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Q. $\lim\limits_{x\to0} \frac{tan\,2x - x}{3x - sin \,x}= $

Limits and Derivatives

Solution:

$\lim\limits_{x\to0} \frac{tan\,2x - x}{3x - sin \,x} $
$= \lim\limits_{x\to0} \left\{\frac{\frac{2\,tan\,2x - 1}{2x}}{3 - \frac{sin\,x}{x}} \right\}$
$= \frac{2-1}{3-1} = \frac{1}{2} = 0.5$