Key Concepts

• • A Maclaurin series (Taylor expanded at x = 0) approximates f(x) as a polynomial
• • T_n(x) = f(0) + f′(0)x + f″(0)x²/2! + … + f⁽ⁿ⁾(0)xⁿ/n!
• • sin x = x − x³/6 + x⁵/120 − … (odd terms only, alternating)
• • More terms → better approximation over a wider range
• • The radius of convergence limits where the series converges to the true function