Finding the limit

[calchere]

Find the limit, if it exists, or show that the limit does not exist.

lim (x,y)->(0,0) (x^4 - y^4)/(x^2 + y^2)

I did:
f(x,0) = x^4/x^2 = x^2
f(0,y) = -y^4/y^2 = -y^2

Now i'm wondering if, since x^2 and -y^2 are different the limit does not exist, or i take the limit of x^2 and -y^2 being 0, so the limit would be 0?

 

[pka]

\(\displaystyle \L f\left( {x,y} \right) = \frac{{x^4 - y^4 }}{{x^2 + y^2 }} = x^2 - y^2 ,\quad \left( {x,y} \right) \not= \left( {0,0} \right).\)

Surely that helps you.

 

[calchere]

x^2 - y^2

the limit of x^2 as x aproaches 0 would be 0
the limit of -y^2 as y aproaches 0 would be 0

so the limit would be 0?

I think i'm missing something here. I'm trying to separate the variables like they did in the book.

 

[pka]

so the limit would be 0?
I think i'm missing something here. I'm trying to separate the variables like they did in the book.

But that is the answer. Do you see why?