Let (x) = e x and T 3 (x) = 1 x + x 2 /2

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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,

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

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

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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