1. (a) Approximate f(x) = (1+z) by finding Ts(r) (the 5th degree Taylor polynomial of f) centered at 0. (b) Find the remainder Rs(z) for the above approximation and use this to show Ts(r) is not actually an approximation of f(x), but it is in fact exactly f(z); that is, Ts(x) = f(x). (c) Consider instead g(x) = (1+z)5/2, Find Rs(r) of g(x) and use this to show Ts(z) centred at 0 is not exactly g(x). (You only need to find Rs(z), not Ts(z)). Furthermore, deduce that for z € [-0.5, 0.5] the absolute error in using Ts(z) to approximate g(z) is bounded by . 8192

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