On a One Type of Zero-Over-Zero Form Limits

It is hard to evaluate some limits by only making use of L'Hôpital's rule. In this paper, we consider the way to evaluate a one type of zero-over-zero form limits which has form of \(\begin{align} \lim_{x\rightarrow0} \frac{f(x) - a}{g(x)} \end{align}\) where where \(f\) and \(g\) are functions such that \(\displaystyle \lim_{x \rightarrow 0} f(x) = a\) and \(\displaystyle \lim_{x \rightarrow 0} g(x) = 0\). In conclusion, we found the way to evaluate a one type of zero-over-zero form limit: \(\begin{align} \lim_{x \rightarrow 0} \frac{f_1(x) f_2(x) \cdots f_n(x) - a_1 a_2 \cdots a_n}{g(x)} \end{align}\) where \(g \) is a function such that \(\displaystyle \lim_{x \rightarrow 0} g(x) = 0\) and \(f_1, f_2, ..., f_n\) (\(n\in\mathbb{N}\)) are functions such that, for every \(k \in \{1, 2, \ldots, n\}\), \(\displaystyle \lim_{x \rightarrow 0}f_k(x) = a_k\) and \(\displaystyle \lim_{x \rightarrow 0} \frac{f_k(x) - a_k}{g(x)}\) exists as sum of the same type of zero-over-zero form limits without making use of L'Hôpital's rule.