Respostas

2013-12-01T21:57:03-02:00
\frac{ \sqrt{x}- \sqrt{5}}{\sqrt{x+5}- \sqrt{10}}=\frac{ \sqrt{x}- \sqrt{5}}{\sqrt{x+5}- \sqrt{10}}.\frac{\sqrt{x+5}+\sqrt{10}}{\sqrt{x+5}+\sqrt{10}}=\frac{ (\sqrt{x}- \sqrt{5})(\sqrt{x+5}+\sqrt{10})}{\sqrt{x+5}^2- \sqrt{10}^2}

=\frac{ (\sqrt{x}- \sqrt{5})(\sqrt{x+5}+\sqrt{10})}{x+5-10}=\frac{ (\sqrt{x}- \sqrt{5})(\sqrt{x+5}+\sqrt{10})}{x-5}.\frac{(\sqrt{x}+\sqrt{5})}{(\sqrt{x}+\sqrt{5})}

=\frac{ (\sqrt{x}^2- \sqrt{5}^2)(\sqrt{x+5}+\sqrt{10})}{(x-5)(\sqrt{x}+\sqrt{5})}=\frac{(x-5)(\sqrt{x+5}+\sqrt{10})}{(x-5)(\sqrt{x}+\sqrt{5})}=\frac{\sqrt{x+5}+\sqrt{10}}{\sqrt{x}+\sqrt{5}}

\lim_{n \to 5} \frac{ \sqrt{x}- \sqrt{5}}{\sqrt{x+5}- \sqrt{5}}=\lim_{n \to 5} \frac{\sqrt{x+5}+\sqrt{10}}{\sqrt{x}+\sqrt{5}}=\frac{\sqrt{5+5}+\sqrt{10}}{\sqrt{5}+\sqrt{5}}

=\frac{\sqrt{10}+\sqrt{10}}{\sqrt{5}+\sqrt{5}}=\frac{2\sqrt{10}}{2\sqrt{5}}=\sqrt{\frac{10}{5}}=\sqrt{2}


Guidorizzi, quanto tempo!!!! (Época boa)

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