It fails on the limit of x divided by the square root of x-squared plus one as x goes to infinity.
It has a discrete analog in the Stolz-Cesaro theorem, which holds that the limit of the ratio of the difference between consecutive terms of two sequences is equal to the limit of the ratio of the terms. It is usually proved using the extended mean value theorem, and this statement holds only when one of the functions it describes does not change from positive to negative infinitely many times. It fails on the limit of x divided by the square root of x-squared plus one as x goes to infinity. FTP, identify this method that uses derivatives to compute indeterminate limits.
It has a discrete analog in the Stolz-Cesaro theorem, which holds that the limit of the ratio of the difference between consecutive terms of two sequences is equal to the limit of the ratio of the terms.
{L'Hopital's} rule (or {Bernoulli's} rule)