For ten points, name this mathematician who showed the limit of such an indeterminate function will equal the limit of the ratio of derivatives.
He was one of the four solvers of the brachistochrone problem, with Newton, Leibniz, and Jacob Bernoulli. He had been taught by another Bernoulli, Johann. In 1696 this French cavalry officer (who resigned due to nearsightedness) published the first known textbook on differential calculus titled The Analysis of the Infinitely Small for the Study of Curves. He is best perhaps known for the method of calculating the limiting value of a rational function whose numerator and denominator approach zero. For ten points, name this mathematician who showed the limit of such an indeterminate function will equal the limit of the ratio of derivatives.
He was one of the four solvers of the brachistochrone problem, with Newton, Leibniz, and Jacob Bernoulli.
Guillaume François Antoine, Marquis de {l'Hôpital}