L'Hôpital's Rule is a mathematical theorem to evaluate limits of indeterminate forms using derivatives. In other words, it is used to circumvent "0/0" and "∞/∞" such as lim(x->0) (sinx/x) when computing limits. The rule is as follows:
Suppose that lim(x->c)f(x) = lim(x->c)g(x) = 0 or ±∞, f(x) and g(x) are differentiable on an open interval *I* containing c, and g'(x) ≠ 0 in *I* if x ≠ c. Then
lim(x->c)[f(x)/g(x)] = lim(x->c)[f'(x)/g'(x)]
As part of the calculus, L'Hôpital's Rule is commonly used in real world to deal with mathematical problems. For example, it is used to deal with entropy in thermodynamics and information, calculate limiting cases in Box-Cox transform and Kullback-Leibler divergence in statistics, and prove the Gamma Function in engineering, quantum physics, etc. However, for one whose work or hobbies are not related to calculus, it is unlikely to be involved in the day-to-day life.
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