So, in 10.1 [11.1], you learned about Taylor (and MacLaurin) Polynomials*, then in 10.2 [11.2], we looked at what power series are, and how to find the radius of convergence.
*As prevously mentioned, MacLaurin Series are just a special case of Taylor Series. with the series centered at x = 0 which is by far the most common situation for any power series; i.e., being centered at x = 0.
In this section, we'll put those two concepts together to form Taylor Series, which are a specific type of power series.
Videos:
MacLaurin Series (Note: this video just extends the MacLaurin polynomial development to making an infinite power series.
Taylor Series (expanding about a value other than x = 0)
Assigned Problems from Textbook
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1st Edition Section, Section 10.3 page 714 Find a Taylor Series (using derivatives): 9, 10, 13, 16, 23, 25 Manipulating series (same idea as in 10.2): 29, 30, 31, 33 Concepts: 1, 2, 61ade Combining series, 62, 63 3rd Edition Section, Section 11.3 page 740 Find a Taylor Series (using derivatives): 9, 11, 12, 17, 20, 25 Manipulating series (same idea as in 10.2): 35, 36, 37, 39 Concepts: 1, 2, 67ade Combining series, 68, 69 |