level curves

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A level curve is just a 2D plot of the curve f(x,y) = k, for some constant value k. Thus by plotting a series of these we can get a 2D picture of what the three-dimensional surface looks like.

In the following, we demonstrate this. This is essentially an animation that you can go through step by step. As you click through, you'll see a little pop-up window that explains what you want to look for as you step through each frame in the demonstration. Click here to open the pop-up window for the current frame of the demonstration.

Figure 1: graph of the level curves of this function.

Finally, we can graph all of the level curves in a countour plot, as shown in the figure to the right. Here we've highlighted the level curve corresponding to z = 1 in magenta.

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