Let f(x) = e x .

(a) Find the Taylor Series for f about the point x = 0. Include two or three versions of the remainder term.

(b) Find the minimum number of terms needed to compute e with an error less than 108 .

(c) Find the minimum number of terms needed to compute e 2 with an error less than 2m. Your answer should be an inequality.

(d) Suppose we use the Taylor polynomial of degree n = 2 to compute e. Determine the error bound given by this approximation.