## 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.