4

Lji } H 8 ~ 1 [ T{ W W { 1 [ g 2 V L 4 2...

Question

Lji } H 8 ~ 1 [ T{ W W { 1 [ g 2 V L 4 2

Lji } H 8 ~ 1 [ T{ W W { 1 [ g 2 V L 4 2



Answers

$$h(t)=\frac{t^{2}-2 t}{t^{4}-16}$$

Okay, so he were given a suppose transform of six times E to the negative three T minus T squared, plus two times T minus eight. Okay, so there is some other break rules week, Remember? Um, somewhere it's like intervals. We can When we have things added, it's attracted week. And then just add a little cross transforms of each components. This is equal to the Lacoste transform of six times E to the negative three t, then minus at the transform of T squared, plus transform of T t and then minus and from the And so there's another algebraic things we can do here. Um, we can pull out a constantly being multiplied to the fronts, would get six times the transform, uh, e to the negative three t We do that. There's nothing to pull out for this 2nd 1 but for the next two, we can follow suits who pulled the two out and then here will pull the eight out in this little one inside. Okay, so now this isn't a place week, actually, um, figure things out a little bit. So some rules to remember here that we'll be using is that the transform. Ah E to the A. T is equal to one over as minus a the transform ah t to the A is equal to a factorial over s to the power of a plus one. Then lastly, that the transform of one is equal to one over s. So using that, we can convert this. We're gonna get six times. This is in the e to a t. Right. So we'll get one over s minus negative three or as plus three. Okay, let me get minus. This is a T square. This, Tita, a second rule here us is gonna be two factorial over. That's two out of two plus one. Just three they will have. Plus two times. This is in the same format. But with a one rights would get one factorial over s. Sloan plus twos is gonna be out of two here, then. This last one, this minus eight is gonna end up being minus eight times. One over s here using this third form, uh, like this. And so these factorial two factorial is actually equal to to one. Factorial is equal to one. Um, Sue for s greater than zero. Uh, no. Further algebra is involved, and this is our answer.

In this question we will understand the concept of general power rule like and how to find the derivative of the function. So the given function is 1- T Square to the powerful. We have to find the differentiation of this function. So when you differentiate this with respect to D we get four one minus D squared. You multiplied by a derivative of 1- Day Square. Like. So this can be within us for one minus T. Is like you when we differentiate one dynasty is where we get minus today. So when you simplify this we get minus eight P one minus T squared to the power terry. This would be equal to HD SDI right? And this is the derivative of the given function HD right. In this way we can find the differentiation of any function with the help of power Good.

And this problem we're being asked to multiply the mono meal for W squared by the triangle meal three W to the third minus two w squared minus w. To do this, I'm going to use the distributive property. So first we need to multiply for w squared by the first term three w to the third, which will give us 12 w to the fifth hour. Next, we're going to multiply for w squared by the second term negative to W squared which will give us negatives which will give us negative eight w to the fourth And lastly, we need to multiply for w squared by the last term. Negative w Well, that's going to give us negative four w to the third and now because none of these


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