Resposta 10

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10. Como $-1 \leq \sin n \leq 1$, então $\displaystyle \frac{-1}{n} \leq \frac{\sin n}{n} \leq \frac{1}{n}$. Pelo teorema das sucessões enquadradas, como $\displaystyle \lim \frac{-1}{n}= \lim \frac{1}{n}=0$, concluímos que $$\displaystyle \lim \frac{\sin n}{n}=0$$

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