Math Problem Statement

Explain how taylor theorem formed

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Function Approximation
Polynomials

Formulas

Taylor Polynomial: P_n(x) = f(a) + f'(a)(x - a) + (f''(a)/2!)(x - a)^2 + ... + (f^(n)(a)/n!)(x - a)^n
Taylor Series: f(x) = Σ (f^(k)(a)/k!)(x - a)^k, k=0 to ∞
Error Term: R_n(x) = (f^(n+1)(c)/(n+1)!)(x - a)^(n+1), c ∈ (a, x)

Theorems

Taylor's Theorem

Suitable Grade Level

Grades 11-12, Undergraduate