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2DETAILSSCALCET8M 14.4.001 |Find an equation of the tangent plane to the given surface at the specified point 2 Sy, K(1;,2/02)...

Question

2DETAILSSCALCET8M 14.4.001 |Find an equation of the tangent plane to the given surface at the specified point 2 Sy, K(1;,2/02)

2 DETAILS SCALCET8M 14.4.001 | Find an equation of the tangent plane to the given surface at the specified point 2 Sy, K(1;,2/02)



Answers

Find an equation of the tangent plane to the given surface at the specified point.
$ z = e^{x - y} $,
$ (2, 2, 1) $

In this question will recall about the formula to compute the attention plan. We have the first derivative respecting the X times next month. Next zero plus the first derivative respect the Y times Y minus quite zero plus the first derivative speculation see terms the ministry is they're all, it will equal to zero. And now we are given the question where we have the X square just to the square gy square and we've even given the .13 months to I understand the first time we need to turn it into the function of the F. So F equal to X square managed to y square plus to the square. And therefore we will continue to come build the slop here. The first one to be the first director was watching the X will be the two X blocking the value. We have F X. And the pond. They were equal to two times one would be to Similarly the F. Y. It will equal to the minus four Y. Therefore we're looking the value. We got echo two months trial and fc. It will go to the pharmacy and they found the F. C. And a point It was echoed you the minus eight. And then we are ready to write down the tension plan. Now, so we have this one will be two times x minus one. This will be minus 12 Y minus three minus eight times E plus two equal to zero. Now, the next time we can get to simplify this expression two x minus two minus training, Y plus 36 minus eight. Z minus 16 equals zero and one month step. We will have to X monster and why monastery to see here we have. This will be ego to 20. Minister will be equal to 18, So plus 18 equal to zero. And this will be the question we are looking for.

In this question we recall about the formula to compute attention plan in herself form Z equals qz zero plus the first derivative respecting the X times x minus next zero plus the first derivative, especially the Y times y minus y zero. Yeah. Well given the function F x Y. You go to the x square minus two X Y plus y square. And and a pond 121 here notice that before we continue to fight the pension plan we can simply find the expression from the F X Y. This particularly coach x minus y square. So like this will help us to compute the first degree with you easier. So I have thanks to it, we go to two and then x minus Y times one. Therefore evaluate and the point we get to go to x minus y will be one managed to b minus one. So we have here will be managed to similarly the f Y. We go to the managed to x minus y times uh This will be a set and then we will have the fy evaluate and appoint you can go to the to so therefore we are ready to write down the attention plan here. So it has a form is the echo 20 will be one plus F x will be minus two. So we have b minus two. Thanks Manasquan, I? M going to be two y minus two. If we simplify we have the Z equal to one minus two, X plus y plus two y minus far. And if we bring everything to one side we will have minus two X plus two y minus C. Here we have one plus two minus four, with b minus one equal to zero. And this will be the question we are looking for.

In this question we record about a formula to compute a dental plan here we will have the first degree to whisper to the X. Times x minus x zero plus the first derivative whispered to the Y. Times Y minus Y Zero plus the first derivative whispered to the C. 10 C minus zero equals zero. And here we are given the questions the ico joe a about banks and then say why plus one and the 10.0 pi up to two here because the question honoree in terms of the Z. So we can rewrite this down into a simple form by writing the Z. E. Co +200 plus this. So they found the first time we need to fight will be the slump. F. X. And F one here. So we have the F. X. It will go to now that the river to again you go to the E. To the X. Side Y plus one. So therefore it will compute the And a given point. We should get Echo two evo is equal to one. So I'm the pint of Jericho to one. So 1 plus one. That's why we have you could you chew similarly the first there everything was switching the wine. We got to go to the each and the X times the rivers in the side equity to go side Y. And we're looking the point inside we should get a go to one times go side of the pride of two equal to zero. So we have a zero here and then we're ready to compute attention plan. Here. See we go to zero. B. Two plus F x will be two X minus zero, and why? It will be equal to zero? Why -91? It was something finest expression. We have The two X -C Plus two equal to zero. And this will be the question we're looking for.

Let's find the equation of the tangent plain to the given surface at a given point. Ex not. Why not Xena? And here we used the books convention of just replacing Z with F so that here by F we're just referring to the right hand side of the given equation. So here recalled the equation for the tension plane right out of the book and then similarly partial derivative with respect to why, Oops, That's a why there so in our case, will have to go ahead and compute these partial derivatives. We see them in the formula. So first partial derivative. And in this case, we just get for X. And when we plug in the point one two, that's are given X and y, we have four. Similarly, go ahead and use the power rule again. Differentiate with respect a why only and then go ahead again and plug in the point one two that'LL give you four minus five. So negative one. So let's come back to our equation over here and just replace what we can. Oops, so z not. This's given his minus four FX, which has found that to be four then x minus X Not and then here we have a minus one And then why minus? Why not simplify this a bit? And then we'LL have negative for because of this minus and then plus two so negative four plus two that's minus two. This may be rearing, but it's still represents the same plane, so I'll stop right here and that's the final answer.


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