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Find the Maclaurin series of $ f $ (by any method) and its radius of convergence. Graph $ f $ and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and $ f? $
$ f(x) = xe^{-x} $
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Calculus 2 / BC
Chapter 11
Infinite Sequences and Series
Section 10
Taylor and Maclaurin Series
Sequences
Series
Campbell University
Baylor University
University of Michigan - Ann Arbor
Boston College
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.
02:28
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.
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Find the Maclaurin series …
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It's a problem. Find Michael Aris theories and its radius of convergence. Graff half on his first of your tail upon our meals on the same screen. What do you notice about the relationship between this part? Our meals. So first we have into axe Sacred Psalm on from zero to twenty ax to end our fucked our view. Relax. You see Moto X has Internet access, which is a good X times, some from zero between vanity, negative backs to the power. And really this is called SOM from zero to infinity. You want the power off ham's fax to power Paswan over. In fact, Then they find three years off Convergence Lim and fostering unity have some value ofthe next you want and cold plus one over Pass one factorial tams factorial over Thank you want to spend? This is the limit and cost with unity one over us one. This is Cyril, so the readers of Convergence is a go to infinity. Now let's look at is a graph. The vital curve is the function Ex tells into kickbacks blue on this zero green. Wise to Juan, our in ju on Misty, too. We can see that as and Chris is, he and Max becomes a fighter approximation to function, extends into nectar backs
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