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Question 7 (1 pl)f (z)dz-25iQueston 8 (1 p"} Res;(-2i) = -1Now; consider the regular distnbulion . Txassoclated t0 the (unction Then; x(t) =1 + sgn(t = 1) Ques...

Question

Question 7 (1 pl)f (z)dz-25iQueston 8 (1 p"} Res;(-2i) = -1Now; consider the regular distnbulion . Txassoclated t0 the (unction Then; x(t) =1 + sgn(t = 1) Question (1 pl) Txts temperedQuestion 10 ( P) TX(t) = 28(t - 1) H(t) sin(t)Question 11 (1 F") T' has compact supportQuestion 12 (1 PY) The Lapiace transtorm € 0i * I5 c(x)(s)Question 13 (Tpl) Tne Founer Y() = transtorm otT" (t) 2e-Zrif H(c) = sin(t)isToshiba

Question 7 (1 pl) f (z)dz -25i Queston 8 (1 p"} Res;(-2i) = -1 Now; consider the regular distnbulion . Txassoclated t0 the (unction Then; x(t) =1 + sgn(t = 1) Question (1 pl) Txts tempered Question 10 ( P) TX(t) = 28(t - 1) H(t) sin(t) Question 11 (1 F") T' has compact support Question 12 (1 PY) The Lapiace transtorm € 0i * I5 c(x)(s) Question 13 (Tpl) Tne Founer Y() = transtorm otT" (t) 2e-Zrif H(c) = sin(t)is Toshiba



Answers

For Problems $1-16,$ solve for $t$ using natural logarithms. $$2 P=P e^{0.3 t}$$

Okay buy a size wolf so by exercise. So mm section 13 points four. We have C. To be equal to Swap divided by 13. Cause to it see hi mine it's Swap divided by 30 etc. Sign suit see G Last five divided by 13 key. Then end it's equal to mine it's signed suit. See I mine it's cause suit see G. So this implies that by norma victor B. It's a call to see of course aim and this is equal suit. You have your eye components To have to off divided by 13 of course two, etc. Then my next sign to see then G components we have- Wolf divided by 13 saying to see then my next cause to see then for key We have five divided by 13 and Sarah here. So this thing is going to give us five divided by 13. Of course she would see hi mine it's mine. It's five divided by 13 saying suit see G minus wolf divided by they'd seen key Also we know V. To be equal to so of course suit C. I minus two Wolf. Sign to see she plus five key. So this implies that oh I. E. It's equal to minus 24. My next 24. Since before saying to T. Hi minus 24. Cause suit see gee Okay so therefore the derivative of air with respect to see the A. Uber D. C. Is going to be equal to minus 48. Cause to T hi less 48 sign to it. See. G. So this implies that the cost products gov. Because E. Because he is going to be so you have I. Which is worf because because to see Then I have -24 sign tutsi. Then the J. Components we have minus two of sign two etc. And -24. Course so it's C. Then K. Components we have five and so and this is equal to 100 and swing. See because cause suit see hi -120 sign to T. She would see g minus 288. Key so this implies the magnitude of deaths. It could zvi cause a. It was E. It's going to be equal to this. So 102 8 c. Because to a T squared Plus minus wanted in 20 saying to it see squared Plus -288s squid. And this is going to be up equal to 9000 700 90 7340 four. So then our tossing uh So is she? It's going to be equal to you have caused two of so of course to t so I -20 for sign two etc. Then -48 because to it see Then you have -2 off saying two etc minus 24. Of course to it see then 40 seats sign to see In key components we have five. So so divided by 990 7344. And this is going to be equal to five. Thanks -24 points 4, 8. Divided by 97,000 344. And this is going to be quote too. Yes, you've seen divided by 169 so therefore are so shame. It's equal to saying minus staying divided by 160 Nice.

This question strikes us to solve for tea using natural logarithms. What we know that the first thing we can do is divide both sides by Pee Wee. Then know that we can take the not drawing of both sides. Natural sometimes is one. This leaves us with natural log of B minus natural of p. Remember, this is an equivalent way of writing best. This is equivalent to our times. Teeth getting tea by itself. We have tea. Is the natural order B minus the natural order of P over our

This question instructs us to solve for tea by using natural algorithms. The first step is weaken recon. Use cross multiplication to write three to the power of tea Over two to the power of tea is 5/7. Taking the natural order of book sides. We have the natural log of 3/2 to the power of tea as the natural log of five divided by seven. This fraction over here this leaves us with tea is equivalent to the natural log of five minus the natural of seven. Divided by the natural log of three minus the natural log of two as a decimal, this is approximately negative 0.83

By exercise 14. So by exercise 14 in section 18 points four we have C. To be equal to minus courts. See I legs sign, see G. Then in it's equal to sign, see I floods because C. G. Who is C. G. So this implies that by normal vets to be is C. Well it's mm which is equal to you have your eye, the eye components you have mine. It's cause see saying see the energy components. We have sci fi because see Then UK complainants you have observed zero. So they cross borders of this gives us mine. It's key. That's awesome. We have V. So my next key. You have the two vehicle to -3 cause squared. See sci fi I let's do we same squared see of course. See G. So this implies that A it's equal to the A. D. C. Equals C. D. Uber did see of minus three because squid sea sci fi I last d over DT of three. Science quake. See cause she G. So this implies that the air you ever did see it's going to be equal to de cuba D. T. Uh The Uber did see -3 calls squared T. Sign T. I plus D. Uber D. C. The Uber D. C. You have three. You have three science squared. See who's she G. Okay. So then to find a so shame we have. So this implies that you take the cross radars of minus three cores squared sine cosine squared T. So I see then you have D to D C minus three cause squared C. Saying see then we Uber D. C. Of D you ever did see of minus T. V course quaid C. C. T. Then you have three so squared C. Was see then the Uber D. C. Of three same square T. Cause see they have the Uber D. C. Of D. Uber D. C of three science squid. See this times square T. Cause T close T. Then you have zero for the K. Components And this is equal to zero. So this implies that I was so ashamed, is equal to zero.


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