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Use multiplication or division of power series to find the first three nonzero terms the Maclaurin senes for the given function. (Enter vour answers as comma separa...

Question

Use multiplication or division of power series to find the first three nonzero terms the Maclaurin senes for the given function. (Enter vour answers as comma separated list )y = e'X Inf 1 _Need Help?Erm

Use multiplication or division of power series to find the first three nonzero terms the Maclaurin senes for the given function. (Enter vour answers as comma separated list ) y = e'X Inf 1 _ Need Help? Erm



Answers

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for each function.

$$y=e^{x} \ln (1+x)$$

The problem is use multiplication of division of power. Siri's to find Arrested three. Nancy returns in the McClaren series called Each Function. Why is he so to each black stamps out in one us Max, First of all, have to axe is safe too. One class specs us exploit told me to us. Access three over six plus dot, dot, dot one Last act. This is the cultural X minus. X squared over it too. US. Axe killed over three minus x two four over for us dot, dot dot And why is he could into x times now Want us, Max? It was the first term. Thanks. Degree of AKs. Secret who? Why? But the degree of axe is a to half. This is us X squared and minus exclaimed over two. Help for the power power off axes sickles three Behalf one times X cubed over three ex terms a negative. X squared over two on DH X squared over two comes. Thanks us. Don't Don't don't. This is a call to ACS. US. X squared over two is this plus X killed over three. Ask times. Don't don't

The problem is years. Much publication of the vision of power. Siri's to finding the first of three Nancy returns in My club series. Which function? Why secret talks interacts time Sign Ex boy. So first sign Aye, Squire is home to one month's sign. Two mikes over. It's you. Please assign two packs assigned to axe Single too one minus to squire, over to us to X to the power for over or factorial minus two packs to the power of things over six. Bacterial Scott Don't, which is in control. Juan Linus Explain class shoot times X to for over three monster dot dot So we have sine X squire. This in court, too. One man is cosign tracks over to which is it going to x squared? Two minus thanks to the public for over three and last dot, Dot, dot into Axe and psycho, too. One plus X aspects Squire for Britain to US X Cube off three. Factorial trust dot, dot dot So have I. Why is he would be to act ham sign X Square. The first term X squared over two second terminus. Thanks Q House two. Chairman X squared over two times X corner over too minus thanks for over three. I start that dot It's a sequel to exclaim over too. Plastics Q. Over, too, and Max the oneness to power for over four minus packs to or with reasons it's negative access to the public or over twelve must dot, dot dot

So for this problem, we want to use the multiplication of division of power Siri's in order to find the first three, none zero terms in the MacLaurin series. So we're given the function y equals e to the negative X squared coastline X. So we already know that co sign X McLaurin Siri's were given it already in table one. If you want to refer to that and it's negative one to the N of X to the to end time over two n factorial. So with that in mind, we also have e to the negative X squared, Equalling the sum of an equal zero to infinity of negative X squared to the end over in factorial. So with that in mind, another way we could write this would be if we want to rewrite it. We could write it as, um, negative one to the end. Since that's often preferred notation Negative one to the end times X to the two n over n factorial. So that being said, we see that four terms of each will probably be enough. So the first four terms of this will be one minus x squared over two factorial put us back into the boards over four factorial minus X to the sixth over six sectorial. And that obviously keeps going on. But we don't need any more. And then this is gonna be one minus X squared over two factorial plus X to the fourth over two factorial. Um, actually, this will be just X squared, Um, minus X to the sixth over three factorial and then plus go on. So what we'll do is we'll multiply these terms. So what we're gonna end up getting as a result is this right here and then we're gonna multiply this Bye. This right here. So when we do that, what we're gonna end up getting as a result, is simplifying it further. We'll get about one minus X squared over to minus two X squared over two. So these will combine to give us a negative three x squared over two so we can do that right there, and then we'll get plus X to the fourth over 24 plus two x to the fourth over to turning this into 24 will make this into 24. So we'll end up getting 25 x to the fourth over 24 so those would be our first three non zero terms within the MacLaurin series for the specific function.

The problem is use much application of division of power. Siri's to find the first of three Nancy returns in the micro miniseries for each action. Why is he going to obtain in the X Squad? So first behalf I can Didn't axe? Is that true? Linus X Cube over three. Last access Over Linus back. Someone selling Don't don't don't anything cams X minus x Q three x two over far minus x seven over. Someone starts dot dot But the first German MRIs X How's Max exploiter? Generous axe terms Negative facts cubed over three This town negative X cubed over three last negative X cube over three times Specs, then thirty. Germany's Axe Holmes, thanks to the power five over minus plus Tax Cube over three times X Cube over three. Plus I just power foul off our backs Start. This is equal to a tax lawyer minus to food. From sex to the problem for you. Class is this is twenty three over forty five. How kind towards Apartment six last night


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