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
{\displaystyle f}
and
g
{\displaystyle g}
which are continuous over an interval, if
lim
x
→
c
f
(
x
)
=
lim
x
→
c
g
(
x
)
=
0
or
±
∞
{\displaystyle \lim _{x\to c}f(x)=\lim _{x\to c}g(x)=0{\text{ or }\pm \infty }
and
g
′
(
x
)
≠
0
{\displaystyle g'(x)\neq 0}
and
lim
x
→
c
f
′
(
x
)
g
′
(
x
)
{\displaystyle \lim _{x\to c}{\frac {f'(x)}{g'(x)}
exists, 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)}
When the rule is used, it usually simplifies the limit or changes it to a limit that can be solved.
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