$\lim _{x \rightarrow 0} \frac{\tan x-\sin x}{\sin ^3 x}$
$\lim _{x \rightarrow 0} \frac{\sin x-\tan x}{\left(\sqrt[3]{1+x^2}-1\right)(\sqrt{1+\sin x}-1)} $
求极限 $\lim _{n \rightarrow \infty} \sqrt[n]{\sin \frac{\pi}{2 n} \sin \frac{2 \pi}{2 n} \cdots \sin \frac{n \pi}{2 n}}$
$\lim _{n \rightarrow \infty}\left(\frac{2}{3}\right)^{\frac{1}{2^{n-1}}}\left(\frac{4}{7}\right)^{\frac{1}{2^{n-2}}} \cdots\left(\frac{2^{n-1}}{2^n-1}\right)^{\frac{1}{2}}$
$\lim _{n \rightarrow \infty} \frac{1-\cos x \cdot \cos 2 x \cdots \cos n x}{x^2}, n \in N^*$
求极限 $\lim _{n \rightarrow \infty} \frac{1}{n} \sqrt[n]{n(n+1) \cdots(2 n+1)}$