a 2 variable function limit

**vonflex1** · November 19th 2010, 06:47 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** · November 19th 2010, 07:18 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** · November 19th 2010, 10:51 AM

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

**vonflex1** · November 19th 2010, 11:00 AM

ok, ok, my bad...

i understand now... thanks.

Math Help - a 2 variable function limit

LinkBack

Thread Tools

Display

a 2 variable function limit

Similar Math Help Forum Discussions

Limit of a two variable function

A two variable limit

Limit of a 2-variable function

two variable limit

Taking the limit of this multiple variable function

Search Tags