limites con raices corregido

7/24/2019 Limites Con Raices Corregido

1/8

Sergio Yansen Nez

Recuerde:

a ba b a2 b 2

a ba2 ab b2 a3 b3

a

ba2 ab b2 a3b3

En caso de existir, calcule los siguientes lmites:

1.x3

lim x 1 2

x2 x 6

2.x2

lim x 7 3

x 2 2

3.

x

3

lim x2 7 4

x

2

5

2

4.x4

lim7 x 3

x2 3x 4

5.x1

lim3 x 9 2

x2 7x 6

6.x2

lim3 x 6 23 x 3 1

7.x1lim

3 x2 26 3

3 x2 2 1

8.x1

lim5 3 x 2

37 x 2

9.x1

lim x 3 x 2

x 1

10.x2

lim 2x 3 4x

x 2

Lmites


2/8

Sergio Yansen Nez

Resolucin

1.x3

lim x 1 2

x2 x 6

Solucin:

x3

lim x 1 2

x2 x 6

x3

lim x 1 2

x 3x 2

x 1 2

x 1 2

x3

limx 1

222

x 3x 2 x 1 2

x3

lim x 1 4

x 3x 2 x 1 2

x3

lim x 3

x 3x 2 x 1 2

x3

lim 1

x 2 x 1 2

1

3 2 3 1 2

120

2. x2lim

x 7 3

x 2

2

Solucin:

x2

lim x 7 3

x 2 2

x2

lim x 7 3

x 2 2

x 7 3

x 7 3

x 2 2

x 2 2

x2

limx 7 3 x 7 3

x 2 2 x 2 2

x 2 2

x 7 3

x2lim

x 7 2

32 x 2 2

x 2 2

22 x 7 3

x2lim

x 7 9 x 2 2

x 2 4 x 7 3

x2

limx 2 x 2 2

x 2 x 7 3

x2

lim x 2 2

x 7 3

2 2 2

2 7 3

23

Lmites


3/8

Sergio Yansen Nez

3.x3

lim x2 7 4

x2 5 2

Solucin:

x3lim

x2 7

4x2 5 2

x3lim

x2 7

4x2 5 2

x2

7

4x2 7 4

x2

5

2x2 5 2

x3

limx2 7 4 x2 7 4

x2 5 2 x2 5 2

x2 5 2

x2 7 4

x3

limx2 7

242 x2 5 2

x2 5222 x2 7 4

x3

lim x2

7

16 x2

5

2x2 5 4 x2 7 4

x3

lim x2

9 x2

5

2x2 9 x2 7 4

x3

lim x2

5 2

x2 7 4

32 5 2

32 7 4

12

4.x4

lim7 x 3

x2 3x 4

Solucin:

x4

lim7 x

3

x2 3x 4

x4

lim7 x

3

x 4x 1

7 x 3

7 x 3

x4

lim7 x

29

x 4x 1 7 x 3

x4

lim 7 x 9

x 4x 1 7 x 3

x4

lim x 2

x 4x 1 7 x 3

x 2

x 2

x4

lim x

222

x 4x 1 7 x 3 x 2

x4lim x

4x 4x 1 7 x 3 x 2

x4lim 1

x 1 7 x 3 x 2

1

4 1 7 4 3 4 2

1120

Lmites


4/8

Sergio Yansen Nez

5.x1

lim3 x 9 2

x2 7x 6

Solucin:

x1lim

3 x 9

2x2 7x 6

x1lim

3 x 9

2x 1x 6

3 x 9 2

3 x 9 2 22

3 x 9 2

3 x 9 2 22

x1

lim3 x 9

323

x 1x 6 3 x 9 2

2 3 x 9 4

x1

lim x 9 8

x 1x 6 3 x 9 2

2 3 x 9 4

x1

lim x 1

x 1x 6 3 x 9 2

2 3 x 9 4

x1

lim 1

x 6 3 x 9 2

2 3 x 9 4

x1

lim 1

1 6 3 1 9 2

2 3 1 9 4

160

6.x2

lim3 x 6 23 x 3 1

Solucin:

x2

lim3 x 6 23 x 3 1

x

2

lim3 x 6 23 x

3

1

3 x 6

2

3 x 6 2 2 2

3 x 6

2

3 x 6 2

22

3 x 3

2

3 x 3 1 12

3 x3

2

3 x3 1

12

x2

lim

3 x 6 2 3 x 6 2

2 3 x 6 4

3 x 3 1 3 x 3 2

3 x 3 1

3 x 3

2

3 x 3 1

3 x 6 2

2 3 x 6 4

x2

lim

3 x 6 3

2 3 3 x 3 2

3 x 3 1

3 x 3 3

13 3 x 6 2

2 3 x 6 4

x2

limx 68 3 x 3

2

3 x 3 1

x

3 1 3 x 6 2

2 3 x 6 4

x2

limx 2 3 x 3

2

3 x 3 1

x

2 3 x 6 2

2 3 x 6 4

x2

lim3 x 3

2

3 x 3 1

3 x 6 2

2 3 x 6 4

3 2 3 2

3 2 3 1

3 2 6 2

2 3 2 6 4

312

1

4

Lmites


5/8

Sergio Yansen Nez

7.x1

lim3 x2 26 3

3 x2 2 1

Solucin:

x1lim

3 x2 26

33 x2 2 1

x1

lim3 x2 26 3

3 x2 2 1

3 x2 262

3 x2 26 3 32

3 x2 262

3 x2 26 3 32

3 x2 22

3 x2 2 1 12

3 x2 22

3 x2 2 1 12

x1

lim

3 x2 26 3 3 x2 262

3 x2 26 3 32

3 x2 2 1 3 x2 22

3 x2 2 1 1 2

3 x2 22

3 x2 2 1 12

3 x2 262

3 x2 26 3 32

x1

lim3 x2 26

3

33 3 x2

2

2

3 x2

2 1

3 x2 2313 3 x2 26

2

3 x2 26 3 3 2

x1

limx2 26 27 3 x2 2

2

3 x2 2 1

x2 2 1 3 x2 262

3 x2 26 3 32

x1

limx2 1 3 x2 2

2

3 x2 2 1

x2 1 3 x2 262

3 x2 26 3 32

x1

lim

3 x2 22

3 x2 2 1

3 x2 262

3 x2 26 3 3 2

3 12 22

3 12 2 1

3 12 262

3 12 26 3 3 2

327

1

9

Lmites


6/8

Sergio Yansen Nez

8.x1

lim5 3 x 2

37 x 2

Solucin:

x1

limx1

lim5 3 x

2

37 x 2

x1

lim5 3 x

2

37 x 2

5 3 x 2

5 3 x 2

37

x 2 37

x 2 22

37 x2 37 x 2 22

x1

lim5 3 x 2 5 3 x 2

37 x 2 37 x22 37 x 4

37 x

22 37 x 4

5 3 x 2

x1

lim5 3 x

222 37 x

22 37 x 4

37 x323 5 3 x 2

x1

lim5 3 x 4 37 x

22 37 x 4

7 x 8 5 3 x 2

x1

lim1 3 x 37 x

22 37 x 4

x 1 5 3 x 2

12 1 3 x 3 x2

12 1 3 x 3 x2

x 1

x 1

x

1

lim1 3 x 1 3 x 3 x

237 x

22 37 x 4

x

1 x

1 5 3 x

2

x 1

1

3 x

3 x

2

x1

lim13 3 x

337 x

22 37 x 4 x 1

x21 2 5 3 x 2 1 3 x 3 x

2

x1

lim1 x 37 x

22 37 x 4 x 1

x 1 5 3 x 2 1 3 x 3 x2

x1

lim1 x 37 x

22 37 x 4 x 1

x 1 5 3 x 2 1

3 x 3 x 2

x1

lim37 x

22 37 x 4 x 1

5 3 x 2 1 3 x 3 x2

Lmites


7/8

Sergio Yansen Nez

3 7 12

2 3 7 1 4 1 1

5 3 1 2 1 3 1 3 1 2

2

9.x1

lim x 3 x 2

x 1

Solucin:

x1

lim x 3 x 2

x 1

x1

lim x 1 3 x 1

x 1

x1

lim x 1

x 1

3 x 1

x 1

x1

lim x 1

x 1

x1

lim x 1

x 1

x 1

x 1

x1

lim x

212

x 1 x 1

x1

lim x 1x 1 x 1

x1

lim 1x 1

1

1 1

12

x1

lim3 x 1

x 1

x1

lim3 x 1

x 1

3 x2 3 x 1 12

3 x2 3 x 1 12

x1

lim 3 x

313

x 1 3 x2 3 x 1

x1

lim x 1

x 1 3 x2 3 x 1

x1

lim 1

3 x2 3 x 1

1

3 1 2

3 1 1

1

3

Comox1

lim x 1

x 1

12

yx1

lim3 x 1

x 1

13

, entonces por lgebra de lmites:

x1

lim x 1

x 1

3 x 1

x 1

12

13

56

Lmites


8/8

limites con raices corregido

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