$\underset{x→\frac{π}{3}}{\lim}\frac{\tan^3x-3\tan x}{\cos\begin{pmatrix}x+\frac{π}{6}\end{pmatrix}}$ is equal to
Answer & explanation
Correct answer: option 1
$\underset{x→\frac{π}{3}}{\lim}\frac{\tan^3x-3\tan x}{\cos\left(x+\frac{π}{6}\right)}=\frac{0}{0}$ form
applying L'Hopital's rule
$\underset{x→\frac{π}{3}}{\lim}\frac{3\tan^2x\sec^2x-3\sec^2x}{-\sin\left(x+\frac{π}{6}\right)}=-24$