L'Hôpital's Rule is a mathematical theorem that allows for the evaluation of certain limits involving indeterminate forms. It states that if an expression has two functions in the form of 0/0 or ∞/∞, then its limit can be found by taking the derivative of both functions and evaluating them at the same point. This rule was named after French mathematician Guillaume de l'Hôpital who first published it in 1694. The rule can be rewritten as: given two differentiable functions f(x) and g(x), where either f(a)=0 or g(a)=0, then lim x→af (x)g (x) =lim x→ag '(x)f '(x). This means that if both derivatives exist at some point a, then one could take their ratio to determine the value of the original expression when evaluated at a. In other words, L'Hôpital's Rule provides us with a way to calculate limits without having to compute long expressions.