L'Hopital's rule does not help with the given limit. Find the limit some other way.
-$\lim _ { \theta \rightarrow \pi / 2 ^ { - } } \frac { \csc \theta } { \cot \theta }$
A) 1
B) $\infty$
C) 0
D) $- 1$

Question

Quizplus · Accepted Answer

As $\theta$ approaches $\pi/2$ from the left, $\csc \theta = 1/\sin \theta$ approaches infinity because $\sin \theta$ approaches 1, and $\cot \theta = \cos \theta / \sin \theta$ approaches 0 because $\cos \theta$ approaches 0. Thus, the fraction $\csc \theta / \cot \theta$ approaches infinity.

L'Hopital's Rule Does Not Help with the Given Limit lim⁡θ→π/2−csc⁡θcot⁡θ\lim _ { \theta \rightarrow \pi / 2 ^ { - } } \frac { \csc \theta } { \cot \theta }limθ→π/2−​cotθcscθ​

L'Hopital's Rule Does Not Help with the Given Limit $\lim _ { \theta \rightarrow \pi / 2 ^ { - } } \frac { \csc \theta } { \cot \theta }$