Question

Using the L'hopitale rule.
What is
Lim x^sinx
x->0+

Answer 1

\[e^{\ln(x^{\sin(x)})} =x^{\sin(x)} \text{ for } x>0 \\ e^{\ln(x^{\sin(x)})}=e^{\sin(x) \ln(x)}=e^\frac{\ln(x)}{\frac{1}{\sin(x)}}=e^{\frac{\ln(x)}{(\sin(x))^{-1}}}\]