1. ## Continuous function

Hey.
How can I show that this is a Continuous function?

2. You need to show that $f(0,0)=\underset{(x,y)\to (0,0)}{\mathop{\lim }}\,=\frac{x^{2}y^{2}}{x^{2}y^{2}+(x-y)^{2}}=1.$

3. Originally Posted by Krizalid
You need to show that $f(0,0)=\underset{(x,y)\to (0,0)}{\mathop{\lim }}\,=\frac{x^{2}y^{2}}{x^{2}y^{2}+(x-y)^{2}}=1.$

Yeah, I know that.
I don't have a clue how to show that, any idea?

4. Originally Posted by asi123
Yeah, I know that.
I don't have a clue how to show that, any idea?
It is not true.
The path $x=y$ gives the limit $1$.
While the path $x=0$ gives the limit $0$.