10.8 Taylor and Maclaurin Series

• Objectives

  • 1. Find Taylor polynomials generated by f at a.
  • 2. Find Maclaurin series.
  • 3. Find Taylor series generated by f at x = a.
  • 4. Find the values of x for which Maclaurin series converge absolutely.
  • 5. Verify statements involving Taylor and Maclaurin series.
  • 6. Find linearization and quadratic approximations for Taylor polynomials.

  Readings and Lecture Videos

  10.8 Taylor and Maclaurin Series.pdf Download 10.8 Taylor and Maclaurin Series.pdf 
• 10.8 Taylor and Maclaurin Series.pptx Download 10.8 Taylor and Maclaurin Series.pptx 
• m2414 10.8 Taylor and Maclaurin Series-20221126_191450-Meeting Recording.mp4 Links to an external site.

https://www.mathsisfun.com/algebra/taylor-series.html#:~:text=Example%3A%20The%20Taylor%20Series%20for,%2B%20x55! Links to an external site.

Example 1 Finding the Taylor Series of f(x) = 1/x:  https://mediaplayer.pearsoncmg.com/assets/teu14_10_8_1 Links to an external site.

Example 2:  Finding the Taylor Series (Maclaurin Series) of f(x) = e^x at x =0:  https://mediaplayer.pearsoncmg.com/assets/teu14_10_8_2 Links to an external site.

Example 3: Find the Taylor Series (Maclaurin Series) of f(x) = cos x at x =0:  https://mediaplayer.pearsoncmg.com/assets/teu14_10_8_3 Links to an external site.

Example 4: m2414 10.8 Taylor and Maclaurin Series-20221126_191918-Meeting Recording.mp4 Links to an external site.

Checkpoint Find the Maclaurin series of f(x) = 1/(x+2)^2 :  https://mediaplayer.pearsoncmg.com/assets/teu14_10_8_4 Links to an external site.