I've started applying it to any limit that looks hard, and I'm not sure that's right.
Accepted answer
Only when direct substitution gives an **indeterminate form** — specifically `0/0` or `∞/∞`. Always substitute first and write down what you get; that step is what justifies using the rule.
If substitution gives something determinate like `3/0` or `5/2`, L'Hôpital's Rule doesn't apply and using it produces a wrong answer. Forms like `0·∞`, `∞−∞`, or `1^∞` need algebra first (combine into a single fraction, or take a logarithm) to become `0/0` or `∞/∞`.
And differentiate the numerator and denominator **separately** — this is not the quotient rule.