Calulo limites

Problemas de límites
Jesús Espinoza Montelongo
Trabajo Unidad 3
Roberto Rene Rivera Rodríguez
Grupo: Ingeniería Industrial
Horario: 9:00 am a 10 am

1. - lim (3x2+ 7x – 12)
X… 0=3(0)2 + 7 (0) – 12 = -12

2. - lim (4x2 – x + 5)
X… 2 =4(2)2 – 2 + 5
=4(4) - 2 + 5 = 16 – 2 + 5 = 19

3. - lim (2 x2 - x5)
X… -1 =2(-1) – ( -1)5 = -2 + 1 = -1

4. - lim (x2- 2 )5
X… -2 = ((-2)2 – 2)5= (4-2)5 = (2)5 = 32

5. - lim (x - 1)7 (2 x -5)4
X… 3 = (3 - 1)7 (2(3) - 5)4 = (2)7(1)4 = 128

6. - lim x+1x2-x-2
X… 1 =1 +1(1)2-1-2 = 2-2 = -1

7. - lim x-1x2-x-2
X… -1 = (-1) +1(-1)2--1-2 = 00= ∞
Factorizar: x2-x-2 = (x – 2) (x + 1)
lim x-1x2-x-2 = x +1x-2(x +1) = 1(x-2 ) = 1(-1-2) = - 13

8.– lim t2+2t-5t3-2t
X… 2 (2)2+2(2)-5(2)-2(2) = 4+4-58-4 = 34

9. - t2-9t-3 = (3)2-93-3 = 9-93-3 = 0
X… 3
Factorizar t2-9 = (t – 3) (t + 3)
= t2-9t-3 = (t – 3) (t + 3)(t - 3) = t + 3 = 3 + 3= 6

10. - lim 1y- 13y-3 = 13- 133-3 = 00 = ∞
X… 3 1y- 13y-3 = 3-y3 yy-31 = 3-yy-3 (3y) = - (y-3)y-3 (3y) = - 13y = - 19

11. – lim (x2-1)32 = (x2-1)12 (x2-1)22 = x2-1(x2-1)22
X… 3 = (3)2-1 (32-1)22 = 8 (8)22 = 8 (8) = 22 (8) = 16 2

12. – lim t +825-t2 = -4 +825- (-4)2 = 49 = 23
X… -4

13. – lim z23z-2z = 8238-2(8) = 3648-4 = 3644= 44 = 1
Z…8
14. – lim 33 t3 +4t-5
T… 2 = 33 (2)3 +4(2)-5 = 324 +8-5 = 327 = 3

15. – lim x + -2x =0+4-20 =4-20 =2-20 =00 =∞ ((x +4) – 2)((x+4)+2)x ((x+4)+2) = x +4-4x ((x+4)+2) = xx ((x+4)+2) =
X… 0 = 1x+4)+2 = 1+4+2 = 12 +2 = 14
16. – lim 12 +h - 12h =12+0-120 =12-120 =00 =∞ 2-(2 +h)2 (2+h)h1 = 2-(2 +h)2 2 +hh= 2-2-h2 2 +hh = - h2 2 +hh = -12(2 +0) =- 14
X… 0

17. – lim 19 +h- 13h =19+0-130 =19-130 =13-130 =00 =∞ 19 +h- 13 ( 19 +h+ 13 )h (19 +h+ 13) = 19 +h-...