Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Example 1

Example 1 – Solution

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Taylor and Maclaurin Series

Example 2

Example 2 – Solution

Taylor and Maclaurin Series

Example 8

Example 8 – Solution

Example 8 – Solution

DEFINATION

A power series about x=0 is a series of the form

=+++…….++……… A power series about x=a is a series of the form

=+++….++…. In which the center a and the coefficieants , , ,…., are constants.

THE CONVERGENCE THEOREM FOR POWER SERIES

If the power series =+++……. Converges for x=c ≠0,then it converges absolutely for all x with |x|<|c|. If the series diverges for x=d , then it diverges for all x with |x|>|d|..

RADIUS OF CONVERGENCE In previous explainations there is a number R so that power

series will converge for , |x – a|< R and will diverge for |x – a|> R.This number is called the radius of convergence for the series.Note that the series may or may not converge if |x – a| =R .What happens at these points will not change the radius of cnvergencce.