Limiti notevoli
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
sin x
=1
x→0 x
tan x
lim
=1
x→0
x
1 − cos x
1
lim
=
2
x→0
x
2
sinh x
=1
lim
x→0
x
tanh x
lim
=1
x→0
x
1
cosh x − 1
=
lim
2
x→0
x n 2
1
lim 1 +
=e
n→∞
n
x
1
1
= e,
lim (1 + x) x = e
lim 1 +
x→0
x→∞
x
x
t
lim 1 +
= et ,
t∈R
x→∞
x
ln(1 + x)
lim
=1
x→0
x
ln x
=1
lim
x→1 x − 1
loga (1 + x)
1
lim
=
,
a > 0, a 6= 1
x→0
x
ln a
ex − 1
lim
=1
x→0
x
ax − 1
lim
= ln a,
a > 0, a 6= 1
x→0
x
x
e
lim
= 0, ∀ α > 0
x→+∞ xα
loga x
loga x
lim
= 0+ , ∀α > 0 se a > 1; lim
= 0− ,
α
x→+∞ x
x→+∞ xα
lim xα ax = 0,
∀α > 0, 0 < a < 1; lim (−x)α ax = 0,
lim
x→+∞
lim+ xα loga x = 0− ,
∀α > 0 se 0 < a < 1
x→−∞
∀α > 0 se a > 1;
lim+ xα loga x = 0+ ,
x→0
x→0
1
∀α > 0, a > 1
∀α > 0 se 0 < a < 1