Have you seem a single example of finding the limit of$\displaystyle \frac{f(x)}{g(x)}$ where both f(x) and g(x) tend to 0? (Here f(x) = ln(1 + x) and g(x) = sin(x) from post #2.) If not, then you need to read your textbook or lecture notes. This forum is not intended to teach new subjects, only to give hints about subjects that users already know. If yes, then follow the example you read. Read also about the
l'Hôpital's rule, which is the simplest way to find such limits. I prefer the method of expanding f(x) and g(x) into Taylor series, though.