5 answers

J Jusu" 374a8A1F 4eiytt<0a tMAI

Question:

J Jusu" 374a8 A1F 4eiytt<0a t MAI


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\begin{equation}
\begin{array}{l}{\text { F. } \mathrm{NOCHANGE}} \\ {\text { G. } 1} \\ {\text { H. } \mathrm{me}} \\ {\text { J. } \mathrm{it}}\end{array}
\end{equation}

.

Or to reading glasses make you So we are going to discuss what compound we can get man or to johnny in the presence of the jury in a restroom. Okay. So what is the structure of the organization? No or two billion structure is this man correct? So when it is reacting with three journal, then God will compound. We have to bring that development like this and we have to add development oxygen this name. Let's go.

So what we can get from here, we are getting CS three suitable Mommy. Uh huh. Theater from this? Yes or no From this. We are getting also CS three theatre. So we are getting to all of us.

No. And here we are looking to see you too. Let's see you too. The two Blood Theatre. So correct me if I'm gonna get the vote correct? Absolutely.

Okay deep. So he's looking at it upside. Okay, right..

Hi. We're finding the lap. Last transformer off T B to the two. T coast off five t. Now, to do this, we are going two, Um, use the symmetry.

Properties of the lap last transform. Now, when you multiply a function by t, it corresponds to differentiation in the transform domain. And we're supplying by an exponent. Corresponds to a shift in the lap. Last transformed Elaine.

So if we apply the functional across transformer s, that's gonna be saying the same as the lack last transform the 1st 5 t differentiated. That s minus two. Now, the last left or three once by my teeth. The famous maybe sip derivative. Now to find the derivative of the lap last transfer, of course, five t.

First, we have to recall what the lack last transform. Of course, party is, uh, looking at a table is the famous s over s squared plus 25 we're now taking the derivative of this. Now we can apply the product rule differentiating the talk. We get one of X squared plus 25 different chasing. The foursome gives us gives us two x squared over a squared plus 25 squared.

Therefore, if we now look at the past transform here, this is going to be equal to, uh, won Over s minus two squared. Plus 25. The gazes plus two s minus two squared over. Yes, my nephew squared plus 25. And this is sweat.

Now, if we simplify this, we find that we can run the lack west transform as f minus. You squared minus 25 over s minus two squared. Plus 25 right..

Problem. We're asked to calculate the lap last transform of the function e to the negative t sign to t. And to do this, we're just gonna work directly from the definitions integrating each of the negative x t times using the negative t sign to t t T. Now to integrate this, we're just gonna apply a integration by pots. In this case, we're gonna combine these two terms to be able to e to the one plus s thymus negativity.

If we perform the integration by parts anti differentiating this, we're gonna obtain the value negative one of the one plus s corresponding to this negative one plus ask it times E to the negative one plus s T sign to t evaluated at zero. An infinity minus differentiating sign to t gives you to sign coast t. So this equation is e to the negative one plus s t coast to t. Nice thing here is you can also perform an integration by parts to evaluate this side on dhe. This side is completely annihilated because sign of zero zero and each the negative infinity is infinity performing in integration by bus again be obtained.

This is equal to negative to over one plus s squared times e to the negative form plus s t coast to t evaluated at zero and infinity plus two times the integral of each of the negative one plus s t coast True T. Now, unfortunately, these terms are annihilated. If we can't fight them will find that the value of infinity is zero. But the value of zero is one to obtain that this is eagle to negative to over one plus s square minus four over one plus s squared times this integral which you're recognize as the black last transform Look e to the negative t coast duty evaluated s which is nice because we've expressed the lack last transform of a function in terms of itself. If you rearrange this equation will get, uh, that's, um, one plus four over one plus s square times the lack life transform with you to the native t sign to t uh, evaluated.

It s people to to over one plus x squared. And now dividing on this side and simplifying we obtained the lap. Last transform is gonna be equal to two over one plus X squared plus four.

This problem we're gonna be using lap has transformed tables to evaluate the lack class. Transfermarkt t sweat minus three. T minus to you to the negative t sign three t. This is easily done by linearity. It means we only need to calculate the lack.

Last transport squared, the last last transom of tea and the last last transform of each of the negative D sign three teams. Now, the last ransom of T squared is quite easy. It's equal to two over s cubes. House transom of T is equal toe one of the square on the blacklist transform of each of the negative. T sign three t is gonna be equal.

Tow three over s plus one squared plus nine and that's it..

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