Taylor Polynomials

AP Calculus · Axiom Academy

Approximating functions with polynomials centered at a point The n th-degree Taylor polynomial of f centered at a is: Each term matches one more derivative of f at x = a . All derivatives of e^x are e^x , and e^0 = 1 . P_4(1) = 1 + 1 + 0.5 + 0.167 + 0.042 = 2.708 vs. . Higher degree better approximation near x = a When a = 0 , it is called a Maclaurin polynomial Taylor polynomials are the foundation for Taylor series

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