Johann Bernoulli

1. Brachistochrone Problem

Finding the curve of fastest descent between two points.

$$ \frac{\sin \theta}{\sqrt{v}} = \text{constant} \implies y(1 + (y')^2) = C $$

2. L'Hôpital's Rule

Taught to L'Hôpital by Johann Bernoulli (for a fee).

$$ \lim_{x \to c} \frac{f(x)}{g(x)} = \lim_{x \to c} \frac{f'(x)}{g'(x)} $$