Limit of a function
L'Hôpital's rule

This rule uses derivatives to find limits of indeterminate forms 0/0 or ±∞/∞, and only applies to such cases. Other indeterminate forms may be manipulated into this form. Given two functions f (x) and g (x), defined over an open interval I containing the desired limit point c, then if:

then: lim x → c f (x) g (x) = lim x → c f ′ (x) g ′ (x). {\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {f'(x)}{g'(x)}}.}

Normally, the first condition is the most important one.

For example: lim x → 0 sin (2 x) sin (3 x) = lim x → 0 2 cos (2 x) 3 cos (3 x) = 2 ⋅ 1 3 ⋅ 1 = 2 3. {\displaystyle \lim _{x\to 0}{\frac {\sin(2x)}{\sin(3x)}}=\lim _{x\to 0}{\frac {2\cos(2x)}{3\cos(3x)}}={\frac {2\cdot 1}{3\cdot 1}}={\frac {2}{3}}.}
change_case:capital_word_frequency[8]