Question

how to solve this indeterminate form?

Answer 1

\[\lim_{x \rightarrow 0+} \frac{ \log \cot x }{ \exp ^{\csc ^{x}} }\]

Answer 2

Generally L'Hopital's rule is a good thing to use, unless you're not allowed to.

Answer 3

Can you check if the question is
\(\huge{\lim_{x \rightarrow 0+} \frac{ \log \cot x }{ \exp ^{\csc {x}} }}\)
instead of
\(\huge{\lim_{x \rightarrow 0+} \frac{ \log \cot x }{ \exp ^{\csc ^{x}} }}\)

Answer 4

L'Hôpital's rule could be used here, but please, not before some simplifications and possibly an appropriate substitution.