Taylor Series and Maclaurin Series

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Presentation transcript:

Taylor Series and Maclaurin Series

Taylor Series and Maclaurin Series The following theorem gives the form that every convergent power series must take.

Taylor Series and Maclaurin Series The coefficients of the power series in Theorem 8.22 are precisely the coefficients of the Taylor polynomials for f at c. For this reason, the series is called the Taylor series for f at c.

Example 1 – Forming a Power Series Use the function f (x) = sin x to form the Maclaurin series and determine the interval of convergence.

Taylor Series and Maclaurin Series