Limits and Continuity: Examples

1. Find the limits and discuss the continunity of the following : lim(2,4) (x+y)/(x-y), lim(0,0)=sqrt(x+y+z).

Anwser:

To do this, we use the limit command. We can also graph to see:

>	limit((x+y)/(x-y),{x=2,y=4});

>	plot3d((x+y)/(x-y),x=-5..5, y=-5..5);

For the other equation, Maple can not do the equation.

2. Discuss the continunity of the function: f(x,y,z)=1/sqrt(x^2+y^2+z^2).

Anwser

Again, Maple does not perform with more than two independant variables, and hence can not simplify this problem.