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Question Number 186821 by yaslm last updated on 10/Feb/23

Answered by CElcedricjunior last updated on 11/Feb/23

$$★\underset{x;\mathit{y}\to 0}{\lim }\frac{\mathit{s}\mathit{i}\mathit{n}({\mathit{x}}^2+{\mathit{y}}^2)}{{\mathit{x}}^2+\mathit{y}}◼\mathit{M}oivre$$$$\mathit{p}\mathit{o}\mathit{s}\mathit{o}\mathit{n}\mathit{s}{\mathit{x}}^2+{\mathit{y}}^2=\mathit{A}$$$$\mathit{q}\mathit{d}:\mathit{x};\mathit{y}->0\mathit{A}->0$$$$<=>\underset{A\to 0}{\lim }\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{A}}{A}=1$$$$★\underset{x;\mathit{y}\to \mathrm{\infty }}{\lim }\frac{\mathit{s}\mathit{i}\mathit{n}({\mathit{x}}^2+{\mathit{y}}^2)}{{\mathit{x}}^2+{\mathit{y}}^2}\approx \underset{\mathit{x}\to \mathrm{\infty }}{\lim }\frac{\mathit{s}\mathit{i}\mathit{n}\mathit{x}}{\mathit{x}}=0★\mathit{c}\mathit{e}\mathit{l}\mathit{e}\mathit{b}\mathit{r}\mathit{e}\mathit{c}\mathit{e}\mathit{d}\mathit{r}\mathit{i}\mathit{c}\mathit{j}\mathit{u}\mathit{n}\mathit{i}\mathit{o}\mathit{r}$$$$$$

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