Question

Find the limit of (sinx)^x as x approaches to 0+.

Answer 1

\[(\sin(x))^x=e^{x\ln(\sin(x)})\]

Answer 2

so your job is to find
\[\lim_{x\to 0^+}x\ln(\sin(x))\] usual gimmick is to write is as
\[\frac{\ln(\sin(x))}{\frac{1}{x}}\] and use l'hopital