Carefully Checking Hypotheses of L'Hopital's Rule - Expii

If you are not careful when applying l'Hospital's rule, you might reach a false conclusion (if you use the rule when it doesn't apply). First, you should make sure that your limit of f(x)/g(x) is indeterminate of type 0/0 or ∞/∞. A less common error occurs when the limit of f'(x)/g'(x) does not exist (and is also not infinite); in these cases, l'Hospital's rule doesn't apply.