The **Taylor formula** is a representation of a function as an infinite sum of terms, calculated from the values of its derivatives at a single point. This formula allows a smooth function to be approximated as a polynomial near that point. The **Taylor series** is typically written as:

\[
f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f^{(3)}(a)}{3!}(x-a)^3 + \cdots
\]

In general, for a function \( f(x) \) that is infinitely differentiable at a point \( a

Explore the Taylor formula, a powerful tool in calculus for approximating functions using a series expansion based on derivatives. Learn how to use this formula to express functions as polynomials around a specific point. Suitable for undergraduate students studying advanced calculus topics.

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