determine *analytically)the smallest degree taylor expansion that is needed to a

Question

determine *analytically)the smallest degree taylor expansion that is needed to approximate f(x)=ex-1/x

such that the absolute error of the approximation is no more then 10-14 for all   x[o,1/2].

{note: to get taylor expansion of f ,start with a general taylor polynomial   for ex at x=0 and build a taylor expansion for f........also note that for values of close to x=0 the taylor expansion will be an approx of

limx0 ex -1/x}

request: plz solve it step by step and clearify it to me.............tnx

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