - Handout #3 an + b n , 2 n 0. Show that for n 1 we have a1 a 2 a n n b b 2 b 1 and that an bn = a0 b0 = ab ab. Show 3) Show that the sequences {an } and {bn } converge to the same limit, namely moreover that for...

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6021 Math Let a and b be two strictly positive real numbers. 2ab a+b ab . 1) Show that a+b 2 2) Define a0 = a and b0 = b and put an+1 = 2an bn an + b n and bn+1 = Summer 2007 - Handout #3 an + b n , 2 n 0. Show that for n 1 we have a1 a 2 a n n b b 2 b 1 and that an bn = a0 b0 = ab ab. Show 3) Show that the sequences {an } and {bn } converge to the same limit, namely moreover that ...

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T1 95 83 79 92 78 91 95 92 83 65 80 93 60 62 55 85 84 75 75 93 58 57 82 70 74 75 73 82 80 61 73 79 72T2 100 100 95 100 98 98 95 100 94 96 70 70 95 80 98 100 68 95 85 89 92 97 94 88 89 87 62 88 77 94 48 87 86T3 95 99 100 100 99 100 90 90 99 100 96
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The Fourier Transform Some background: If we apply the Gram-Schmidt procedure to the sequence of functions {ex2 2 2/2, xex2/2, x2 ex/2, . . .} L2 (R), we get a new sequence of functions n (x) = pn (x)ex/2, n = 0, 1, 2, . . ., whe
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NAME:1. (Section 3.5, Problem 13) Assume that F (0) = 0, and that u is a continuous integral solution of the conservation law ut + F (u)x = 0 u=g in R (0, ),on R {t = 0} ,and that u has compact support in R [0, ). Prove that u(, t)dx =
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Mathematics 1502Test number 2Friday, 16 February 2001 versionNAME_ By signing here you acknowledge being bound by the Georgia Tech Honor Code Instructions: Write the answers where indicated and give clear evidence of your reasoning (or points
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Mathematics 1502Test number 2Friday, 16 February 2001 versionNAME_ By signing here you acknowledge being bound by the Georgia Tech Honor Code Instructions: Write the answers where indicated and give clear evidence of your reasoning (or points
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Mathematics 2401TTest 2 25 September 2008 VERSION GNAME: TA: Instructions: Work absolutely on your own, without reference to notes or text. Answers should be as specific as possible and it should be evident how they were obtained. Write the ans
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