# Taylor Series

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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

### Text of Taylor Series

• 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

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