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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.$x=e^{-t}+t, \quad y=e^{t}-t, \quad-2 \leqslant t \leqslant 2$

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Calculus 2 / BC

Chapter 7

Differential Equations

Section 5

Systems of Differential Equations

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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'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's say roughly seven, this is roughly nine. Why of minus two? Is one over nine minus? Um, I guess, Let'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's oh, it. So this one this start should actually not be here. This dot Should be a nine, too. It's over here. Now. We have the x component is to and why of minus one is one over e. It'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're going this direction. No x of zero is each of the 01 So one plus us, we have one. Why zero? That's actually exactly one. Then why a zero is again One mind zeros one. So now we'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'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.

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