Thread: a 2 variable function limit

hi there,

i am trying to find the limit of the function $\displaystyle \frac{3x^4-2y^4}{x^2-y^2}$ as x and y approach 0.

i see it is 0, but i have no idea how to prove it.

thanks.

Is...

$\displaystyle \displaystyle \frac{3 x^{4}-2 y^{4}}{x^{2}-y^{2}} = 2 (x^{2} + y^{2}) + \frac{x^{4}}{x^{2}-y^{2}}$ (1)

The (1) is composed by two terms. The first term tends to 0 if $\displaystyle \displaystyle (x,y) \rightarrow (0,0)$ and can be 'discharged'. The second term tends always to 0 if $\displaystyle \displaystyle (x,y) \rightarrow (0,0)$... always except in the case $\displaystyle x=\pm y$ so that the limit doesn't exists...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

sorry,
but i don't understand how the two are connected to the original limit problem...

ok, ok, my bad...

i understand now... thanks.