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Imagine that you need to compute e^0.4 but you have no calculator or other aid to enable you to compute it exactly, only paper and pencil. You decide to use a third-degree Taylor polynomial expanded around x =0. Use the fact that e^0.4 < e < 3 and the Error Bound for Taylor Polynomials to find an upper bound for the error in your approximation.

|error| <= _________

User JohnHC
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1 Answer

3 votes

Answer:

0.0032

Explanation:

We need to compute
e^(0.4) by the help of third-degree Taylor polynomial that is expanded around at x = 0.

Given :


e^(0.4) < e < 3

Therefore, the Taylor's Error Bound formula is given by :


$|\text{Error}| \leq (M)/((N+1)!) |x-a|^(N+1)$ , where
$M=|F^(N+1)(x)|$


$\leq (3)/((3+1)!) |-0.4|^4$


$\leq (3)/(24) * (0.4)^4$


$\leq 0.0032$

Therefore, |Error| ≤ 0.0032

User Zulay
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