College Calculus II Unit 4

Taylor Polynomial to the nth order centered at x = a

p_n = f(a) + (f’(a) / 1!)(x - a)¹ + (f’’(a) / 2!)(x-a)² + … + (fⁿ(a) / n!)(x - a)ⁿ

Remainder of a Taylor Polynomial

R_n < (M / (n + 1)!) * |x - a|^{n + 1}, where M is the maximum value on the interval (a, x)

Absolute error of a Taylor Polynomial

|actual - theoretical|

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