Question

Evaluate the limit
$\underset{x\to \frac{\pi }{6}}{lim}\frac{{\cot }^{2}x-3}{\cos ecx-2}$

Answer 1

${lim}_{x\to \frac{\pi }{6}}\frac{{\cot }^{2}x-3}{cosecx-2}$

it is of the form $\frac{0}{0}$

So, we will apply L Hospital rule until we will get determinate form

Differentiating numerator and denominator we will get,

${lim}_{x\to \frac{\pi }{6}}\frac{-2\cot xcose{c}^{2}x}{-\cot xcosecx}={lim}_{x\to \frac{\pi }{6}}2cosecx=2\times 2=4$