(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Describe the level surfaces of f(x,y,z) = z + sqrt(x^2 + y^2)

3. The attempt at a solution

First of all, what is actually a level surface? Just a normal surface in space?

I followed an example I found on the internet, and this is my attempt at a solution:

First replace f(x,y,z) with a constant

k = z + sqrt(x^2 + y^2)

Then square (k is now another constant)

k = z^2 + x^2 + y^2

This is an ellipsoid, so the level surfaces are ellipsoids centered at the origin.

Is this the right solution? If so, is it possible to say more about the ellipsoids?

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# Level surfaces of a function

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