Mathematics
L'Hôpital's Rule and Its Conditions for Indeterminate Forms
Quick fact
L'Hôpital's rule can turn a tricky limit like sin(x)/x as x approaches 0 into a simple evaluation of cos(x) at 0, giving 1. But it only works under very specific conditions—misapplying it leads to wrong answers.
Why this is interesting
You're calculating a limit and get 0/0. That's not an answer—but it's also not a dead end. What if the answer is hiding in the slopes?