回復 12# cut6997 的帖子
第14題
\(\begin{align}
& \frac{\tan \theta -\sin \theta }{{{\theta }^{3}}} \\
& =\frac{\sin \theta -\sin \theta \cos \theta }{{{\theta }^{3}}\times \cos \theta } \\
& =\frac{\sin \theta \times 2{{\sin }^{2}}\frac{\theta }{2}}{{{\theta }^{3}}\times \cos \theta } \\
& =\frac{\sin \theta }{\theta }\times {{\left( \frac{\sin \frac{\theta }{2}}{\frac{\theta }{2}} \right)}^{2}}\times \frac{1}{2\cos \theta } \\
& \\
& \underset{\theta \to 0 }{\mathop{\lim }}\,\frac{\tan \theta -\sin \theta }{{{\theta }^{3}}}=1\times 1\times \frac{1}{2}=\frac{1}{2} \\
\end{align}\)
