Use-the-definition-of-the-limit-of-a-function-to-prove-that-lim-x-y-0-0-x-4-y-4-x-2-y-2-0-

Tinku Tara June 3, 2023 Vector Calculus 0 Comments

Question Number 4596 by Yozzii last updated on 10/Feb/16

Use the definition of the limit of a function to prove that lim_((x,y)→(0,0)) ((x^4 +y^4 )/(x^2 +y^2 ))=0.

$${Use}\:{the}\:{definition}\:{of}\:{the}\:{limit}\:{of}\:{a}\:{function} \\ $$$${to}\:{prove}\:{that}\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\frac{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }=\mathrm{0}. \\ $$

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