1. Let f(x)=e* cos(x).

(a) Give the order 2 Taylor polynomial p2 with c = 픔..

(b) Determine a reasonable constant C such that f(x) - P2(x)| ≤ Cx-³ for all x = [0, 1].

(c) Compute p2(4).

(d) How does the upper bound for your error (part (b)) compare to the actual error |p2(4-

ƒ(4)?