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Question Number 131444 by rs4089 last updated on 04/Feb/21

Answered by Olaf last updated on 05/Feb/21

$$\mathrm{polar}\mathrm{coordinates}:$$$$\frac{xy+2}{x^2+y^2}=\frac{r\cos \theta .r\sin \theta +2}{r^2{\cos }^2\theta +r^2{\sin }^2\theta }$$$$=\frac{\frac{1}{2}{r}^2\sin \left(2\theta \right)+2}{r^2}=\frac{\sin \left(2\theta \right)}{2}+\frac{2}{r^2}$$$$\underset{r\to 0}{\lim }\frac{xy+2}{x^2+y^2}=+\mathrm{\infty }$$

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