Taylor series visualized
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The Taylor series is a way to represent a function as an infinite sum of terms based on its derivatives at a single point, typically around zero (Maclaurin series). It approximates functions using polynomials, where each term involves higher-order derivatives of the function divided by factorials. For sin(x), its Taylor series expansion around x = 0 consists of only odd-powered terms, alternating in sign, since sine is an odd function. The series begins with x, followed by -x³/3!, then x⁵/5!, an
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