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

$$4=x^{2}+y^{2}+z^{2}$$

Calculus 3

Chapter 14

Partial Derivatives

Section 1

Functions of Several Variables

Johns Hopkins University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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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Write the level surface $x…

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In Exercises $61-64$ , fin…

We're trying to get the equation of the level curve of the didn't function at the 0.1 negative born square to, So we know that the level curve will have an equation of the form. Heard of X Squared plus y squared was this. Where is equal to some constant so that constant being will being the value we get when we build with the function at the given point. But here we haven't squared on squared negative one squared was this word of two cleared, and that is a fortune squared off for people to Rick. Luge in will be heard of X squared plus y squared. That's a square is equal to two. We can simplify this by getting rid of scoot. Squaring both sides gives us the equation X squared. Most voice squared those they square equal to four. Someday soon, I'll level curve at the point warning. Negative born er two

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