Question: 3. Consider f(x) = et, and find a general formula for the Taylor polynomial Pn(x) for f about xo = 0. (a) Using the remainder

3. Consider f(x) = et, and find a general formula for the Taylor polynomial Pn(x) for f about xo = 0. (a) Using the remainder term, find a minimum value of n necessary for Pn (x) to approx- imate f(x) to within 10- on [0, 0.5]. (b) Prove that f(x) analytic on (-00, 00) = R

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