Point of Approximation

Definition

The point of approximation is the specific location (x-value) chosen on which we base our Taylor polynomial approximation. It serves as a reference for estimating values close to it using higher-order derivatives.

Related terms

Taylor Series Expansion: An infinite sum representation used to approximate functions by expressing them as polynomials based on their derivatives evaluated at a particular point.

Order/degree of polynomial: Determines how many terms are included in our Taylor polynomial approximation, reflecting how accurate our estimation will be around the chosen point.

Convergence Interval: The range or interval within which we can guarantee that a Taylor series converges and accurately approximates the original function.