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Make the given changes in the indicated examples of this section, and then find the resulting series.In Example 3 , change $e^{x}$ to $e^{-x}$.

Calculus 2 / BC

Chapter 30

Expansion of Functions in Series

Section 3

Operations with Series

Series

Campbell University

University of Michigan - Ann Arbor

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

00:55

Complete the rewriting of …

00:44

00:23

00:41

00:47

Rewrite each series using …

00:36

00:56

Use the methods of this se…

00:45

00:32

In Exercises 1 - 3, fil…

to find the serious expansion for this expression. We need to find the serious experiencing for a to the power of minor sex. So we just use this formula, you know the substitute X. With minor self. It's one minus X plus X squared true factorial miners. X. Killed or three factor room and plus the acts to a force over four factorial and X. Agile. And next we need to find the serious expansion for co signing up. It just use this formula. It's one miners that square over two factorial plus extra force or full factorial and Aunt Sandra. This echoes While Minors Act squared over two Plus X. to force over 24 miners. It's uh huh execute well virtue and then class ax squared over two Liners. Eggs flows over four miners X square over six. Class extra force over 24 annex natural. And now we come by the similar terms. Eddie calls one Miner's tax plus served facts killed miners 16 X to the 4th and Alexandra. Here, I want to mention a little more about this exercise. Notes out in example three. It's Acts eight to the power of Acts Times cause I ants. And if it's substitute acts with minors X, it becomes E to empower minus X times cosine minus X. This just tickles E to the power of minors. There times co sign X. This is the expression in this exercise. And also if we substitute X with minors act in a series given example three, we also get these results.

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In mathematics, integration is one of the two main operations in calculus, w…

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Complete the rewriting of each series using the new index as indicated. …

Rewrite each series using the new index j as indicated.

$\sum_{i=0}^…

Use the methods of this section to find the power series centered at 0fo…

In Exercises 1 - 3, fill in the blanks.

The change-of-base f…

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