Question

Find the following limit:
$\underset{x\to 0}{lim}x\cot 3x$

Answer 1

$\underset{x\to 0}{lim}x\cot 3x$

$\Rightarrow \underset{x\to 0}{lim}\frac{3x}{\tan 3x}\times \frac{1}{3}$

$=\underset{x\to 0}{lim}\left(\frac{3x}{\tan 3x}\right)\times \frac{1}{3}$

$=1\times \frac{1}{3}$

Because $\underset{t\to 0}{lim}\frac{t}{\tan t}=1$

$=\frac{1}{3}$.