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Math Help - a 2 variable function limit

  1. #1
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    a 2 variable function limit

    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.
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  2. #2
    MHF Contributor chisigma's Avatar
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    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
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  3. #3
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    sorry,
    but i don't understand how the two are connected to the original limit problem...
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  4. #4
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    ok, ok, my bad...

    i understand now... thanks.
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