Question

${lim}_{x\to \frac{\pi }{6}}\left(\frac{3\sin x-\sqrt{3}\cos x}{6x-\pi }\right)$

Answer 1

$\underset{x\to \frac{\pi }{6}}{lim}\left(\frac{3\sin x-\sqrt{3}\cos x}{6x-\pi }\right)=\frac{\frac{3}{2}-\sqrt{3}\times \frac{\sqrt{3}}{2}}{6\times \frac{\pi }{0}-\pi }\frac{0}{0}$form

$=\underset{x\to \frac{\pi }{6}}{lim}\frac{3\cos x+\sqrt{3}\sin x}{6}=\frac{\sqrt{3}\times \frac{\sqrt{3}}{2}+\sqrt{3}\times \frac{1}{2}}{6}$

$=\frac{2\sqrt{3}}{6}=\frac{1}{\sqrt{3}}$