ESERCIZI SVOLTI SUL CALCOLO DEI LIMITI
1.
Calcola i seguenti limiti:
lim
x→4
log 2 x + 1
=
3 log 4 x
lim sen ( 3 x + 1 − 1 ) =
x → −1
lim log (1 − log x ) =
x →1
log 3 x − 1
=
lim cos
x→3
x+3
lim
x→2
2x −1
lim
=
x → 1 log x − 3
lim
x→2
lim
x→2
log 3 x + log 3
log ( x 2 + x − 5 )
=
2x − 1
lim
x + log 2 x =
limπ
x→
lim log ( cos x ) =
2.
2
lim
x→2
x→0
x →1
x−2
x→3
e cos x + sen x
lim
=
x →π
1 + tg x
lim
x2 + x + 1
=
cos ( π x )
2 x − 2 + 2x
=
1 + log x
3
x =
sen x + cos x
=
2x
2 x2 − x + 1
=
22 x − 2 x + 2
lim ( sen x + 2 cos x − 1) =
x →π
Calcola i seguenti limiti, risolvendo le forme indeterminate corrispondenti:
Forma indeterminata del tipo
−
−
lim (
x → +∞
lim
x → +∞
+∞ − ∞
x+7 −
x
2x −1 −
x − 5) =
2x + 2
=
−
−
lim (
x → +∞
x2 + 1 −
x − 4) =
lim ( x 4 − x 2 − 9 ) =
x → −∞
−
Forma indeterminata del tipo
−
−
−
∞
∞
x6 − 3 x4
=
2 x2 − 2 x + 1
−
lim
2 x5 − x3 + x4
=
x5 − 6 x 2
−
lim
x2 − 2 x + 3 x3
=
2 x4 − x2
lim
x → −∞
x → +∞
x → +∞
−
lim
x → +∞
lim
x → −∞
lim
x → +∞
4 x2 − 3
=
x +1
3x − 2
x2 − x + 1
x3 + x + 2
2 x2 + 1
=
=
Forma indeterminata del tipo
−
3.
lim
x → −5
0
0
x 2 + 3 x − 10
=
x 2 − 25
−
Determina gli asintoti delle seguenti funzioni, dopo averne determinato il dominio:
−
y=
2 x2 + 3 x
x2 − 1
−
y=
2x + 5
x − 4x + 4
−
y=
2 x2 + 3 x
x −1
−
y=
x2 − 4 x
x2 − 5 x + 4
−
y=
x3 + 3 x
x−3
2
lim
x → −2
3 x 2 + x − 10
=
x 2 − 5 x − 14
