\begin{example}
$\lim_{x\to 0} \frac{\cos x - e^{\frac{x^2}{2}}}{x^4}$ . נראה כי \\$\cos x = 1-\frac{x^2}{2}+\frac{x^4}{24}+o(x^4) , e^{-\frac{x^2}{2}}=1-\frac{x^2}{2} + \frac{x^4}{8}+o(x^4) $
לכן
$$\lim_{x\to 0} \frac{\cos x - e^{\frac{x^2}{2}}}{x^4} = \lim_{x\to 0} \frac{1-\frac{x^2}{2}+\frac{x^4}{24}+o(x^4)-1+\frac{x^2}{2}-\frac{x^4}{8}+o(x^4)}{x^4} = $$
$$\lim_{x\to 0} \frac{(\frac{1}{24}-\frac{1}{8})x^4 + o(x^4)}{x^4}=\frac{1}{24}-\frac{1}{8}=\frac{-1}{12} $$
\end{example}