Question:
Evaluate the following limits:
$\lim _{x \rightarrow 0} x \operatorname{cosec} x$
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 are $0 \times \infty$
Formula used: $\lim _{x \rightarrow 0} \frac{x}{\sin x}=1$
So, by using the above formula, we have
$\lim _{x \rightarrow 0} x \operatorname{cosec} x=\lim _{x \rightarrow 0} \frac{x}{\sin x}=1$
Therefore, $\lim _{x \rightarrow 0} x \operatorname{cosecx}=1$