TAVOLA DEI LIMITI
Limiti immediati
Nella somma: lim
x→α
[f(x) + g(x)]
`± ∞ → ±∞,+∞+∞ → +∞,−∞ − ∞ → −∞
Nel prodotto: lim
x→α
f(x)g(x)
(` > 0) ·(±∞)→ ±∞,(` < 0) ·(±∞)→ ∓∞
(+∞)·(+∞)→+∞,(+∞)·(−∞)→ −∞,(−∞)·(−∞)→+∞
Nella quoziente: lim
x→α
f(x)
g(x)
`
±∞ →0,(` > 0)
0±→ ±∞,(` < 0)
0±→ ∓∞
±∞
(` > 0) → ±∞,±∞
(` < 0) → ∓∞
0
±∞ →0,+∞
0±→ ±∞,−∞
0±→ ∓∞
Forme indeterminate
+∞−∞,(0±)·(±∞),±∞
±∞ ,0±
0±,±∞0,1±∞
Limiti notevoli
lim
x→0
sin x
x= 1 lim
x→0
1−cos x
x= 0
lim
x→0
1−cos x
x2=1
2lim
x→+∞
log x
xp= 0 p∈N0
lim
x→0+xplog x= 0 p∈N0lim
x→+∞
ex
xp= +∞p∈N0
lim
x→−∞ xpex= 0 p∈N0lim
x→±∞ 1 + 1
xx
=e
lim
x→0
ex−1
x= 1 lim
x→0
log(1 + x)
x= 1
1
