Homework Exercises: any 2 2 U 20,28, x?1 ~ zez x2) 36 { 32 19 2 4 42 where f (x) 4 4 2 2 % f() 2 <intervol e7 1 2< down 1 dlo ( concave down fumop 0.5 E8 T) ...

In Exercises 27–48, find the open intervals where the functions are concave upward or concave downward. Find any inflection points.
$$f(x)=\frac{-2}{x+1}$$

Okay. Hello. So the ocean is taken Formula less transformation. And the question is find the laplace transformation of 50 for each of the function as defined in exercise. So that will be function is F. 50 is equal to zero. A. T. Line between zero and two and 50 is equal to three at a greater than two. Okay, by definition of lipless transformation, that is equal to they were to infinity into the power minus S. T. F. T. And DT. So F. For face can be read Ernest first zero to T. Two. And that would be zero into ditty because zero multiplied with anything with yourself. Zero there's two infinity into the power minus S. T. F. D. S. D. And then DT So full face will be Uh huh. Uh E to the power minus SD different integration of first function. That is so it is a fast function. It to the power minuses to yeovil minuses minus of integration, differentiation of tea, that is one. And integration of this function divided by minus as into D. P. So from here the value of a first will be equal to T. To the power minus esti over minus of s minus minus plus. So we get into the power minus S. T. So there will be minus are into to the third time and the integration. Second time integration So that would be a square and taking the limit from two to infinity at infinity. The storm become zero at 30 is equal to widget -2. Into the power -2 ways over as minus E. To the power minus two way. So what as square, which is the required laplace transformation of this functionality. Hope this clears your doubt and.

Hello. So the Russian is taken from laplace transformation and we have to find the laplace transformation of the given function. So given the value of function is it's evil at T lying between zero and 2 and and its value is equal to E. To the power minus of T. T. Is greater than two. So by definition of laplace transformation we can evaluate it? S into the power minus S. T. F F. T. Ditty. So that would be equal to the to the power minus T. T. To the power minus ste DT integration limited from zero to infinity. And we can divide it into two past so first party zero and second parties uh to to infinity. So if we solve it we get it's value is equal to My nurse off as Plus one into T. DT limit is from two to infinity. So its integration will be to the minus as plus run into T. Divided by minus of this place one and limit goes from to infinity. So substituting the limit we get zero. Yeah plus E to the minus two as plus one over X plus one. So the correct answer for discussion is It would be -2 x plus one Who work as Plus one which is studied by a solution of the ocean who disclose it out and thank

Person growing even the function If thanks, you go to Tim's age about when it's next square. And it was that we need to find a every my bags way. Should get a good job agent about minus X squared and when a general religion would apply by the derivative of the power here So I could have missed two X Therefore, gonna Gautam as far actually a modest thanks gram. And now the secondary within the function here, we need you blind. A broader rule here and then once again, the minus far agent a minus X squared minus next square. And now we have ah uh, plus minus far x times with the age of minus next square and by the general manager of times minus actual eggs, it will be infected a minus four agent when it's exquisite outside in So everyone on then my my, uh to x square. And then we want to send afterward Bram, go to zero. It implies that one minus two x square echo Jizo and even only if x squared equals to have even on if Mexico to present minus one number squared up to and now for the extra two presidents with up to we confined half off the, uh I say one of us with a two first. Then anything you get using this form of the have exhale. So we have it to each other. Power off miners. They were had 1/2 until recently, tingling due to over a square with them that Yeah, and something for the effort, minus one of its good. Up to get the same answer here. And then we should be able to test this signed f number Problem X now and thanks you excuse for months infinity to infinity. And they will have the manners one was created to when I was going to and does fully with the every mom, Actually, could you zero They wouldn't use the value minus one. You can do so on here. We can trust one here and now. The site of the function it will be, uh, for probably will be this one. And now we should get Ah, this will be minus close on breast hair. Therefore, the functions will be can give up in this in the vote and give Now give up here. So we conclude that the divers in the function can give up on the interval from minus infinity after than minus one of us with two union from one of us quit up to after Infinity can give down under interval from months. One of us could have 2 to 1 over squinted, too. And the inflection point. We'll be at the minus. One was screwed up to and Teoh I was going to obey and the other born every minute will be one of us with two two homos credible E.

Yeah. Hello. So the question is taken from laplace transformation and we have to find a laplace transformation of the given function. So given function is 15 years. Hero. 20 lying between the went bye bye to and it is a call to cause of T. 20. He is greater than by by two. Okay so let us evaluate that laplace transformation by definition it is so you will do immunity exponential my necessity At 4:50 DT Okay so substituting the value of functions. So we get bye bye to doing community And the value of 50 schools of T. Explanation my necessity. DT Okay so let us solve it. Mm let us take this integral as I. Okay I will be equal to Taking a coastal areas 1st function and exponential minus S. T. A second function. So close off key explanation miners is still work kleiner's or fast minus integration. Who stays the first function. So it's differentiation is so we get minus of sci fi explanation minus S. T over minus office. DT Ok so I will be equal to minus schools of T. Exponential minuses tova. Yes yeah minus uh integration of exponential minus S. D. Which is equal to Explanation -4. Over my miners of our square into sign of tea as it is. Okay minus integration. Exponential differentiation of scientists because of T -1 changes to plus. But this differentiation will integration will make when is that still work? One S is already present. So that will become a square along with a minus sign. Okay pretty this this function is a call to I So we get I plus one over the square I. Which is equal to minus cause of D. Exponential minus hasty over ask Plus Exponential -4. Sci fi over S square. Okay so now taking the calcium cricket I squared plus one. Well over I square I net is equal to explanation minus ste scientific. Yeah. Oh well I squared minus explanation minus hasty because of the corvallis. So from here the value of I will be and substituting the limited we get exponential. My necessity sign of K. For what? A squared plus one. My necessity course softy and so well A Square Blessed one. And limit wars film. Bye bye to two infinity. At infinity. Older musical 20 at by by two. We get exponential minus S. Bye bye. Two Divided by a Square. Class one. But along with a minus sign. And for this strong we get deal caused by by 20 which is required lipless transformation of the function. So that will be L. F. 50. So what this clears your doubt and