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. Y

Question

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| <= _________

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3 months 2021-07-25T17:59:54+00:00 1 Answers 1 views 0

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    2021-07-25T18:01:50+00:00

    Answer:

    0.0032

    Step-by-step 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 :

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

             $\leq \frac{3}{(3+1)!} |-0.4|^4$

             $\leq \frac{3}{24} \times (0.4)^4$

             $\leq 0.0032$

    Therefore, |Error| ≤ 0.0032

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