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S1 K3,5282i K3, 12...

Question

S1 K3,5282i K3, 12

S1 K3,528 2i K3, 12



Answers

12. $$\frac{s+1}{\left(s^{2}+1\right)^{2}}$$

Yeah, for that Waas O minus two is a Squire minus three years minus two. Or is in the case last one. So this can bring in as lap less worse. Off uber is Class B over age plus one. Last see over is less fun. That's the ball. Will finding the CBC, Canada's Ben Carson friction. So, fist, If all this is a over case Plus the over is class one class. See your age one. But this one is equal to minus two with Squire minus three is minus. Do or is last one. Now we find the value off is equal to minus two. Me is equal, They see is people Wow for them. We have the left listening. Worst off minus do over is last judo class one over age class one will inspire that is equal to minus two last T to the Power dynasty. So this is the lab

Okay. Hey, guys. In this problem, you're told that I

It's probably given the intuition I did 14 15 16 17 north To solve this, you're gonna need these little facts right here. That idea zero is one eye's ableto I I squared is equal to negative. What I cubed is equal to make by pattern repeats. Well, using this pattern, it is clear than on it. Of the 14 he is going to be the same is going to be the same. Power is going to be the same as I squared. I switch is negative once and literally I to the 15 is going to be I cubed, which is negative. I I to the 16th Who's gonna be equal to you? I to the fourth or high zero which is one and I to the 17 is equal to you. I the first, which is ah, which is I. And if you add all of these are you get the value zero and that is inter choice A in the problem Now the reason why I was able to get these steps is because you take the module is of the expert. You see that these exponents of five repeats of

So in this problem were asked to find the applause inverse of this function here, in a good place to start is by breaking this up into two returns that we can, uh, mess with. So let's go ahead and break this up into e to the negative to s over s plus two. And then we're gonna minus three e to the negative for s over. Ask. Plus two. Breaking this up even further. So we'll go term by term. What's to his first term? So we can say e to the negative to s. It's multiplied by one over s plus two. We're going to minus three e negative for us. That's also multiplied by one over s plus two. Okay, so now we have our function split up into something that's a little bit more easy to manage. Will go to our tables. We can see that you'll applause in verse. Something that looks like he to the negative A s. We know that in verse is going to be the unit step that turns on at T equally A. Likewise, when we take a look at something that looks well right over here, something that looks like one over s plus a we know little applause. Inverse of that. It's just e the minus 80. Okay, so now that we know where arl applause in verses were good going to go, we can go ahead and start evaluating the inverse of each one of these terms. So when we do the first term, we know that. So that applause in verse of e to the negative to s that's going to turn into you t minus to so a being to in this, uh, turn right here in practices. Okay. Likewise, when we go over to here in lacrosse in verse of one whoever s plus two, we can see that that's going to goto e to the minus two t. So a being are too in this train here. So go ahead, scroll down. So we're going to Dio is we're going to do the second term. So let's call this the first term here, So let's do it for the second time. It's a little A plus e to the negative four s that's going to equal you c minus four. And likewise, when we dio the second term over here, we still have the same one over s plus two. However, we can see that we have a constant out front here. You could put that constant either on this or on this. It doesn't matter. But what? We're gonna write it out here just so we could duplicate it. So the plus in verse say we have that constant out here. Three over s plus two. Now, that three. I just I just brought that constant in here just so we can keep track of it. So three over s plus two funny bracket anyways, that will go Teoh three times e to the negative to t. Well, see, that's the second term. Okay, so what we're going to do here is we're going to further evaluate it. So let's go ahead and put these two together. So the first term we know we have e to the negative to t and that's multiplied by at first unit. Step turning on it. T equals two. And we know we haven't minus three e to the negative to t in that unit. Step is turning on at tees equaling for, uh, okay, but recall that we want to get it into this for so half of T minus a well supplied by you of T minus A. We want to get into this form, but we haven't got got there yet. So when we evaluate this first term to try and put it into f T minus a U T minus eight, we could see that are a term is to here. So what we're actually going to do is we're going to put that to term, and we're going to put it in up in this exponential. Wherever we see T, we're gonna put a parentheses, and we're going to go t minus two. That turns out to be e to the negative, too. Multiplied by T minus two, we're going to multiply that by U of T minus two, the parentheses there. Okay, same thing here. But this time our a term in F A T minus a youth team I say is four. So we're going to put that four in conjunction with parentheses inside, where this teak will receive this G. So we're gonna have three minus three you to the negative to correct the seas. T minus eso a Here's for have t minus four in parentheses and then we could have that unit step T minus four. So this is the complete low class in verse of that function up top.


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