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| <= _________

Answer 1

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