<|system|>
Show that l'Hôpital's rule amounts to forming a Taylor expansion of both the numerator and the denominator. Evaluate the limit
$$
\lim _{x \rightarrow 0} \frac{\ln (1+x)-x}{x^2}
$$
both ways.</s>.
<|user|>
Can you answer based on context?
<|assistant|>
-0.5