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Question

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as $t$ increases.
$x=e^{-t}+t, \quad y=e^{t}-t, \quad-2 \leqslant t \leqslant 2$

Nicholas Barvinok · Accepted Answer

we have the Parametric equations. X equals e to the minus T costea. Why equals e to the T minus t for tea? Going between minus two and two. So let&#x27;s sketch this graph if when he is at minus two, we have x of minus two equals E squared plus two. No, if we go again, you squared into our calculator just to get an approximate. Now you get about 7.3. So let&#x27;s say roughly seven, this is roughly nine. Why of minus two? Is one over nine minus? Um, I guess, Let&#x27;s say roughly roughly one over nine. Minus negative. So close to roughly two. So we get something like two nine now acts of minus one. We get e plus minus one. So roughly 1.7 roughly which is based roughly two. But well, it&#x27;s oh, it. So this one this start should actually not be here. This dot Should be a nine, too. It&#x27;s over here. Now. We have the x component is to and why of minus one is one over e. It&#x27;s about 1/3 minus negative one. So plus one So a little bit bigger than one. Get access to Why is one so over here so far, we&#x27;re going this direction. No x of zero is each of the 01 So one plus us, we have one. Why zero? That&#x27;s actually exactly one. Then why a zero is again One mind zeros one. So now we&#x27;re at 11 ex of one equals one over E. So about 1/3 lost one. So a little bit bigger then one so X is getting bigger. And then why of one is e minus one, right, So even bigger than one, roughly two ish. So you go back up here finally exit, too. It&#x27;s going to be won over about 1/9 plus two about to but a little bit bigger. And why two will be about seven minus too. So five somewhere over here go this direction.

Wen Zheng · Answer

the problem is sketch the curve by using the parametric equations to plot points and you can&#x27;t always a narrow. It&#x27;s the direction in which the curve is trist as Team pres is first of a compute. What he is equal to zero and teeth physical. Nick, do you want? Axe is equal to zero. Why is he could need you want connective three when he is equal to zero Axe is a good one. Why is he what zero When he is he got one acts Is it zero? Why is it one? He is too Axe is the go to next three Why is equal to zero Then let&#x27;s sketch the curve if you want. Who in the year to selective three This is Juan Long One negative three so five plotting points So the curve is as follows On this arrow is the direction in which the clear ofthis trist as tea increases

Wen Zheng · Answer

The problem is sketch the curve by using the parametric equations to cross points indicate weighs an arrow to direction. In bench Curve is Trist as being gracious. First we computed the value&#x27;s off axe and why? But he is equal to negative, too. We have X is equal to negative. Ten. Why is equal to six? But he is a secret. One axe is he got nicked. You, too. Why is equipped with three? He is equal to zero. X is equal to zero. Why is this photo too? But he is a good one. Is he going to? Why is the go to three? Twenty is equal to two. Ax is equal to ten. Why is the one to six? Then? Let&#x27;s catch the curve is Juan two three four. Our fix Oven it. Nine. Conectiv ten. Negative two. One, two, three Or thinks nine. It&#x27;s just Juan Shit. Three. Uh, thanks. Two three is too negative. Ten. Six This point. Conectiv two three zero to two three. And on six, this&#x27;s a curse. Hands of animal is the direction invades the curve. It&#x27;s trist. As tea increases

Nicholas Barvinok · Answer

we have the Parametric functions. X equals t squared. Why equals t cubed minus 40 with T going between minus three and three. So let&#x27;s graph this I want so let&#x27;s start A T equals minus three. So a T equals minus three X is going to be so let&#x27;s hear it. Ex of minus three. We&#x27;re going to get nine. And then why of minus three? We&#x27;re going to get minus 27 plus 12 meaning that we&#x27;re going to get minus 25. So our first point is, let&#x27;s put some mark Stone one too. Three for 5678 9 10 And then let&#x27;s have wise go by. So this will be by one. So this is going to be a bit smushed. This will go by five So 5 10 15 2025 30 minus 5 10 15 2025 30. But it&#x27;s 12345 6789 10 Prints would get nine minus 25 right there. So now when t equals negative too, accept negative too is going to be four. Why of negative too is going to be minus eight plus eight zero. So we have 1234 zero. Now ex of minus one is going to be one. Why? Of minus one? Going to be minus one plus force three. So where one three now? Exit zero Going to be zero. Why? Of zero? It&#x27;s going to be zero. So we&#x27;re right at the origin. Now. We are. Let&#x27;s do. Except one. And right. So so far, graft appears to be going like this with T increasing in this direction. Ex of one is one. Why have one is one minus four equals minus three one minus three. Um, now, except to before why of two is going to be eight minus 80 for a zero. Find the exit. Three nine. Why off three. 27 minus 12 25. So, like, Looks like that goes from here. Looks around

Ankit Gupta · Answer

The question is X the surgical toe T minus one And why is equal to P Squire Anti the perimeter with pollutes from minus to do two. Okay. And we have to play on the curb. Survivors of sex using the point lording mattered. Okay, so for society Okay, very brother table. Ok, and then we will find a differently off X lie responding to different Really off be ok, So that&#x27;s it. D minus one and why this is equal to the squad. So first of all, put equal to minus two for just put people to manage to So we regret. Except what? Minus two minus one to ex pickled x ministry. And why minus two? Holy Squire. So this is equal to food. So now we had to Fine Xcor. Why so exit ministry and white food no would be a minus one. So if you put bh minus one so X becomes minus one minus one minus two. Why becomes minus? One is quiet. It means one. So the point It minus two Camembert. The pointed minus two Columbia No. B s not Boutiette zero. So it becomes geo minus one minus one. And why becomes the risk wired 10 So the point becomes minus one comma. No, Boutiette. Equal to one. So one minus one X becomes equal to do. And why becomes one is quiet. Quota one for the point becomes Jiro cummerbund. No, no, He had toe theoretical toe, so just put equal toe. So we got to minus one. OK, so x value we got to minus on the surgical to one and viatical groupie squad. So logical toe. Holy Squire, this is four to the point. We get it. One comma. Four. So the point we caught it. One call for no reply. All the points. Okay. Under ex away plane. Okay, so first pointed minus take off. Okay, so minus three. It means that this is our Oregon GOP magic. Okay, so we have to applaud. Minus three. Power food. So here. Minus one minus two. Minus three. And food. Okay, so it means that Vicodin before, So this is vital to one. This is viable toe. Why? I called you three and vibrato food so minus take off. Or it means that between come here. So this is the point. OK, so we have got the one point so similarly, we will find all the points and plotted here. So the second point, it pointed minus two government. Okay, So second pointed managed to government. So they sit minus two and decision one. So this is a second point. And the third point hard pointed minus one. Command you so we&#x27;ll plot again minus this is minus one. And this is due to This is the point, So joined the points. Okay, you tinker handling. So we have joined again on the appointed. You look on one and one caller four. Okay, so under pointed joke alone means executed zero vicryl one. So this is the point. So join it. And another born and one gone for eight minutes when x is equal to one. Why they could afford to the center point. Ok, so just drop Enjoying. So this is the girl which we had to find and the sea level varieties and discover x axis. And this is our answer

Wen Zheng · Answer

the trouble on this sketch the curve by using the perma tricky questions. Your plot points indicated with a marrow is the direction in which the kerchief is trist As TV in prison the first of a computer to values of acts and why? But he is equal to negative Pie X is equal to negative pie. Why is Psi Corps too negative? One p is equal to negative high over too. Behalf X is equal to negative High over too minus one Why is Seiko too Cyril twenty is equal to zero. Axe is equal to zero. Why his secret to one He is the Goto high over too. Axe is before two pi over too. Plus one. Why is the go to zero? Auntie is equal to Pi. Half X is equal to Hi. How serious is this? A pie and why it&#x27;s before too. Negative one. Now let&#x27;s get to the curve person too. Ugh! This is nicht high over too. And negative. Hi. I over it too. Armed. All right, Actually got connective. Hi. Why is it you want Nick to one? Siro could want negative pie next to one. Oh, here. Negative pile returned minus one. It&#x27;s about here. Serial one here. Here. Yeah, So Graff is like this. This is a proof. By using the Parametric equations to plot points, Andi is a direction Ero is a direction in waged the crew if it&#x27;s traced as tea increases.

Problem

(a) Sketch the curve by using the parametric equa…

Problem 4 Medium Difficulty

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as $t$ increases.
$x=e^{-t}+t, \quad y=e^{t}-t, \quad-2 \leqslant t \leqslant 2$

Answer

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