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math119: fail sketching variables

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eggy 2023-01-10 16:04:33 -05:00
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@ -23,3 +23,14 @@ $$f: \mathbb R^n \to \mathbb R$$
Please see [level set](https://en.wikipedia.org/wiki/Level_set) and [contour line](https://en.wikipedia.org/wiki/Contour_line) for example images. Please see [level set](https://en.wikipedia.org/wiki/Level_set) and [contour line](https://en.wikipedia.org/wiki/Contour_line) for example images.
In order to create a sketch for a multivariable function, this site does not have enough pictures so you should watch a YouTube video.
!!! example
For the function $z=x^2+y^2$:
For each $x, y, z$:
- Set $k$ equal to the variable and substitute it into the equation
- Sketch a two-dimensional graph with constant values of $k$ (e.g., $k=-2, -1, 0, 1, 2$) using the other two variables as axes
Combine the three **contour plots** in a three-dimensional plane to form the full sketch.