Question

Evaluate : $\underset{x\to 0}{lim}\frac{\tan 2x-x}{3x-\sin x}=\frac{1}{2}$

Answer 1

$\underset{x\to 0}{lim}\frac{\tan 2x-x}{3x-\sin x}$

Applying L-Hospital Rule

$\underset{x\to 0}{lim}\frac{2{\text{sec}}^{2}2x-1}{3-\cos x}=\frac{1}{2}$

Hence, this is the answer.