\(\frac 1{\sin^2x} - \frac 1{\sh^2x} \to \frac 23\) lorsque \(x\to 0\).
\(\frac {\sin x\sh x - \tan x\tanh x}{\sh^4x - \tanh^4x} \to -> -\frac1{12}\) lorsque \(x\to 0\).
\((\ch x)^\alpha - (\sh x)^\alpha \to \begin{cases}+\infty &\text{ si }\alpha>2,\cr 1 &\text{ si } \alpha=2,\cr 0 &\text{ si } \alpha<2.\cr\end{cases}\) lorsque \(x\to +\infty\)
\(\frac {\exp(x^2) - \ch(x\sqrt2\,)}{(\ch x - \cos x)(\ch2x - \cos2x)} \to \frac1{12}\) lorsque \(x\to 0\).
\((2x^2-3x+1)\tan \pi x \to \frac1\pi\) lorsque \(x\to 1/2\).
\(\frac{\cos\pi x}{4x^2-9} \to -> \frac\pi{12}\) lorsque \(x\to 3/2\).
\(\frac{\sin 3x}{1-2\cos x} \to-\sqrt3\) lorsque \(x\to \pi/3\).
\(\frac{e^{\sin x}-e^x}{\sin x-x} \to 1\) lorsque \(x\to 0\).
\(\frac 1x \ln\ch x \to 1\) lorsque \(x\to +\infty\).