Fórum de Matemática
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Boas.
Tentei fazer este limite(14) , mas deu-me +infinito.
Alguém sabe resolver?

\((1)\; \lim_{x\rightarrow 0}\left ( \frac{2}{x\, ^{2}}\: \tan ^{2}\left ( \frac{x}{3} \right ) \right )\; ^{\infty \times 0}\)

\((2)\; \lim_{x\rightarrow 0}\left ( \frac{2}{x\, ^{2}}\; \frac{\sin ^{2}\left ( \frac{x}{3} \right )}{\cos ^{2}\left ( \frac{x}{3} \right )} \right )\)

\((3)\; \lim_{x\rightarrow 0}\left ( \frac{2}{\cos ^{2}\left ( \frac{x}{3} \right )}\; \frac{\sin ^{2}\left ( \frac{x}{3} \right )}{x^{2}} \right )\)

\((4)\; \lim_{x\rightarrow 0}\left ( \frac{2}{\cos ^{2}\left ( \frac{x}{3} \right )}\; \frac{\sin \left ( \frac{x}{3} \right )}{x}\; \frac{\sin \left ( \frac{x}{3} \right )}{x}\right )\)

\((5)\; \lim_{x\rightarrow 0}\left ( \frac{2}{\cos ^{2}\left ( \frac{x}{3} \right )}\; \frac{\sin \left ( \frac{x}{3} \right )}{\frac{x}{3}}\times \frac{1}{3}\; \frac{\sin \left ( \frac{x}{3} \right )}{\frac{x}{3}}\times \frac{1}{3} \right )\)

\((6)\; \frac{2}{\cos 0}\times \frac{1}{9}\times 1\times 1=\frac{2}{9}\)

Opção B