How to use L'Hospital's Rule : Calculus 1 (Limits)

L'Hôpital's rule (/ˌloʊpiːˈtɑːl/, loh-pee-TAHL), also known as Bernoulli's rule, is a mathematical theorem that allows evaluating limits of indeterminate forms using derivatives. Application (or repeated application) of the rule often converts an indeterminate form to an expression that can be easily evaluated by substitution. The rule is named after the 17th-century French mathematician Guillaume de l'Hôpital. Although the rule is often attributed to l'Hôpital, the theorem was first introduced to him in 1694 by the Swiss mathematician Johann Bernoulli.
The differentiation of the numerator and denominator often simplifies the quotient or converts it to a limit that can be evaluated directly.
The general form of L'Hôpital's rule covers many cases. Let c and L be extended real numbers (i.e., real numbers, positive infinity, or negative infinity). Let I be an open interval containing c (for a two-sided limit) or an open interval with endpoint c (for a one-sided limit, or a limit at infinity if c is infinite). The real valued functions f and g are assumed to be differentiable on I except possibly at c, and additionally {\displaystyle g'(x)
eq 0} on I except possibly at c. It is also assumed that {\textstyle \lim \limits _{x\to c}{\frac {f'(x)}{g'(x)}}=L.} Thus, the rule applies to situations in which the ratio of the derivatives has a finite or infinite limit, but not to situations in which that ratio fluctuates permanently as x gets closer and closer to c.
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[@lolkorea8841]

Nice

[@iqinitiative]

👍

[@waffles6132]

Sadly it is a forbidden technique for me. (removed from school program)

[@iqinitiative]

Ohh i see. So you use it directly when finding limits?

[@waffles6132]

@@iqinitiative no we aren't allowed to use it at all.