Finding limit using l'hôspital We're supposed to find the following limits by applying l'Hôspital rule: $$ \lim_{x \to \infty} x^{sin(1/x)} $$ My idea was to view the limit as y, then evaluate ln(y). However, I wasn't sure how we could rewrite this to a fraction.

HINT. $$e^{\frac{\ln x}{\sin^{-1} (1/x)}}=e^{-\frac{\ln t}{\sin^{-1} t}}\underbrace=_H e^{\frac{\sin t}{t}\frac{\sin t}{\cos t}}\rightarrow 1 \ \ \ (t\rightarrow 0)$$