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Problem 47 Medium Difficulty
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} $
Answer
$$\sum_{n=1}^{\infty}(-1)^{n-1} \frac{x^{n}}{(n-1) !}$$
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Video Transcript
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
Top Calculus 2 / BC Educators
Grace H.
Numerade Educator
Heather Z.
Oregon State University
Kristen K.
University of Michigan - Ann Arbor
Samuel H.
University of Nottingham