Taylor's

Taylor's theorem provides a way to approximate complicated functions using polynomials based on their value and derivatives at a specific point. Essentially, it expresses a function as a sum of terms that involve the function’s derivatives, allowing us to estimate the function's behavior near that point. This is useful in calculations, modeling, and understanding how functions change. The more terms we include, the more accurate the approximation becomes. It's widely used in mathematics, physics, and engineering to simplify complex functions and analyze their local behavior.