# Lim xcscx x →0 how to get the answer ?

May 7, 2018

${\lim}_{x \rightarrow 0} x \csc x = 1$

#### Explanation:

${\lim}_{x \rightarrow 0} x \csc x$ $=$

${\lim}_{x \rightarrow 0} \frac{x}{\sin} x$ ${=}_{x \ne 0}^{x \to 0}$

${\lim}_{x \rightarrow 0} \frac{\frac{x}{x}}{\sin \frac{x}{x}}$ $=$

${\lim}_{x \rightarrow 0} \frac{1}{\cancel{\sin \frac{x}{x}}} ^ 1$ $= 1$

or

${\lim}_{x \rightarrow 0} \frac{x}{\sin} x$ ${=}_{D L H}^{\left(\frac{0}{0}\right)}$

${\lim}_{x \rightarrow 0} \frac{\left(x\right) '}{\left(\sin x\right) '}$ $=$

${\lim}_{x \rightarrow 0} \frac{1}{\cos} x$ $= 1$