Math Problem Statement

Find the third order Taylor polynomial at x=0 of f(x)=(1−x)1/7.

Solution

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Math Problem Analysis

Mathematical Concepts

Taylor Series
Polynomial Approximation
Derivatives

Formulas

P_n(x) = f(0) + f'(0)x + \frac{f''(0)}{2!}x^2 + \frac{f^{(3)}(0)}{3!}x^3
Derivative of power functions using the chain rule

Theorems

Taylor Series Expansion

Suitable Grade Level

Undergraduate Calculus