Taylor series

A Taylor series is a way to approximate a complex function using a sum of simpler polynomial terms like powers of \(x\). It expresses a function as an infinite sum of its derivatives at a specific point, providing increasingly accurate approximations as more terms are added. This approach allows us to understand and estimate the behavior of functions that are difficult to compute directly, by breaking them down into a series of manageable, polynomial components around a chosen point. It’s a fundamental tool in calculus for analyzing and approximating functions smoothly near a given point.