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Math Help - limit of quotient

  1. #1
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    limit of quotient

    im supposed to take the limit as (x,y) approaches (0,0) of a function f(x,y)=\frac{\sqrt{x^4+y^4}}{\sqrt{x^2+y^2}}. pretty sure this is zero. am i right?
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  2. #2
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    Quote Originally Posted by da kid View Post

    im supposed to take the limit as (x,y) approaches (0,0) of a function f(x,y)=\frac{\sqrt{x^4+y^4}}{\sqrt{x^2+y^2}}. pretty sure this is zero. am i right?
    yes, the limit is 0. given \epsilon > 0, choose \delta=\epsilon. now if 0 < \sqrt{x^2 + y^2} < \delta, then: \frac{\sqrt{x^4 + y^4}}{\sqrt{x^2 + y^2}} \leq \sqrt{x^2 + y^2} < \delta = \epsilon.
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  3. #3
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    the confirmation was adequate and appreciated, but you even used the epsilon-delta definition to show it! that was cool!
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