limiti notevoli

LIMITI NOTEVOLI
1.
2.
3.
+ ∞ → a > 1
lim a =
→+∞ 0 → 0 < a < 1
x
x
0 → a > 1
lim a =
→−∞ + ∞ → 0 < a < 1
x
x
+ ∞ → b > 0
lim x =
→+∞ 0 → b < 0
b
x
4. lim log(
x)
= +∞
x→+∞
5. lim log(
x)
= −∞
6.
x→−∞
log
x
lim
x→+∞
b
( x)
= 0
( b > 0)
7. lim x log(
x)
= 0 ( b > 0)
b
8.
+
x→0
lim
x→+∞
lim
x→−∞
x
a
a
x
b
x
x
b
= 0
= 0
x
9. lim x ⋅ e = 0
x→−∞
1
10. lim 1+
= e
x→±∞
x
11.
lim
sen
x→0
x
x
( x)
= 1
( a > 1,
b > 0)
x x0
12. lim a = a ( a > 0)
x→x
0
b
13. lim x = x ( x > 0)
b
x→x
0
0
14. log(
x)
= log(
x ) ( x > 0)
lim
x→x0
15. sen(
x)
= sen(
x )
lim
x→x0
16. cos(
x)
= cos(
x )
17.
18.
lim
x→x0
log
a
lim
x→+∞
x
( x)
= 0
0
0
0
0
( a > 1)
0