Question

find lim as x goes to 0 2/(x csc x)

Answer 1

does it help to know that
\[\frac{2}{\csc(x)}=2\sin(x)\]?

Answer 2

\[\large
\lim_{x \rightarrow 0}\frac{2}{x\csc(x)} =
\lim_{x \rightarrow 0}\frac{2\sin(x)}{x} =
2 * \lim_{x \rightarrow 0}\frac{\sin(x)}{x} = ?
\]

Answer 3

The last part is a well-known limit.

https://www.khanacademy.org/math/differential-calculus/limits_topic/squeeze_theorem/v/proof-lim-sin-x-x