Question

Calc III/Multivariable calculus problem:
Construct a function whose level curves are lines passing through the origin.
Please explain to me how you got to the answer, thank you.

Answer 1

maybe
|x|=|y|

Answer 2

Ah ok. That makes sense but there are many functions that would fit this problem right? Also, I still don't understand what a level curve actually means :/

Answer 3

yes there is well gtg nw
i list down to u when to do when i come back

Answer 4

ok thank you

Answer 5

Hello I still need an answer to this question. If someone could explain a function that satisfies these requirements and how I might come to a new one that would be great. Thank you so much.

Answer 6

scientific version of your problem
http://en.wikipedia.org/wiki/Level_set

Answer 7

In the weather map on the news you may have seen those curves of equal temperature or equal pressure lines. Those are the level curves. If z = f(x,y), you can set z to various constants. For example, 5 = f(x,y) and plot f(x,y). That curve is one level curve where any point on the curve will give the same f(x,y) of 5. You can then set 13 = f(x,y) and draw another level curve. Any point on the second curve will give the same f(x,y) of 13.