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Question Number 187611 by otchereabdullai last updated on 19/Feb/23

$$Usepolarcoordinatetofind$$$$lim(x,y)\to (0,0)\frac{y^2}{x^2+y^2}$$

Answered by mahdipoor last updated on 19/Feb/23

$$notexist$$$$gety=0andx\to 0\Rightarrow lim=\frac{0}{x^2+0}=0$$$$gety\to 0andx=0\Rightarrow lim=\frac{y^2}{0+y^2}=1$$$$get(y=x)\to 0\Rightarrow lim=\frac{x^2}{x^2+x^2}=\frac{1}{2}$$$$...$$

Answered by a.lgnaoui last updated on 19/Feb/23

$$Ithinkthataruleoflhopital$$$$cangetasolutiin$$$$f\left(x\right)=x^2+y^{2}g\left(x\right)=y^2$$$${lim}_{x\to a}\left(\frac{f}{g}\right)={lim}_{x\to a}\left(\frac{f^{\prime }}{g^{{}^{\prime }}}\right)$$$$with\frac{d(x^2+y^2)}{d(x,y)}=?$$

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