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I LIMITI NOTEVOLI
1. lim
x → 0 e x − 1 x
a) lim
x → 0 e f (x) − 1 f (x)
b) lim
x→ R¿ e f ( x) − 1 f (^ x )^
2. lim
x → 0 sen x x
a) lim^
x → 0 sen f ( x) f (x )
b) lim^
x → R¿ sen f ( x ) f ( x )
3. lim x → 0
1 −cos x x^2
a) lim
x → 0 1 −cos f (x) f 2 (x)
b) lim
x→ x 0 1 −cos f ( x ) f 2 ( x )
4. lim^
x → 0 ln( 1 +x) x
a) lim^
x → 0 ln ( 1 + f ( x ) ) f (x)
b) lim^
x → x 0 ln ( 1 + f ( x )) f (x )
5. lim^
x → 0 ( 1 + x) α − 1 x =α
a) lim^
x → 0 ( 1 + f (x)) α − 1 f (x) =α
b) lim^
x → x 0 ( 1 + f ( x)) α − 1 f ( x ) =α
NOTA BENE!
Valgono anche i reciproci ad esempio: lim x → 0 1 −cos x x
2 =^
lim x → 0 x 2 1 −cos x
DECOMPOSIZIONE CANONICA DEL LIMITE
CASO 1
ex^1 + x
ex− 1 x
e
f (x) − 1 f ( x)
e
f ( x ) 1 +f ( x )
CASO 2
sen x x
sen f ( x ) f (x)
CASO 3
1 −cos x
x 2
cos^ x^1 −^
x 2
cos f ( x) 1 −
f (x) 2
CASO 4
ln ( 1 + x) x
ln ( 1 +f ( x ) ) f ( x)
CASO 5
( 1 +x)a− 1 a∗x
( 1 + f ( x ) )
a − 1 a∗f ( x )
LIMITI NOTEVOLI FORMA DI INDECISIONE^1
∞
1. lim
x→ ∞ (
x )
x =e
a) lim
x→ ∞ (
f ( x ))
f (x) =e
GLI ASINTOTI RETTILINEI
