A Taylor polynomial is a polynomial used to approximate a function. It is centered at a point $a$ and its degree is $n$. The Taylor polynomial of degree $n$ for a function $f$ at a point $a$ is given by:
\[P_n(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 +
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