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Question Number 139432 by normabaru last updated on 27/Apr/21

Answered by Jme Eduardo last updated on 27/Apr/21

$$\left(a\right)ifx=t^{2}andy=t$$$$$$$$\underset{t\to 0}{\lim }\left[\frac{2t^4}{t^4+t^4}\right]=1$$$$$$$$ifx=tandy=t^2$$$$$$$$\lim \left[\frac{2t^4}{t^2+t^8}\right]=\underset{t\to 0}{\lim }\left[\frac{2t}{1+t^6}\right]=0$$$$$$$$the\underset{(x;y)\to (0;0)}{\lim }f(x;y)notexist,becauseifweapproachparametriccurvesthefunctionhasdifferentlimits$$

Answered by Jme Eduardo last updated on 27/Apr/21

$$\left(a\right)ifx=t^{2}andy=t$$$$$$$$\underset{t\to 0}{\lim }\left[\frac{2t^4}{t^4+t^4}\right]=1$$$$$$$$ifx=tandy=t^2$$$$$$$$\lim \left[\frac{2t^4}{t^2+t^8}\right]=\underset{t\to 0}{\lim }\left[\frac{2t}{1+t^6}\right]=0$$$$$$$$the\underset{(x;y)\to (0;0)}{\lim }f(x;y)notexist,becauseifweapproachparametriccurvesthefunctionhasdifferentlimits$$

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