Re: Sketching level curves

Quote:

Originally Posted by

**SyNtHeSiS** Sketch the level curves for the function

.

Attempt:

Now I am not sure how I would draw each of these graphs due to the

part. (Worried)

Also when asked to sketch the level curves, does that mean you just let z = k and draw one graph? (as opposed to also letting x = k and y = k)

So, the level curves are circles in the xy-plane that are centered at the origin.

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Re: Sketching level curves

Thanks :). Would drawing the graph give you a circular paraboloid (or do you have to draw the traces for and before drawing ?

Re: Sketching level curves

Quote:

Originally Posted by

**SyNtHeSiS** Thanks :). Would drawing the graph give you a circular paraboloid (or do you have to draw the traces for

and

before drawing

?

No, because the equation of a circular paraboloid is .

Re: Sketching level curves

Oh ok. What steps would you use to draw the correct graph?

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Re: Sketching level curves

Quote:

Originally Posted by

**SyNtHeSiS** Oh ok. What steps would you use to draw the correct graph?

I have attached a graph generated using MATLAB.

Re: Sketching level curves

Any function of the form has circular symmetry. In particular, is a logarithm graph. Draw that and rotate around the z-axis.