Let (x) = e x and T 3 (x) = 1 x + x 2 /2 x 3 /6. (a) Use the Error

Let ƒ(x) = e^−x and T₃(x) = 1 − x + x²/2 − x³/6.

(a) Use the Error Bound to show that for all x ≥ 0,

(b) Illustrate this inequality by plotting y = ƒ(x) − T₃(x) and y = x⁴/24 together over [0, 1].

\f (x) - T3 (x) | s | 24