Common functions expressed as Taylor series

 Objective: Recognize the Taylor series expansions of common functions

Earlier we showed how to combine some power series to create new power series.

In the following table we summarize the results for the Mclaurin series of the exponential, logarithmic and trigonometric functions.

Example

Deriving Mclaurin series from known series

Find the Mclaurin series of each of the following functions by using one of the series in the table above

Solution

a. The Mclaurin series for cosx is given by:

Let's substitute x by ⎷x:

b