We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
GO TO SAT PREP GO TO ACT PREP
Series

Series

Taylor and Maclaurin Series Examples

Example 1

Graph the function f(x) = ex. Then add, on the same set of axes:

(a) the first-degree Taylor polynomial for f(x) at 0.

(b) the second-degree Taylor polynomial for f(x), centered at 0.

(c) the 3rd-degree Taylor polynomial for f(x) at 0.

(d) the 4th-degree Taylor polynomial for f(x) at 0.

(e) the 5th-degree Taylor polynomial for f(x) at 0.

Example 2

What is the Maclaurin series for f(x) = ex?

Example 3

Find the MacLaurin series for f(x) = sin x.

Example 4

Find the second-degree Taylor polynomial for  near x = 4.

Example 5

Find the Taylor series for the function sin x near .

Advertisement