Tareas

1

Ejercicios de límites Ficha I

Calcula los siguientes límites
x2 5x + 2
2
3
x! 2 x + 3x

1
5

2x2 7x 4
x!4 x3 + x2
10

0

1. lim
1
2. lim

3. lim

x!3+ x2

4. lim
x!3x2

5. lim

x!3 x2

x+2
4x + 3

+1

x+2
4x + 3

1

x+2
4x + 3

No existe (1 )

x2 + 5
x!3 x2
6x + 9

+ 1:(2 )

6. lim

7. lim

x! 1 x3

x+1
+ 3x2 + 3x + 1

+1x2 + 4x + 4
.
x! 2 x3 + 6x2 + 12x + 8
2
x + 4x + 4 = (x + 2)2
Ayuda:
3
x + 6x2 + 12x + 8 = (x + 2)3
r
x3 2x + 5
9. lim
x!3
4x2 x + 2
8. lim

x2
x!5 10

10. lim

No existe

r25
2x

5

(x 1)(x 3)3
x!3 (2x + 1)(2x
1)(x 3)2

11. lim

0

x2 16
x!4 2x + 1
3
p
x+1 2
p
13. lim p
x!1 2x + 10
5x + 1
p
x+1 2
p
14. lim p
x!3 2x + 10
5x + 1
12. lim p

1lim

2 x2

24
1
3

2
3

x+2
x2 + 5
= +1 y lim 2
=
4x + 3
6x + 9
x!3 x
2
6x + 9 = (x 3)

x!3+

26
35

x2

1

1

p

3

15. lim
x!

x5 + a5
a x4
a4

(x + h)4h!0
h

16. lim

5
a
4
x4

x2 4
2x2 + 4x

17. lim

x!2 x3
3

4x3
1
2

8

2

2x + 9x + 12x + 4
x! 2 3x3 + 11x2 + 8x
4
p
x+4 2
19. lim
x!0
x
p
p
x+h
x
20. lim
h!0h
p
3
x2 1
21. lim p
6
x!1 x3
3x + 2

3
7

18. lim

1
4
1
p
2x
r
64
3

2x 10
22. lim p
x!5 x + 4
3
x2 + 2x 8
6x2 + 11x

23. lim

x!2 x3

12
6

6

x2 x
x!0 5x2+ 3x

1
3

24. lim

x3 4x2 + 4x
x!2 x3
3x2 + 4

2
3

25. lim

x
x2
26. lim
x!2
x2
px

13x + 22
8x + 12

1
3
2

2

1
3
p
x
6+x
28. lim
x!3
x3

27. lim

x!329. lim
x!

1
6

3

x

5
6

x4 1
1 x3 + 1

x2 + x
30. lim p
x!1 x + 3

4
3
2
2

12

2x 4
24

p

ex
x!3

31. lim

2

e

p
3

x+6 2
x2 + 3x 2
Este límitepresenta la indeterminación

32. lim

x!2

1
12
0
0

p
3
3
p
x+6
23
A3 B 3
entonces: 3 x + 6 2 = p
p
2
2 + AB + B 2
3
A
x+6 +23x+6+4
p
3
3
23
x+6
2
i
=
= lim h p
p...