Taylor Series and Approximations

Why It Matters

What is a Taylor Series

Maclaurin Series

A Maclaurin series is simply a Taylor series centered at . It is the most commonly used form because derivatives at zero are often easier to compute.

Common Taylor Expansions

Memorizing these standard expansions is essential — they appear constantly in calculus, differential equations, and numerical methods.

Convergence

Not every Taylor series converges to its original function. Understanding convergence is critical.

Taylor's Theorem with Remainder