Unformatted text preview: , a ] for any a ∈ (0 , 1). 3) Does the series converge uniformly on [0 , 1)? Prove your idea. 3. Let s ( x ) = ∞ s n =0 (1) n x 2 n +1 (2 n + 1)! c ( x ) = ∞ s n =0 (1) n x 2 n (2 n )! . Here, s ( x ) = sin( x ) and c ( x ) = cos x but without using these facts answer the following questions. 1) Show that s ′ = c and c ′ =s . 2) Show that ( s 2 + c 2 ) ′ = 0. 3) Show that s 2 + c 2 = 1. 1...
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 Fall '07
 Fukuda
 Uniform convergence, MAT 125A Homework, N. Suppose fn

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