Question:
Evaluate the following limits:
$\lim _{x \rightarrow 0}(x \cot 2 x)$
Solution:
To Find: Limits
NOTE: First Check the form of imit. Used this method if the limit is satisfying any one from 7 indeterminate form.
In this Case, indeterminate Form is $0 \times \infty$
Formula used: $\lim _{x \rightarrow 0} \frac{x}{\tan x}=1$
So, by using the above formula, we have
$\lim _{x \rightarrow 0} x \cot 2 x=\lim _{x \rightarrow 0} \frac{2 x}{2 \tan 2 x}=\frac{1}{2}$
Therefore, $\lim _{x \rightarrow 0} x \cot x=\frac{1}{2}$