Question-131444

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

Answered by Olaf last updated on 05/Feb/21

polar coordinates :

\frac{x y + 2}{x^{2} + y^{2}} = \frac{r \cos θ . r \sin θ + 2}{r^{2} \cos^{2} θ + r^{2} \sin^{2} θ}

= \frac{\frac{1}{2} r^{2} \sin (2 θ) + 2}{r^{2}} = \frac{\sin (2 θ)}{2} + \frac{2}{r^{2}}

\lim_{r \to 0} \frac{x y + 2}{x^{2} + y^{2}} = + \infty

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