The first appearance in print of L’Hˆopital’s Rule was in the book Analyse des Infiniment Petits published by the Marquis de L’Hopital in 1696. This was the first calculus textbook ever published and the example that the Marquis used in that book to illustrate his rule was to find the limit of the function

x =

(√(2a^{3}x−x^{4})) − (a(^{3}√(aax)))

a - (^{4}√(ax^{3}))

as x approaches a, where a > 0. (At that time it was common to write aa instead of a^{2}.) Solve this problem

N.B. : √ = route