صيغة غير معينة
الشروط
التحويل إلى 0/0
التحويل إلى ∞/∞
0/0
lim
x
→
c
f
(
x
)
=
0
,
lim
x
→
c
g
(
x
)
=
0
{\displaystyle \lim _{x\to c}f(x)=0,\ \lim _{x\to c}g(x)=0\!}
—
lim
x
→
c
f
(
x
)
g
(
x
)
=
lim
x
→
c
1
/
g
(
x
)
1
/
f
(
x
)
{\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {1/g(x)}{1/f(x)}}\!}
∞/∞
lim
x
→
c
f
(
x
)
=
∞
,
lim
x
→
c
g
(
x
)
=
∞
{\displaystyle \lim _{x\to c}f(x)=\infty ,\ \lim _{x\to c}g(x)=\infty \!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
lim
x
→
c
1
/
g
(
x
)
1
/
f
(
x
)
{\displaystyle \lim _{x\to c}{\frac {f(x)}{g(x)}}=\lim _{x\to c}{\frac {1/g(x)}{1/f(x)}}\!}
—
0 × ∞
lim
x
→
c
f
(
x
)
=
0
,
lim
x
→
c
g
(
x
)
=
∞
{\displaystyle \lim _{x\to c}f(x)=0,\ \lim _{x\to c}g(x)=\infty \!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
lim
x
→
c
f
(
x
)
1
/
g
(
x
)
{\displaystyle \lim _{x\to c}f(x)g(x)=\lim _{x\to c}{\frac {f(x)}{1/g(x)}}\!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
lim
x
→
c
g
(
x
)
1
/
f
(
x
)
{\displaystyle \lim _{x\to c}f(x)g(x)=\lim _{x\to c}{\frac {g(x)}{1/f(x)}}\!}
1∞
lim
x
→
c
f
(
x
)
=
1
,
lim
x
→
c
g
(
x
)
=
∞
{\displaystyle \lim _{x\to c}f(x)=1,\ \lim _{x\to c}g(x)=\infty \!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
exp
lim
x
→
c
ln
f
(
x
)
1
/
g
(
x
)
{\displaystyle \lim _{x\to c}f(x)^{g(x)}=\exp \lim _{x\to c}{\frac {\ln f(x)}{1/g(x)}}\!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
exp
lim
x
→
c
g
(
x
)
1
/
ln
f
(
x
)
{\displaystyle \lim _{x\to c}f(x)^{g(x)}=\exp \lim _{x\to c}{\frac {g(x)}{1/\ln f(x)}}\!}
00
lim
x
→
c
f
(
x
)
=
0
+
,
lim
x
→
c
g
(
x
)
=
0
{\displaystyle \lim _{x\to c}f(x)=0^{+},\lim _{x\to c}g(x)=0\!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
exp
lim
x
→
c
g
(
x
)
1
/
ln
f
(
x
)
{\displaystyle \lim _{x\to c}f(x)^{g(x)}=\exp \lim _{x\to c}{\frac {g(x)}{1/\ln f(x)}}\!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
exp
lim
x
→
c
ln
f
(
x
)
1
/
g
(
x
)
{\displaystyle \lim _{x\to c}f(x)^{g(x)}=\exp \lim _{x\to c}{\frac {\ln f(x)}{1/g(x)}}\!}
∞0
lim
x
→
c
f
(
x
)
=
∞
,
lim
x
→
c
g
(
x
)
=
0
{\displaystyle \lim _{x\to c}f(x)=\infty ,\ \lim _{x\to c}g(x)=0\!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
exp
lim
x
→
c
g
(
x
)
1
/
ln
f
(
x
)
{\displaystyle \lim _{x\to c}f(x)^{g(x)}=\exp \lim _{x\to c}{\frac {g(x)}{1/\ln f(x)}}\!}
lim
x
→
c
f
(
x
)
g
(
x
)
=
exp
lim
x
→
c
ln
f
(
x
)
1
/
g
(
x
)
{\displaystyle \lim _{x\to c}f(x)^{g(x)}=\exp \lim _{x\to c}{\frac {\ln f(x)}{1/g(x)}}\!}
∞ − ∞
lim
x
→
c
f
(
x
)
=
∞
,
lim
x
→
c
g
(
x
)
=
∞
{\displaystyle \lim _{x\to c}f(x)=\infty ,\ \lim _{x\to c}g(x)=\infty \!}
lim
x
→
c
(
f
(
x
)
−
g
(
x
)
)
=
lim
x
→
c
1
/
g
(
x
)
−
1
/
f
(
x
)
1
/
(
f
(
x
)
g
(
x
)
)
{\displaystyle \lim _{x\to c}(f(x)-g(x))=\lim _{x\to c}{\frac {1/g(x)-1/f(x)}{1/(f(x)g(x))}}\!}
lim
x
→
c
(
f
(
x
)
−
g
(
x
)
)
=
ln
lim
x
→
c
e
f
(
x
)
e
g
(
x
)
{\displaystyle \lim _{x\to c}(f(x)-g(x))=\ln \lim _{x\to c}{\frac {e^{f(x)}}{e^{g(x)}}}\!}
