# MAT 243 (section 5) - Calculus in Several Variables

## Images and other neat stuff

On this page I have placed various graphics related to the course. Click the links to see the images.
- The graph of \(f(x,y) = x^2-y^2\) is a saddle, or hyperbolic paraboloid.
- The contour of height \(c=0\) for the function \(f(x,y) = x^2-y^2\) is the union of the line \(y=x\) and the line \(y=-x\). This is the intersection of the yellow and blue surfaces in the picture.
- The level sets of the function \(f(x,y,z) = x^2+y^2-z^2\) depend on the value of \(c\). The image shows all three types in the same picture.
- Here is a graph of the function \(f(x,y) = \frac{x^3}{x^2 + y^2}\). Note there are no holes or tears in the graph, as we would expect since we showed \(f\) was continuous.
- Here is the graph of \(f(x,y)=\frac{x^2-y^2}{x^2+y^2}\). Notice the hole or "tear" at the origin, which ties in with our computation that \(f\) was not continuous there.