Question
Math 421: Advanced Calculus for Engineering Homework Assigned Friday , February 13_ 2020 Due On Tuesday: February %5_ '2420 At [:5SpIILQuestionCompute cach of the following Laplacc transforms_L {tcost}C {e sin 2t } L{E()}, where E(t) is Ile periodie [unetion with period T _ dlelinedl on [0.4) byif 0 < t < 2, il 2 < t < +E(t) =Question 2_ Use the Laplace trauslorm l0 solve the iuitial-value problent16y 0({ 2w) , "(0) _ 0, %(0) - 0.Question 3. Use the Lplace transform to solv
Math 421: Advanced Calculus for Engineering Homework Assigned Friday , February 13_ 2020 Due On Tuesday: February %5_ '2420 At [:5SpIIL Question Compute cach of the following Laplacc transforms_ L {tcost} C {e sin 2t } L{E()}, where E(t) is Ile periodie [unetion with period T _ dlelinedl on [0.4) by if 0 < t < 2, il 2 < t < + E(t) = Question 2_ Use the Laplace trauslorm l0 solve the iuitial-value problent 16y 0({ 2w) , "(0) _ 0, %(0) - 0. Question 3. Use the Lplace transform to solve the system T -v =0; +2 -y =0, 3(() =0, wkQ) Question (Jse' the Laplace transfc)I to solve the syxtem v - [ T=l I(U) v() Question Use Gauss-Jordlan elimnination to solve the linexr system 272 314 2[ 372 4Ij 11 402 5,3 Question 6 Copute the: cleteTminant o Ahe Halrix Note: Students should submit this homework assigmmnent electronically Canvas which will acccpt (clcar) photo scnn of thc writtcn assignmont or PDF of thc typed assignment. The assignment closes at midnight on the due date;
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We have a question In this way to find the value of this is question # two. Value of limits X approaches to zero plus affects and Limit x approaches to zero fx according to the graph. Okay. Mhm. So this is a graph, this is X. This is why this is simply by Israel function we should stay. Is it too? This is for so one parties like this and other parties A constant function. This this must be three. What? Okay, no, first part that is Limit X approaches to zero from zero plus, it means zero plus means we will be approaching Approaches x equal to zero from the right side. So let us observe the graph, this is X equal to zero and if we come from right side, approaching from right side, so values of this function. That is why while we're approaching, why is decreasing while we're approaching value of Y is decreasing decreasing and when we reach near the vicinity of oh, vicinity of zero X equal to zero. So The value is approaching 2, 2. So from here, from the Graph two should be the answer. Okay? No, similarly zero -FX means we are approaching approaching X equal to zero from left side. Okay, so let us approach X equal to zero from left side from left side. So value correspondingly remains constant remains constant, remains constant and becomes Yeah, three. So almost three should be their answer. Thank you
We have a question In this way to find the value of this is question # two. Value of limits X approaches to zero plus affects and Limit x approaches to zero fx according to the graph. Okay. Mhm. So this is a graph, this is X. This is why this is simply by Israel function we should stay. Is it too? This is for so one parties like this and other parties A constant function. This this must be three. What? Okay, no, first part that is Limit X approaches to zero from zero plus, it means zero plus means we will be approaching Approaches x equal to zero from the right side. So let us observe the graph, this is X equal to zero and if we come from right side, approaching from right side, so values of this function. That is why while we're approaching, why is decreasing while we're approaching value of Y is decreasing decreasing and when we reach near the vicinity of oh, vicinity of zero X equal to zero. So The value is approaching 2, 2. So from here, from the Graph two should be the answer. Okay? No, similarly zero -FX means we are approaching approaching X equal to zero from left side. Okay, so let us approach X equal to zero from left side from left side. So value correspondingly remains constant remains constant, remains constant and becomes Yeah, three. So almost three should be their answer. Thank you
You have a question and this going to use I V T. Okay, uh to show that affects equal to Access choir -3 has zero in the interval minus four comma for Okay, we have to show it. Yeah, Okay, it is intermediate value theorem. So we have to use it. So let us understand for intermediate to military um first is we will be taking effect is continuous or not Continues in Interval -4- four or Not. If it is continuous and then we will be taking f minus four is not equal to f four. Thirdly uh it says that if any of a number between F A and f B that is if we have any number between F A and F B. So we'll be calculating first then there will be N. If n is a number between f minus four and F for then there must be a point C between A and bases that are equal to end. So then there will be a point A number between my 4-4 c for this fc will be equal to And let us utilize it now question our this is affects equal to access Choir This is a fact equal to That's a Square -3. Okay, access square minus street. This is a parabola, Y-plus three equal to access square. So this is like Parabola. This is X. This is why and its vortex will be zero gone minus three. Here it is a vertex and connectivity A port like this. Zero comma -3. Since this parabola you can easily say that this is continuous between minus four 24. There's a continuous hence will be first finding out the values f minus four. So access Square -3 -4 sq -3. 16 -3 is 13. I have four. That would be for Squire -3. That this is 13. Okay, so we have both the values well to 13. Okay. Therefore they have both the values Equal, we have F -4 Equal to F four Equal to 13 over here. Okay. Okay but we can observe that right -4. These two values are equal so we can't apply. IvP. Thank you an option number. This is option number. See that is 3rd option. Thanks.
Mhm We have a question in this. We have been given a craft given a graph. Like this is why this is X. This is zero. Graph looks like okay uh like this and okay, like this. Okay, we need to find the values, we need to find the values of limit X approaches to zero plus fx Okay, And limit X approaches to zero from the left side. FX This is not a right and limit. When we'll we'll be approaching zero, X equal to zero from right side. So if we approach zero from right side, it is like value is increasing, value, function is increasing and when we come near the vicinity of this zero, it becomes plus infinity. That is when we just as I appear the graph fairies going to be going to infinity and it will reach to infinity. So we should write that limit X approaches to when access approaches to approaching 2, 0 from right side function will become infinite function will approach the infinite. And from here it is the left side. When we are approaching from left side, this negative sign and also from left left side. So value is decreasing decreasing, decreasing. So ultimately, when they uh uh rich Near the vicinity of zero, it becomes zero. Okay, no fourth number questions port number questions, we have to find the limit X approaches to zero plus Ln X limit X approaches to zero place Ln X. And we have been given the graph of L N X. This is this is why This is one. So graph is like this. Okay, this is increasing continuously, increasing. Okay, now this means we are approaching zero from right side so we can see that if we are approaching zero from right side, right side, this is zero outside, the value is getting towards going towards minus infinity. So valuable approach to Earth negative infinity. Thank you.