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Froj 4he cverase Volue Find Fuhctloa FU -Cosls7) 0+ +he Hhe interVc l [e 0Ver...

Question

Froj 4he cverase Volue Find Fuhctloa FU -Cosls7) 0+ +he Hhe interVc l [e 0Ver

Froj 4he cverase Volue Find Fuhctloa FU -Cosls7) 0+ +he Hhe interVc l [e 0Ver



Answers

Find $f^{\prime \prime}(x)$ $$ f(x)=e^{x} \sin x $$

In discussion and is about the introduction to the moon. Variable function on the pushing name is about the function f Thanks. Why people would you do the next blood the lock, waste and land off the X plus y? And then the question asked us to find a the half after 10 and then way have to find the f off to that's one in C. We have to find half on the zero. The indeed we have to find the f on this. So about you. And before we go to the answer, I just want to review a good definition off the function. So I have Okay. Why? Okay. Mm. Of function? Yes. For each input, every my dad does will be called input. Thanks. Why way? Get exactly one. Uh, I recall this one will be, uh, Z. Okay, So it means that we only have for each input, we will have exciting One are put on. We can really function will be some black box, which is we don't know. Whatever inside on, we're going to put some in creating inside. So we would ingredient X Also, we would increasingly we're inside on then after it will run through the procedure to get the output will commit with Z on in this particular discussion Here we have this function. I'm in the process. We had to compute the f off the one on Dhere. We are given the X equals G one on why equal to the zero. So all we need to do will be Whenever we see the X, we could put the one I don't know. We see the why we would Brazil therefore also get close you now the function here we will have e to the power off X So we will have the evil one here must at land off the X now equal to one on the whiner, equal to zero on now The next step will be re signifying the expression that we get Egypt one inches. Britain, The I 30 on one puts ones who have the land after one but remind you that the and I'm the one ever equal to the zero therefore equal to the team Eventually And this would be the answer for the I. And now similarly we can do the B. We have we have the half after the two minus one on again. We will replace the X by the two. And why? By the minus one And then we will have you go to the the off the two because accidentally comes to us. Learn off now X equal to two lost one equal to the minus one. And after some education, we will have the about you which is a bit about you. This one we have two minus one equal to the one. So we have another one again. And another one equal to the zero. So eventually we will have to be about you. This will be the answer for the B. Now again, we would do the posse where we have the half on the zero on. Why equal to the T. So here we have X equal to zero. Why equal to the B on my way to replace X y into the function. So we have about X now we culture the zero. Yes. How long Now execute 20 Why equal to D P? And then here we have any number of hours. They must equal to one love. There are just a little too Is so we have an under a on remind you that it's illegal to the one. Therefore, we have the one last 1 to 2 on. This will be the answer for the past. See? And now the last one will be the party. We will have the f off the zero for the X Y equal to the square. So here we have X equal to zero. Why equal to about you and again we replace it and then we get the zero mhm and then off the now actually go to zero. I mean, why you go to the the to and then we get any number of 50 equal to one plus zero plus the square equal to the island, that square And here one property number laugh. We can bring the power to the coefficient and then we get equal to the one plus Thio a on again along the equal to one. So eventually we have one blood two times. Once we're able to relative to three on, this will be the answer for D, and that's it

Hi in discussion we're going to review the monte variable function. So we recall about some definition here. So we recorded that monty verbal function. F. X. Y. Yeah. A uh function If far H pair Vario of X. Y. We have one hour boat. F. Thanks. Why? So in this question we have the function F. Thanks. Why is the fight as each of the power X. Plus and land after X. Plus Y. And we have to find a. The F. Of 10 be when you fight the F. Of the tu minus one. See where did you find the value of the F. Zero? E. And indeed we had to find the F. Of zero. He about you. Now let's do the part I. First here we notice that the one here would be the value of the X. And zero will be the valuable. Why? So in the part A. We want to find a F. Of the 10. And here on you need to replace the act by the one and why? By the value zero. So therefore we should get the power one plus a line off the one plus zero. And we should get the evil one. We can write S. E. Plus one plus zero equals to one. So we have ended up one and we know a line of one equal to zero. Therefore ended and we have the A. Plus zero equals B. And similarly we can do the B. So we want to find the f. Of the tu minus one. So in this case now this will be the eggs and this will be the Y. And therefore we can get the answer will be a power to plus and land of the two plus minus one. And that's when we have a power to plus. Now the haunting here will be an end up one and I learned one equal to zero. Therefore we have the evil two plus zero and equal to evolve to. Now we will continue to do the pot C. And D. Similarly we can do the C. F. Under zero. E. So in this case act go to zero and why you go to E. And as a result we have E. B. Zero plus and lands on the zero plus D. And equal to E. B. Zero equal to one. So we can write this one will be one plus not soon be and line of E. But and then up equal to one. So we have the one glass one. And could you ju now the last part day we have the F. Off zero about you. So we will have something. This one will be the next to zero. And why it could you eat about you? So we have the eba. Zero plus A land of the zero plus the about you. And echo two Again a bow. Is there equal to one plus. And then I'm going to be able to do and we know Ellen able do we use the property of a lock. We can bring the power to the front so we should get the jew and then on the day, but Ellen on the equal to one. So therefore at the end we should get one plus two attempts one and go to three. And that's gonna be the answer found a part a part B, part C, and a party.

Hi in this question we will reveal about the function of two variables. So we define a function F. X. Y. Is a function off two variables. If far each pam X. Y. Yeah we. Uh huh. Exactly one. I'll put F. Thanks Why? And in discussion we are given the F. Thanks why echoed through the each of our X. Plus and then on the X plus Y. And in the part way we have to fight the F. Of 10. Here we noticed that the value one would be the value of the X. The value zero will be the value of the Y. So all we need to do will be replaced the X. By one and then the wife by zero. So if we do that we should get the E. Power one plus a land after one plus zero. And we get the evil one would be E. Plus one plus zero would be one. So we have another one. But we know Ellen I'm the one echo to the zero. So therefore we sugar the A. Only. And this will be the answer for the part. I similarly we can do the puppy. And about be asking that you find the F. Of the two power and then why would you want this one? So we should get to go to something that you will be developed. X. The man is only be developed of wine. We looked in and we get to E power to plus a land of the X. Now chu. Why? Equity minus one. So we have the power to plus Now chairman is going to be equal to one and one. It will be equal to the zero game. So we'll be chew. And this will be the answer for the party. Something we do the sea where we have to find a F after zero. So zero would be the volume X. It will be the first to y. And then we look into Ghenda Evil zero plus a land of zero plus E. And we obtain even zero. We get equal to one plus zero plus equal to E. So we have an N. B. And a line of equal to one. So we have one plus one and equal to two. And this will be the answer for the sea. Last one D went to find the F. Of zero about you. So we have this one X. Equals zero. And why I called you about you. So we can have the Eva zero plus a land of the zero plus even to do we get Eva zero equal to one. Their blood is square will be about very about you and Ellen about you using the property of the lock. We can bring that to the front together to and then under a so there's an echo to the to only So everything comes up with the one plus two and three. And this will be the answer founded D.

We're told that half of ax equals sign of axe and capital F of T equals little F of t squared minus one. So that means that we're gonna we're basically saying that this is X right here, T squared minus one is X. And so they want us to find the capital F DT? Well that's the little F D X at times. Um this dx did he and dx DT is just to T F prime of X driven over the sign is simply the co sign. So we get to t co sign of X, which is t squared minus one. and so evaluating that one, that was one, we get that we get this is zero in here, so this is one and this is one, this is one. So we get to. So this is really just a pretty a simple application of the chain rule where we could have actually written F of T out explicitly and that's just sign of He squared -1. Again just applied the chamber. But they basically broke it up for us. They broke it up for us here in terms of these two functions, and we just needed to identify the relationship between X and T. So whatever we're putting in the function here, we're gonna get that X.


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