Let x0 = 0.5. Given f (x) = −2e−x + 1/4x4 − 1 120 x5 + 2x f ′(x) = 2e−x + x3 − 1 24 x4 + 2 f ′′(x) = −2e−x + 3x2 − 1 6 x3 f ′′′(x) = 2e−x + 6x − 1 2 x2 f (4)(x) = −2e−x + 6 − x f (5)(x) = 2e−x − 1 f (6)(x) = −2e−x (a) (5 points) Find the Taylor Polynomial, T3(x), of degree at most 3 for f (x) expanded about x0. (b) (5 points) Give the general error formula for f (x) − T3(x) for any x. (c) (5 points) Find the absolute error in using T3(0.65) to approximate f (0.65