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Unformatted text preview: x-3) 2-+ ··· + (-x-3 2 ) n + ··· . Ans . 2 x-1 MA1505 Tutorial 3 5. Find the Taylor series for the following functions: (a) x 1-x 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)( x-1) 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 x-1 x to show that S = 1. 2...
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This note was uploaded on 05/10/2011 for the course MATH 1505 taught by Professor Yap during the Winter '11 term at National University of Singapore.
- Winter '11