Non ironically, the professor I had had it banned for a while in order to make us learn that there are other ways (which sometimes work when L'Hopital doesn't)
And of course the final exam had such case.
By use of Taylor expansion ... (tan(x)-x)/x^3=(sin(x)-x*cos(x))/(x^3*cos(x)) \approx ((x-x^3/3!+x^5/5!)-x*(1-x^2/2!+x^4/4!)/(x^3*(1-x^2/2!+x^4/4!)) ... for x to zero = (1/2!-1/3!)+x^2*O(1)=1/3
In the UK, former Prime Minister Johnson promised 40 new l'Hopitals rules - always unrealistic and unfunded. His government then started claiming any new equation counted as a new rule, trying to convince us the target would be met.
