MATH 6B CALCULUS II 11.3 Taylor Series. Determining the Coefficients of the Power Series Let We will determine the coefficient c k by taking derivatives.

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Presentation transcript:

MATH 6B CALCULUS II 11.3 Taylor Series

Determining the Coefficients of the Power Series Let We will determine the coefficient c k by taking derivatives of the functions at x = a.

Determining the Coefficients of the Power Series

Taylor and Maclaurin Series The last series displayed is known as a Taylor Series centered at x=a. A Maclaurin series is a Taylor Series centered at x = 0.

Binomial Coefficients

Binomial Series

Remainder of the Taylor Series n-th degree Taylor polynomial (p n ).

Other Topics Important Maclaurin Series.