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Thread: Limits in two Dimensions

  1. #1
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    Limits in two Dimensions

    How can I calculate the following limits or prove that don't exist:

    a) $\displaystyle \lim_{(x,y) \to (0,0)} \frac {x^4 + y^4}{x^2 + y^2}$

    b) $\displaystyle \lim_{(x,y) \to (0,0)} \frac {x^2 - y^2}{x^2 + y^2}$

    Thanks in advance
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  2. #2
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    Quote Originally Posted by ypatia View Post
    How can I calculate the following limits or prove that don't exist:

    a) $\displaystyle \lim_{(x,y) \to (0,0)} \frac {x^4 + y^4}{x^2 + y^2}$

    b) $\displaystyle \lim_{(x,y) \to (0,0)} \frac {x^2 - y^2}{x^2 + y^2}$

    Thanks in advance
    Hi

    a) $\displaystyle \frac {x^4 + y^4}{x^2 + y^2} \leq x^2+y^2$

    b) On the x axis $\displaystyle \frac {x^2 - y^2}{x^2 + y^2} = 1$ but on the y axis $\displaystyle \frac {x^2 - y^2}{x^2 + y^2} = -1$
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