Evaluate the following limit.
$$ \lim_{x\to 0^+} (sin\ x)^x $$
What i have tried:
$$ ln\ [\lim_{x\to 0^+} (sin\ x)^x] $$
$$ \lim_{x\to 0^+} ln\ (sin\ x)^x $$
$$ \lim_{x\to 0^+} \frac{ln\ (sin\ x)}{\frac{1}{x}} $$
Applying l'hopital's rule.
$$ \lim_{x\to 0^+} \frac{cot\ x}{-x^{-2}} $$
If i keep applying l'hopital's rule, i get indeterminate form. Is what Iam doing right ?
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