How to plot two unknowns in maple 14?

Question

This doesn't works in Maple 14. Why? How can I plot this function? $$\text{plot}\left(\frac{x^2 \cdot y^2}{x^2+y^2},x,y = -\infty .. \infty\right);$$ Here's the original function (where is it continuous?): $$f(x,y) = \begin{cases} \frac{x^2 y^2}{x^2+y^2}, & \text{if } x^2+y^2 \neq 0, \\ 0, & \text{if } x^2+y^2=0. \end{cases}$$

Answer 1

You can use the following codes seperately:

plot3d((x^2*y^2)/(x^2+y^2), x = -10 .. 10, y = -10 .. 10);

or

with(plots);

implicitplot3d(z = (x^2*y^2)/(x^2+y^2), x = -10 .. 10, y = -10 .. 10, z = 0 .. 50, numpoints = 20000);

In both cases, your plot is

Note that in 3D, Maple cannot handle the infinite ranges as you desired.

Answer 2

Your function is $f(x,y)=\frac{x^2y^2}{x^2+y^2}$. The function depends of two variables. So, if you want to draw the function, you will result with a 3-dimensional-plot.

The maple-function is called plot3d.