Integral Formula
by Mathematics Navigator
last update 03/04/11
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(
log
x
)
′
=
lim
Δ
x
→
0
log
(
x
+
Δ
x
)
−
log
x
Δ
x
=
lim
Δ
x
→
0
log
(
x
+
Δ
x
x
)
Δ
x
=
lim
Δ
x
→
0
1
Δ
x
log
(
1
+
Δ
x
x
)
When
Δ
x
x
=
t
,
Δ
x
=
x
t
. Therefore, if
Δ
x
→
0
,
t
→
0
.
As a result,
=
lim
t
→
0
1
x
t
log
(
1
+
t
)
=
lim
t
→
0
1
x
log
(
1
+
t
)
1
t
=
1
x
log
{
lim
t
→
0
(
1
+
t
)
1
t
}
=
1
x
log
e
=
1
x
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