L’Hôpital’s rule states that the value of the fraction was equal to the derivative of the top expression divided by the derivative of the bottom expression. For instance, consider the expression x/(sin x) when x=0; x=0, as does sin x, so the expression is equal to 0/0. Using L’Hopital’s rule, we see that the expression goes to 1/(cos x), as 1 is the derivative of x and cos x is the derivative of sin x. Cos x=1 when x=0, so the whole expression equals 1/1=1. Clever manipulations could also bring l’Hopital’s rule to resolve other odd expressions: ∞/∞, 00, 0∞, and ∞0.
