Taylor Series

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    19-Jan-2016

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Taylor Series. Theorem. Definition. The series is called the Taylor series of f about c (centered at c). Definition. The series is called the Maclaurin series of f about c (centered at c) Thus a Maclaurin series is a Taylor series centered at 0. Examples I. - PowerPoint PPT Presentation

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  • Taylor Series

  • Theorem

  • DefinitionThe series

    is called the Taylor series of f about c (centered at c)

  • DefinitionThe series

    is called the Maclaurin series of f about c (centered at c)Thus a Maclaurin series is a Taylor series centered at 0

  • Examples I

  • Example (1)Taylor Series for f(x) = sinx about x = 2

  • Taylor Series for sinx about 2

  • Example (2)Taylor Series for f(x) = sinx about x =

  • Taylor Series for sinx about

  • Example (3)Taylor Series for f(x) = sinx about x = /2

  • Taylor Series for sinx about /2

  • Example (4)Maclaurin Series for f(x) = sinx

  • Maclaurin Series for sinx

  • Example(5)The Maclaurin Series for f(x) = x sinx

  • Examples II

  • Example (1)Maclaurin Series for f(x) = ex

  • Maclaurin Series for ex

  • Example (2)

    Find a power series for the function

    g(x) =

  • Example (3)TaylorSeries for f(x) = lnx about x=1

  • Taylor Series for lnx about x = 1

  • I-1Taylor Series for f(x) = cos2x about x = 5

  • Taylor Series for cos2x about 5

  • I-2Taylor Series for f(x) = cosx about x = 3/4

  • Taylor Series for cosx about 3/4

  • I.3Taylor Series for f(x) = cosx about x = /6

  • Taylor Series for cosx about /6

  • I.4Taylor Series for f(x) = e3x about x = 5

  • Homework