a 2 variable function limit

**vonflex1** · Nov 19th 2010, 07:47 AM

hi there,

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

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

thanks.

**chisigma** · Nov 19th 2010, 08:18 AM

Is...

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

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

Kind regards

$\chi$ $\sigma$

**vonflex1** · Nov 19th 2010, 11:51 AM

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

**vonflex1** · Nov 19th 2010, 12:00 PM

ok, ok, my bad...

i understand now... thanks.

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