Question

Evaluate $\underset{\pi \to \frac{\pi }{3}}{lim}\frac{\sqrt{3}-\tan x}{\pi -3x}$

Answer 1

$\underset{x\to \frac{\pi }{3}}{lim}\frac{\sqrt{3}-\tan x}{\pi -3x}$

using L' hospital rule

$=\underset{x\to \frac{\pi }{3}}{lim}\frac{-{\sec }^{2}x}{-3}$

$=\frac{1}{3}\times {\left(2\right)}^2=\frac{4}{3}$