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"Centered" in the context of Taylor polynomials means choosing a specific point on the x-axis around which we construct our polynomial approximation. This point is often denoted as "a".
An interval refers to a continuous portion of numbers on the number line between two points.
Endpoint: An endpoint is one of the boundaries that define an interval.
In calculus, radius often refers to how far away from the center point (in this case, "a") we extend our approximation using Taylor polynomials.