Bài soạn congthuctoan12

Hoµng Nam Ninh - §HSPTN

§T: 0956 866 696
C¸c c«ng thøc hµm sè mò logarit cÇn nhí–
I - c«ng thøc cña hµm sè mò
nm
a
n
a
m
a
+
=
..1
nm
a
n
a
m
a
−
=
.2
nm
a
n
m
a
.
.3
=







( )
n
b
n
a
n
ba ...4
=
n
n
n
b
a
b
a
=






.5
nnn

baba ...6
=
n
n
n
b
a
b
a
=.7
( )
n
m
m
nn
m
aaa
==
.8
nm
m
n
aa
.
.9
=
10:1:.10
<<<>>⇔>
akhinmakhinmaa
nm

;
nn
balebaba
<→<
:,,.11
II- C«ng thøc hµm sè logarit
100log.1
≠<>=⇔=
a, DK:bbab
a

α
α
1log01log.2
==
a
aa
;
baba
b
b
a
a
==
log
log.3 ;
( )
cbcb
aaa
loglog.log.4

+=
cb
c
b
aaa
logloglog.5
−=






a
b
a
b
a
b
b
c
c
a
ln
ln
lg
lg
log
log
log.6

===
bb
a
a
log
1
log.7
α
α
=
a
b
b
a
log
1
log.8
=
10::loglog.9
<<<>>⇔>
ac: khi: bakhicbcb
aa
1;
III- §¹o hµm cña hµm sè :
aayay
xx
ln'.1
=→=
xx
eyey

=→=
'.2
ax
yxy
a
ln
1
'log.3
=→=
x
yxy
1
'ln.4
=→=
IV- Giíi h¹n cña hµm sè:
( )
ex
x
x
=+
∞→
1
1lim.2
a
x
a
x
x
ln
1

lim.3
0
=
−
→
( )
a
x
x
a
x
=
+
→
1
lim.4
0
( )
e
x
x
a
a
x
log
1log
lim.5
0
=
+

→
e
x
x
x
=






+
∞→
1
1lim.1