aug3109 - Math 1502 D, August 31st 2009 1 School of...

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Unformatted text preview: Math 1502 D, August 31st 2009 1 School of Mathematics Math 1502 Georgia Tech Calculus II, Section D Quiz # 2 August 31st 2009 First Name : Last Name : −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− 1. If p(x) = 1 + 41x19 /12! − 52x123 /123! + 87x144 /144! give p(123)(0) = 2. Give the Taylor series of the function cos x near x = 0 cos x = 3. Give the Taylor expansion to order 2 around x = 0 of f (x ) = 1 (1 − x)1/5 Math 1502 D, August 31st 2009 2 4. (a) Give the Taylor polynomial up to order 2n + 2 of ln 1+x 1−x = (b) Admit that the remainder R2n+2 of the previous expansion satisfies 0 ≤ R2n+2 2x2n+3 ≤ (2n + 3)(1 − x2 ) Use question 4a, with n = 3, to compute the number ln 3 with less than 0.1% of error. (Use x = 1/2 and 1/12 = .083333, 1/80 = .01250, 1/448 = 0.00223, 1/(64 × 27) ≤ 0.00058) ln 3 = ...
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This note was uploaded on 11/30/2009 for the course MATH 1502 taught by Professor Mcclain during the Fall '07 term at Georgia Institute of Technology.

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