exo7 5426

$\lim_{x\rightarrow \pi/2}(\sin x)^{1/(2x-\pi)}$

$\lim_{x\rightarrow \pi/2}|\tan x|^{\cos x}$

$\lim_{n\rightarrow +\infty}\left(\cos(\frac{n\pi}{3n+1})+\sin(\frac{n\pi}{6n+1})\right)^n$

$\lim_{x\rightarrow 0}(\cos x)^{\ln|x|}$

$\lim_{x\rightarrow \pi/2}\cos x.e^{1/(1-\sin x)}$

$\lim_{x\rightarrow \pi/3}\frac{2\cos^2x+\cos x-1}{2\cos^2x-3\cos x+1}$

$\lim_{x\rightarrow 0}\left(\frac{1+\tan x}{1+\tanh x}\right)^{1/\sin x}$

$\lim_{x\rightarrow e,\;x<e}(\ln x)^{\ln(e-x)}$

$\lim_{x\rightarrow 1,\;x>1}\frac{x^x-1}{\ln(1-\sqrt{x^2-1})}$

$\lim_{x\rightarrow +\infty}\frac{x\ln(\ch x-1)}{x^2+1}$

$\lim_{x\rightarrow 0,\;x>0}\frac{(\sin x)^x-x^{\sin x}}{\ln(x-x^2)+x-\ln x}$

$\lim_{x\rightarrow +\infty}\left(\frac{\ln(x+1)}{\ln x}\right)^x$

$\lim_{x \rightarrow 1/\sqrt{2}}\frac{(\Arcsin x)^2-\frac{\pi^2}{16}}{2x^2-1}$

$\lim_{x\rightarrow +\infty}\left(\frac{\cos(a+\frac{1}{x})}{\cos a}\right)^x\;(\mbox{où}\;\cos a\neq0)$