Esercizi su limiti di funzioni
Calcolare i seguenti limiti (quando occorre ricondursi ai limiti notevoli):
1. lim
x→+∞
3x2+ 2x+ 1
4x+ 3
2. lim
x→0
tan3x
x(1 −cos x)
3. lim
x→2
x3−2x2−4x+ 8
x3+x2−2x−8
4. lim
x→2
x3+x2−2x−8
x3−2x2−4x+ 8
5. lim
x→0
1−cos x+ sin2x
1−cos2x
6. lim
x→− π
2
sin2x+ 3 sin x+ 2
sin2x−1
7. lim
x→+∞
4x2+x−1
8x3+ 3x2−5
8. lim
x→+∞
(√x2+ 1 −√x2−3)
9. lim
x→0
sin(3x)
e2x−1
10. lim
x→+∞
(1
√x+ 1 −√x)
11. lim
x→0
esin x−1
sin x
12. lim
x→0
x−sin x
x+ sin x
13. lim
x→0(1 + x)tan x
14. lim
x→π
2
(ecos x−1) tan x
15. lim
x→+∞
(√x2−2x−1−√x2−7x+ 3)
16. lim
x→+∞
1−cos 1
x+ tan 1
x
x
√3−1
