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Unformatted text preview: (a) x 1x at x = 0; (b) 1 x 2 at x = 1; (c) x 1 + x at x =2; Ans . (a) ∞ X n =0 x n +1 (b) ∞ X n =0 (1) n ( n + 1)( x1) n (c) 2 + ∞ X n =1 ( x + 2) n 6. Find a quadratic (2nd degree) polynomial to approximate each of the following functions near x = 0: (i) e sin x and (ii) ln(cos x ). Ans . (i) 1 2 x 2 + x + 1 (ii)1 2 x 2 7. Let S = ∞ X n =0 1 n !( n + 2) . In this question, we will introduce two diﬀerent ways to ﬁnd the value of S , one by integration and the other by diﬀerentiation. (i) Integrate the Taylor series of xe x to show that S = 1. (ii) Diﬀerentiate the Taylor series of e x1 x to show that S = 1. 8. Let f ( x ) = 1 x 2 + x + 1 . Suppose f ( x ) = ∞ X n =0 c n x n is the Taylor series representation for f ( x ) at x = 0. Find the value of c 18c 19 + c 20 . Ans. 2 2...
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This note was uploaded on 11/30/2011 for the course EEE 1001 taught by Professor Phoon during the Spring '11 term at National University of Singapore.
 Spring '11
 phoon

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