L'Hopital's rule greatly simplifies the evaluation of limits of indeterminate forms, especially those with polynomial terms. This is because every time you take the derivative of a polynomial, the exponent decreases by 1, until it becomes a constant function, at which point the limit can be evaluated.(adsbygoogle = window.adsbygoogle || []).push({});

So the question is, how can you apply L'Hopital's rule to an indeterminate form such as e^x/x^x? or x^x/x!? for some functions, such as the double exponential, factorial, and hyperoperations (tetration, pentation...) each successive ordered derivative increases everytime you differentiate.

So is there a way to resolve this problem using the tools of elementary calculus? I know that for series there are tests to test convergence, but is there a similar procedure for continuous functions?

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# L'Hopital's rule for increasing functions

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