Relacionat: Sèries de Taylor i de Laurent típiques
$$ e^x\approx 1+x\textcolor{gray}{+\frac{x^2}{2}} $$
$$ \sin x\approx x\gray{-\frac{x^3}{6}} $$
$$ \cos x\approx 1\gray{-\frac{x^2}{2}} $$
$$ \sqrt{1+x}\approx 1+\frac{x}{2}\gray{-\frac{x^2}{8}} $$
$$ \frac{1}{1-x}\approx1+x\gray{+x^2} $$
$$
\frac{1}{1+x} \approx 1-x \gray{+ x^2} $$
$$ \frac{1}{(1-x)^2} \approx 1 + 2x \gray{+ 3x^2} $$
$$ \frac{1}{(1+x)^2} \approx 1 - 2x \gray{+3x^2} $$
$$ \ln(1+x)\approx x\gray{-\frac{x^2}{2}} $$
I per tant… (a ordre zero)
$$ \tan x\approx\sin x\approx \sinh x\approx x \qquad \cos x\approx \cosh x\approx1 \qquad e^{x}-1\approx x
$$
$$ \coth(x)\approx \cot(x)\approx \frac{1}{x} $$
$$ \coth(x)\approx \tanh(x)=1 $$