Colectiovs

1

Ejercicios de límites Ficha I
x2 5x + 2 2 3 x! 2 x + 3x 2x2 7x 4 x!4 x3 + x2 10 x+2 4x + 3 x+2 4x + 3 1 5 0 +1 1 No existe (1 ) + 1:(2 ) +1 No existe

Calcula los siguientes límites 1. lim 12. lim

3. lim

x!3+ x2

4. lim
x!3

x2

5. lim 6. lim

x!3 x2

x+2 4x + 3

x2 + 5 x!3 x2 6x + 9
x! 1 x3

7. lim

x+1 + 3x2 + 3x + 1

x2 + 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 10. lim x2 x!5 10 25 2x

r

26 35 5 0

11. lim

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

x2 16x!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
1 x!3+

24
1 3

p

3

2 3
1

lim

2 x2

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

1

15. lim
x!

x5 + a5 a x4 a4 x4 1 2 3 7 1 4 4x3

5 a 4

16. lim 17. lim

(x + h)4 h!0 h

x!2 x3 3

x2 4 2x2 + 4x
2

8

18. lim

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!0 h p 3 x2 1 21. lim p 6 x!1 x3 3x + 2

1 p 2 x r 6 4 3 12 6 1 3 2 3

2x 10 22. lim p x!5 x + 4 3 23. lim
x!2 x3

x2 + 2x 8 6x2 +11x

6

24. lim 25. lim

x2 x x!0 5x2 + 3x

x3 4x2 + 4x x!2 x3 3x2 + 4 x 1 2 13x + 22 8x + 12

x2 26. lim x!2 x2 px 27. lim
3 x!3

3 2 1 6 5 6 4 3

1 3 p x 6+x 28. lim x!3 x 3 x
x!29. lim

x4 1 1 x3 + 1 2 2 12 p

x2 + x 30. lim p x!1 x + 3 31. lim

ex x!3

2x 4 2 4

e

2

32. lim

x+6 2 x2 + 3x 2 Este límite presenta la indeterminación
x!2

p 3

1 12 0 0Ayuda: Como A B = lim p 3 x+6 x2 + 3x

x!2

x!2

x!2

33. lim

x! 2

3x 2 + 2 x2 + 3x + 10 Este límite presenta la indeterminación

lim h p 3

lim h p 3

x+6 x+6

p 3

p 3 3 px+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 2 2 x!2 3 x + 6 + 2 3 x + 6 + 4 ( x2 + 3x 2) x 2 i = p 2 3 + 2 x + 6 + 4 ( x + 1) (x 2) 1 1 1 i...