ABSTRACT
The differentiation formulas of calculus were needed for eval uation of derivatives because derivatives are of the indetermi nate form g. L’Hopital’s rule exploits differentiation to eval uate limits of the form | or This rule, devised originally by J. Bernoulli, allows one to substitute the derivatives F', G' for the functions F, G on (a, b) to evaluate the limit of as t —> a+ (or as t —> b-) when this ratio has the limiting form 2. To deal with as t —»· a+ one must have G'(t) φ 0 ultimately. So G must be strictly monotone ultimately since a derivative Gf has the intermediate value property on intervals.
