# Taylor and Maclaurin Series

Taught by Houston
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Meets NCTM Standards:
Lesson Summary:

In this lesson on Taylor and Maclaurin series, we learn about the power series representation of functions and how to find the coefficients of their terms. We also explore the Taylor series expansion of a function about a given number x0 and the conditions for its convergence. We see examples of finding the Maclaurin series for e^x, sin x, and cos x, as well as using Taylor series to find the closed form of power series. Overall, this lesson provides a thorough understanding of power series and their applications in mathematics.

Lesson Description:

Maclaurin series. Expansions of e^x, sin x, and cos x, and related series. Taylor series expansions about x0.

Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.

• What is a Taylor Series?
• What is a Maclaurin Series?
• How do you find a Taylor or Maclaurin series?
• What is the Maclaurin series of e^x and e^-x?
• What is the Maclaurin series of sin x and cos x?
• What is the Maclaurin series of sinh x and cosh x?
• What is sinh x?
• What is cosh x?
• How do you find a closed form of a power series?
• What is the Taylor series expansion of sin x centered at pi/4?
• What is the Taylor series expansion of square root of x centered at 1?
• What is a double factorial?
• #### Staff Review

• Currently 4.0/5 Stars.
Taylor and Maclaurin Series are explained and defined using power series. Then, some of the most famous Maclaurin series are found. Several examples of finding closed forms of power series are shown. Finally, Taylor Series centered at x0 are shown. Some really great images and animations are shown for these series.
• #### naklugman

• Currently 4.0/5 Stars.
well put together, although could have used some more in between steps on how to find the final summation equation