Calcul de limites

Exercice 1047. Calculer $\displaystyle \lim_{x \to \frac{\pi}{2}} \Frac{\ln(\sin^2(x))}{\parenthese{\Frac{\pi}{2}-x}^2}$.

Exercice 1048. Calculer $\displaystyle \lim_{x \to +\infty} \parenthese{\Frac{\ln(x+1)}{\ln(x)}}^{x\ln(x)}$.

Exercice 1049. Calculer $\displaystyle \lim_{x \to 0} \parenthese{\Frac{x}{\sin(x)}}^{\frac{\sin(x)}{x-\sin(x)}}$.