# Continuity & Limits

• Oct 6th 2008, 04:37 PM
Len
Continuity & Limits
For what points is the function continuous?

$f(x,y)=\frac{xy}{x^2-y}$

Intuition tells me that it would be continuous everywhere except where the denominator equals zero so... Would it be continuous everywhere except on the parabola $y=x^2$?

Also

$f(x,y)=\frac{x^4-4y^4}{x^2+2y^2}$

Find the limit of $f(x,y)$ as $(x,y)\rightarrow(0,0)$

Thanks for the help.(Happy)
• Oct 6th 2008, 04:42 PM
icemanfan
Quote:

For what points is the function continuous?

$f(x,y)=\frac{xy}{x^2-y}$

Intuition tells me that it would be continuous everywhere except where the denominator equals zero so... Would it be continuous everywhere except on the parabola $y=x^2$?
Yes.

Quote:

$f(x,y)=\frac{x^4-4y^4}{x^2+2y^2}$

Find the limit of $f(x,y)$ as $(x,y)\rightarrow(0,0)$
$f(x, y) = \frac{(x^2 - 2y^2)(x^2 + 2y^2)}{(x^2 + 2y^2)}$.

Does this help?
• Oct 6th 2008, 04:44 PM
Len
Quote:

Originally Posted by icemanfan
Yes.

$f(x, y) = \frac{(x^2 - 2y^2)(x^2 + 2y^2)}{(x^2 + 2y^2)}$.

Does this help?

Saw that after I typed it up, but thought I better clarify :P, thanks a lot :D