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Unformatted text preview: a = 0 for each function. (a) y = ex 2 cos x (b) y = e x ln(1x ) 9 (8) Solve exactly for the variable. (a) xx 2 2 + x 3 3x 4 4 + ... = 0 . 6 (b) xx 3 2! + x 5 4!x 7 6! + ... = . 5 x 10 (9) (a) Expand e x in powers of xa . (b) Use the expansion to show that e x 1 + x 2 = e x 1 e x 2 11 (10) Let i = √1. We deﬁne e iθ by substituting iθ in the Taylor series for e x . Use the Taylor series for sin θ and cos θ to show that e iθ = cos θ + i sin θ...
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 Spring '09
 HarvanshManocha
 Calculus, Taylor Series, #, Polytechnic Institute of NYU MA

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