Try not to use L'Hôpital!

Calculus Level 3

Find the value of $\displaystyle\lim_{x\to0} \left( \frac1x - \frac1{\sin x} \right)$ .

Alternatively, find the value of the reciprocal function minus the cosecant function, as the variable approaches zero from both sides.

\pm\infty

does not exist

-\infty

0 1

+\infty