L'Hôpital's rule

L'Hôpital's rule is a mathematical rule that can calculate limits of an indeterminate form using derivatives. When the rule is used (it can be used multiple times), it turns an indeterminate form into a value that can be solved.

L'Hôpital's rule states that for functions $f$ and $g$ which are continuous over an interval, if $\underset{x\to c}{\lim }f(x)=\underset{x\to c}{\lim }g(x)=0\text{ or }\pm \mathrm{\infty }$ and $g^{\prime }(x)\ne 0$ and $\underset{x\to c}{\lim }\frac{f^{\prime }(x)}{g^{\prime }(x)}$exists, then

$\underset{x\to c}{\lim }\frac{f(x)}{g(x)}=\underset{x\to c}{\lim }\frac{f^{\prime }(x)}{g^{\prime }(x)}$

When the rule is used, it usually simplifies the limit or changes it to a limit that can be solved.

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