This isn't a homework question-- it is a general question about curve sketching in multivariable calculus.(adsbygoogle = window.adsbygoogle || []).push({});

In order to draw graphs in 3D, we use level sets, then-- if the level sets are something "nice" like circles or parallel lines-- we take a cross section when y=0 and then transform the cross section on to the level sets.

However, it is at the stage of the cross sections where I begin to be confused. We are given a function such as [tex]e^{-x^2}[/tex]. I do not already know what this function looks like.

What is a quick way to draw this graph (or any other) without going through the whole curve sketching process (learned in single variable calculus)?

Are there any tricks to drawing graphs quickly that you don't already know?

Another example is [tex]sin(x^2)[/tex]. (I already know what this looks like-- but how would I figure it out quickly if I didn't?).

Thank you.

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# Predicting the Shape of Complicated Functions

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