Question

Let f be the function given by f(x)= e^(-2x^2) (read as e raised to the negative 2 x squared)

(a) Find the first four nonzero terms and the general term of the power seriews for f(x) about x=0.

(b) Find the interval of convergence of the power seriews for f(x) about x = 0. Show the analysis that leads to your conclusion.

(c) Let g be the function given by the sum of the first four nonzero terms of the power seriews for f(x) about x=0. Show that l f(x) - g(x) l < 0.02 for -0.6 less than or equal to x less than or equal to 0.6.