A 3 - Taylor expansion and error estimate 3.1 Compute the Taylor expansion of the e-function f(x) = er around point 0. Also give the formula for the expansion coefficients. 3.2 What is the meaning of the convergence radius r of a power series? Compute the conver- gence radius of the Taylor series for f (x) = ex. 3.3 The function g(x) = - shall be approximated by a Taylor expansion in the intervall [0, 1] with an accuracy of one per mill at least. Up to which order has the Taylor expansion to be evaluated? Then compute 1/e up to this order and estimate the maximal error