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The Taylor series for a function $f(x)$ about $a$ is given by:
\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \cdots\]
The nth-order Taylor polynomial $P_n(x)$ is the polynomial formed by the first $n+1$ terms of the
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