Continuity & Limits

**Len** · October 6th 2008, 03:37 PM

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.

**icemanfan** · October 6th 2008, 03:42 PM

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.

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

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?

**Len** · October 6th 2008, 03:44 PM

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

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