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Basic Mathematical Relations
e =
n
n
n
⎟
⎠
⎞
⎜
⎝
⎛
+
∞
→
1
1
lim
≈
2.718
Log and power
L
L
xy
y
x
ln
ln
ln
=
+
+
,
y
x
y
x
ln
ln
ln
=
−
,
a
x
x
a
ln
ln
=
a
b
b
c
c
a
log
log
log
=
,
x
x
10
log
log
=
,
x
x
e
log
ln
=
z
y
x
z
y
x
a
a
a
a
+
+
=
,
y
x
y
x
a
a
a
−
=
/,
( )
xy
y
x
a
a
=
Derivatives
dg
df
g
f
d
+
=
+
)
(
,
gdf
fdg
fg
d
+
=
)
(
2
g
fdg
gdf
g
f
d
−
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
dx
x
dg
x
dg
x
g
df
dx
x
g
df
)
(
)
(
))
(
(
))
(
(
=
1
−
=
n
n
nx
dx
dx
(for
0
≠
n
) ,
ax
ax
ae
dx
de
=
,
x
dx
x
d
1
ln
=
Integrals
∫
+
+
=
+
const
n
x
dx
x
n
n
1
1
,
const
x
dx
x
+
=
∫
ln
1
,
const
e
a
dx
e
ax
ax
+
=
∫
1
Sum and multiplication
∑
=
+
+
+
=
n
i
i
a
a
a
a
1
3
2
1
L
,
∏
=
=
n
i
i
a
a
a
a
1
3
2
1
L
Taylor expansions
()
∑
∞
=
=
−
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
0
!
1
)
(
n
n
a
x
n
n
a
x
dx
f
d
n
x
f
,
L
+
+
+
=
2
2
1
1
x
x
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This note was uploaded on 04/03/2009 for the course CH 353M taught by Professor Lim during the Spring '08 term at University of Texas at Austin.
 Spring '08
 LIM
 Physical chemistry, pH

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