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Use the Taylor series generated by $e^{x}$ at $x=a$ to show that$$e^{t}=e^{\alpha}\left[1+(x-a)+\frac{(x-a)^{2}}{2 !}+\cdots\right]$$

$$e^{=} e^{a}\left[1+(x-a)+\frac{(x-a)^{2}}{2 !}+\dots+\frac{(x-a)^{n}}{n !}+\cdots\right]$$

Calculus 2 / BC

Chapter 10

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

Series

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:59

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

14:11

In mathematics, the partial sums of a series are the sums of all terms of the series except possibly the first and last.

00:50

Use the Taylor series gene…

Use the Taylor series for …

03:35

01:04

01:30

problem 41. We want to compute its head. Nurseries about acts eat It acts when accidents equals to a So you get the ax. The crime is also you two decks. So oh, eat attacks His ego's too Martin from zero to infinity eats with the A united by an factorial and time sex Finest A pretty head Okay, so just you today is this part Ah X minus A to the antibody by end It's just this serious, so the big question is true.

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