Pade approximants are rational functions used to approximatemore complicated functions

Chapter 10, Problem 39

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Pade approximants are rational functions used to approximatemore complicated functions. In this problem, youwill derive the Pade approximant to the exponential function.(a) Let f(x) = (1 + ax)/(1 + bx), where a and b areconstants. Write down the first three terms of theTaylor series for f(x) about x = 0.(b) By equating the first three terms of the Taylor seriesabout x = 0 for f(x) and for ex, find a and bso that f(x) approximates ex as closely as possiblenear x = 0.

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