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Find an equation for the level surface of the function through the given point.$$g(x, y, z)=\frac{x-y+z}{2 x+y-z}, \quad(1,0,-2)$$

Calculus 3

Chapter 14

Partial Derivatives

Section 1

Functions of Several Variables

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Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

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Find an equation for the l…

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In Exercises $61-64$ , fin…

and this problem. We're trying to find the equation of the level curve for the different function at the point. Warns they were negative too. So we know that the level close have the question of the four X men. It's worth seeing order to it. Close warring financing vehicle to come. Some kinds the figure out this constant. We're going to valued or burn our function at a given point. And what we have here is one minus zero. That's negative. Two comes minus two for her to terms worn, zero minus negative to become supposed to. So what we have here is magazine 1/4 so you can go ahead and replace oversee negative 1/4 the only home Multiply both sides by the denominator we have X minus y is equal to negative born quarter Learned to work foreign money. I would like to get rid of the fraction so more to play. What science? Brave or so what? We are work. Let us Why? Minus four y minus four Screen equal to negative to work minus y lusty, combining like terms we have minus three wine. This is a close it badly must freezing is equal to zero. Okay, so everything here is a multiple of three. So weekend Simplify that by dividing both sides by three. Which gives us final equation of work minus for why? First thing is equal to zero. But this is the equation of the level curl at the point one. We're all no getting to.

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