Hoµng Nam Ninh - §HSPTN §T: 0956 866 696
I - c«ng thøc cña hµm sè mò
n m a
n
a
m
a . = +
.
( ) a . b n a n . b n
.
n n
b
a b
a
=
5 6 n a.b =n a.n b
n
n
n
b
a
b
a
=
.
a a
1 0
: 1
:
10a m >a n ⇔ m> n khi a> ; m< n khi < a<
n
a le
b
a
b
a< , , : → <
.
II- C«ng thøc hµm sè logarit
1 0
0 log
1α = a b⇔ aα = b DK:b> , < a≠
1 log 0
1
log
.
2 a = ; a a=
b a
b
a
a =
log
.
c b
c
b
a a
log
.
a
b a
b a
b b
c
c a
ln
ln lg
lg log
log log
.
b
log
.
7
α
a
b
b a
log
1 log
.
1 0 :
: log
log
.
9 a b> a c⇔ b>c khi a>1; b<c: khi: <a<
III- §¹o hµm cña hµm sè :
a a y
a
.
a x y x
ln
1 ' log
.
3 = → =
x y x
.
4 = → =
IV- Giíi h¹n cña hµm sè:
x→∞ 1 + 1 = lim
.2
a x
a x
lim 3
→
x
x a
lim
.
x
x
a a
lim
5 →0 + =
e x
x
+
∞
→
1
1
lim
.
1