tmt1
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I am examining the polynomial approximation for $e^x$ near $x = 2$.
From Taylor's theorem:
$$e^x = \sum_{n = 0}^{\infty} \frac{e^2}{n!} (x - 2)^n + \frac{e^z}{(N + 1)! } (x - 2)^{N - 1}$$
Now, I don't get the next part:
We need to keep $\left| (x - 2)^{N + 1} \right|$ in check so we can specify $\left| (x - 2) \right| \le 1$ so $x \in [1,3]$.
From Taylor's theorem:
$$e^x = \sum_{n = 0}^{\infty} \frac{e^2}{n!} (x - 2)^n + \frac{e^z}{(N + 1)! } (x - 2)^{N - 1}$$
Now, I don't get the next part:
We need to keep $\left| (x - 2)^{N + 1} \right|$ in check so we can specify $\left| (x - 2) \right| \le 1$ so $x \in [1,3]$.