Corso di Laurea in Informatica Applicata Analisi Matematica Limiti

Corso di Laurea in Informatica Applicata
Analisi Matematica
Limiti importanti
−∞ se a > 1
+∞ se 0 < a < 1
x→0
n
+∞ se a > 1
lim loga x =
x→+∞
−∞ se 0 < a < 1
n
+∞ se a > 1
lim ax =
x→+∞
0
se 0 < a < 1
n
0
se a > 1
lim ax =
x→−∞
+∞ se 0 < a < 1
α x
α x
lim 1 +
= lim 1 +
= eα , ∀α ∈ IR
x→+∞
x→+∞
x
x
lim+ loga x =
n
lim+ xα log x = 0, ∀α > 0;
x→0
lim
x→+∞
√
x
a = 1;
lim+ xx = 1;
x→0
lim
log x
= 0, ∀β > 0
x→+∞ xβ
lim
x→+∞
√
x
xβ = 1, ∀β > 0
xα
= 0, ∀α ∈ IR
x→+∞ ex
lim
sin x
= 1;
x→0 x
tan x
=1
x→0
x
lim
lim
arcsin x
=1
x→0
x
arctan x
= 1;
x→0
x
lim
lim
ax − 1
= log a
x→0
x
1 − cos x
1
= ;
2
x→0
x
2
lim
lim
loga (x + 1)
1
=
= loga e
x→0
x
log a
lim
1