Etudier l’existence et la valeur éventuelle des limites suivantes
\(\lim_{x\rightarrow \pi/2}(\sin x)^{1/(2x-\pi)}\)
\(\lim_{x\rightarrow \pi/2}|\tan x|^{\cos x}\)
\(\lim_{n\rightarrow +\infty}\left(\cos(\frac{n\pi}{3n+1})+\sin(\frac{n\pi}{6n+1})\right)^n\)
\(\lim_{x\rightarrow 0}(\cos x)^{\ln|x|}\)
\(\lim_{x\rightarrow \pi/2}\cos x.e^{1/(1-\sin x)}\)
\(\lim_{x\rightarrow \pi/3}\frac{2\cos^2x+\cos x-1}{2\cos^2x-3\cos x+1}\)
\(\lim_{x\rightarrow 0}\left(\frac{1+\tan x}{1+\tanh x}\right)^{1/\sin x}\)
\(\lim_{x\rightarrow e,\;x<e}(\ln x)^{\ln(e-x)}\)
\(\lim_{x\rightarrow 1,\;x>1}\frac{x^x-1}{\ln(1-\sqrt{x^2-1})}\)
\(\lim_{x\rightarrow +\infty}\frac{x\ln(\ch x-1)}{x^2+1}\)
\(\lim_{x\rightarrow 0,\;x>0}\frac{(\sin x)^x-x^{\sin x}}{\ln(x-x^2)+x-\ln x}\)
\(\lim_{x\rightarrow +\infty}\left(\frac{\ln(x+1)}{\ln x}\right)^x\)
\(\lim_{x \rightarrow 1/\sqrt{2}}\frac{(\Arcsin x)^2-\frac{\pi^2}{16}}{2x^2-1}\)
\(\lim_{x\rightarrow +\infty}\left(\frac{\cos(a+\frac{1}{x})}{\cos a}\right)^x\;(\mbox{où}\;\cos a\neq0)\)