Soluciones ejercicios limites 2 bach

7172019 Soluciones ejercicios limites 2 bach

httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 14

983107983137983148983139983157983148983137 983148983151983155 983155983145983143983157983145983141983150983156983141983155 983148983277983149983145983156983141983155983086

1

2

2x 1

x x 2lim

x 2x 1rarrrarrrarrrarr

+ minus+ minus+ minus+ minusminus +minus +minus +minus +

22

x

1lim

x 4x 4rarr+infinrarr+infinrarr+infinrarr+infin minus +minus +minus +minus +

3

2

2x 1

x x 2lim

x 2x 1rarrminusrarrminusrarrminusrarrminus

+ minus+ minus+ minus+ minusminus +minus +minus +minus +

4

2 x3 2 x

2x 2

x 2x 6lim

x 3x 4

minusminusminusminus

++++

rarr minusrarr minusrarr minusrarr minus

+ ++ ++ ++ +

+ minus+ minus+ minus+ minus

5 (((( ))))2

xlim x 2x 1

rarrinfinrarrinfinrarrinfinrarrinfinminus +minus +minus +minus + 6

2

2x 0

x 6x 9lim

xrarrrarrrarrrarr

minus +minus +minus +minus +

7

2

2x 5

x 25lim

x 5xrarrrarrrarrrarr



8 (((( ))))3

xlim 3x xrarrminusinfinrarrminusinfinrarrminusinfinrarrminusinfin

minus +minus +minus +minus + 9

3 2

2x

x 2x xlim

2x 6xrarr+infinrarr+infinrarr+infinrarr+infin



10x

1 1lim

x 2 x 2rarr+infinrarr+infinrarr+infinrarr+infin

++++ + minus+ minus+ minus+ minus 11

2

x 2

x 9

x 3

x 5lim x

x 1

++++



minusminusminusminus ++++ ++++

12

4

4 3x

xlim

2x 3x 6rarr+infinrarr+infinrarr+infinrarr+infin minus + minusminus + minusminus + minusminus + minus

13

1

x 3

x 3

x 1lim

2x 4++++


rarrrarrrarrrarr



14

5 2

2x

3x xlim

2x 1rarrminusinfinrarrminusinfinrarrminusinfinrarrminusinfin


minusminusminusminus 15

x a

x alim

x ararrrarrrarrrarr



16

2

2x

x 1 1lim

x 2 4rarr+infinrarr+infinrarr+infinrarr+infin



17 (((( ))))3 2

x 5lim x 2 x

rarrrarrrarrrarr+ minus+ minus+ minus+ minus 18

2

x

x 1lim

x 1rarrminusinfinrarrminusinfinrarrminusinfinrarrminusinfin

++++

++++

19x 2

x 2lim

x 3 1rarrminusrarrminusrarrminusrarrminus

++++


20x

x 2lim

x 3 1rarr+infinrarr+infinrarr+infinrarr+infin

++++


21(((( ))))(((( ))))

3

4x 3

x 1lim

x 3rarrminusrarrminusrarrminusrarrminus

++++

++++

22x 0

3 x 3lim

xrarrrarrrarrrarr

+ minus+ minus+ minus+ minus 23

x 1

x xlim

2xrarrrarrrarrrarr


24x 1

x xlim

2xrarrminusrarrminusrarrminusrarrminus


25x 0

x xlim

2xrarrrarrrarrrarr


26x

x xlim

2xrarr+infinrarr+infinrarr+infinrarr+infin


27x

x xlim

2xrarrminusinfinrarrminusinfinrarrminusinfinrarrminusinfin


28

2

2x 0x 1lim

x 2 x 1 1rarrrarrrarrrarr


minus minus minusminus minus minusminus minus minusminus minus minus

29

2

2x 1x 1lim

x 2 x 1 1rarrrarrrarrrarr



30

2

2xx 1lim

x 2 x 1 1rarr+infinrarr+infinrarr+infinrarr+infin



31(((( ))))2

2 2x a

x a 1 x alim

x ararrrarrrarrrarr

minus + +minus + +minus + +minus + +


32x

x 1 x 2lim

xrarr+infinrarr+infinrarr+infinrarr+infin

+ minus ++ minus ++ minus ++ minus + 33

3 2

4 3x 1

x 6x 5xlim

x x x 1rarrrarrrarrrarr


minus + minusminus + minusminus + minusminus + minus

34

2

2x 2

x 2 x 4lim

x 4 x 2rarrrarrrarrrarr

minus minusminus minusminus minusminus minusminusminusminusminus

minus minusminus minusminus minusminus minus

35x

x 1lim x 1

x 1rarr+infinrarr+infinrarr+infinrarr+infin

minusminusminusminusminusminusminusminus ++++

36(((( ))))2

2x

x 6x x 3lim

x 3 x 6xrarr+infinrarr+infinrarr+infinrarr+infin


+ minus ++ minus ++ minus ++ minus +

37

2

2x 2

x 3x 1 2x 1limx 2x 8rarrrarrrarrrarr

+ minus minus ++ minus minus ++ minus minus ++ minus minus +


38

2

2x 2

2x 3x 2 3x 2limx 3x 2rarrrarrrarrrarr

+ + minus ++ + minus ++ + minus ++ + minus +


39

2

2x 2

x x 3 2x 1lim

2x 5x 2rarrrarrrarrrarr

+ + minus ++ + minus ++ + minus ++ + minus +


40

2

2x 1

2x x 3lim

x 4x 1 3x 1rarrrarrrarrrarr





412

x 2

x 5 5x 5lim

x 2 x x 6rarr minusrarr minusrarr minusrarr minus

+ minus+ minus+ minus+ minusminusminusminusminus

+ minus minus+ minus minus+ minus minus+ minus minus

422

x 2

x 1 10x 5lim

x 2 x x 6rarrrarrrarrrarr



43

2x 63 x 2

2x 2

x 3x 5lim

2x 3x 1

++++

++++



+ ++ ++ ++ +

44

2x 63 x 2

2x 2

x 3x 5lim

2x 3x 1

++++

++++



+ ++ ++ ++ +

45

2

2x 1

2x x 3lim



+ minus minus ++ minus minus ++ minus minus ++ minus minus + 46

xlim x x x xrarr+infinrarr+infinrarr+infinrarr+infin

+ + minus+ + minus+ + minus+ + minus

47

x

2x 1 2x 1lim




48

(((( ))))(((( ))))x

lim x x 1 x 1rarrinfinrarrinfinrarrinfinrarrinfin


49

3 2

3 2x 3

x 5x 3x 9lim

x 7x 15x 9rarrminusrarrminusrarrminusrarrminus


+ + ++ + ++ + ++ + +

50

4 3 2

4 3 2x 2

x 4x 5x 4x 4lim

x 4x 4xrarrminusrarrminusrarrminusrarrminus

+ + + ++ + + ++ + + ++ + + +

+ ++ ++ ++ +

51

4 3

3 2x 2

x 2x x 2lim

x 4x 11x 2rarrrarrrarrrarr



52

4 2

4 3x 1

x 6x 8x 3lim




53

(((( ))))2

2h 0

ln 5 h ln 5lim

hrarrrarrrarrrarr


54(((( ))))

h 0

ln 3 h ln 3lim

hrarrrarrrarrrarr


55 (((( ))))x 3

xlim ln x 3 ln

x 3++++rarrrarrrarrrarr

minus +minus +minus +minus + minusminusminusminus

56

2

x 0

x 1 xln ln

1 x xlim

3x++++rarrrarrrarrrarr

minusminusminusminus ++++ minusminusminusminus

57 (((( ))))(((( ))))3 5 5

xlim x 1 2x 2x 2x 3xrarr+infinrarr+infinrarr+infinrarr+infin


58 (((( )))) (((( ))))(((( ))))2 2

xlim log x 2x 6 log 2x 3x 5rarr+infinrarr+infinrarr+infinrarr+infin

minus + minus + minusminus + minus + minusminus + minus + minusminus + minus + minus

59x

3lim x log 1


++++

60

2 2

n

n 2 n 2nlim

n 1 n 1rarr+infinrarr+infinrarr+infinrarr+infin

+ ++ ++ ++ +minusminusminusminus minus +minus +minus +minus +

617n n 5n 6 n 3

lim11n n 4 n 10

minus + + minusminus + + minusminus + + minusminus + + minus


62 (((( ))))2

nlim 2n 4n 3n 2rarr+infinrarr+infinrarr+infinrarr+infin

minus minus +minus minus +minus minus +minus minus +

63 (((( ))))2 2

nlim n 4n 1 n 8n 1rarr+infinrarr+infinrarr+infinrarr+infin

+ + minus + ++ + minus + ++ + minus + ++ + minus + +

64 (((( ))))2 2

nlim 2n 3n 3 2n 7rarr+infinrarr+infinrarr+infinrarr+infin


65

3 2 3

n

n 3n 2 n 1

lim n 2rarr+infinrarr+infinrarr+infinrarr+infin

minus + minus +minus + minus +minus + minus +minus + minus +

++++

66 2n

1 2 3 n

lim 3n 1rarr+infinrarr+infinrarr+infinrarr+infin

+ + + ++ + + ++ + + ++ + + +


67

28n 5n n 3n 2

lim6n n 2n 5



23n 3n 13

3n

n 2n 5lim

n 5n 2

+ ++ ++ ++ +

rarr+infinrarr+infinrarr+infinrarr+infin

+ ++ ++ ++ +

+ ++ ++ ++ +



69

2n 1

5n 2

nn

1 1 1

lim 1 2 4 2


++++


+ + + ++ + + ++ + + ++ + + +

70(((( )))) (((( ))))

(((( )))) (((( ))))

3 3

n

3n 1 3n 1lim

3n 1 3n 1rarr+infinrarr+infinrarr+infinrarr+infin



71

24

6 3n

n 3n 1lim

2n n 5rarr+infinrarr+infinrarr+infinrarr+infin

+ ++ ++ ++ +


72

2

5n

3n 5n 4lim



minus + +minus + +minus + +minus + + 73

3 2n

8n n 2 nlim




74(((( )))) (((( ))))

32n

2n 1 5n 3lim

4n 3rarr+infinrarr+infinrarr+infinrarr+infin

+ ++ ++ ++ +


75

2

2n

3n 2n nlim

2n 5n 2rarr+infinrarr+infinrarr+infinrarr+infin

+ ++ ++ ++ +


22 2n 1

2n

3n 2n 5lim

4n n 6

++++





77n

n 9lim


++++ minusminusminusminus

78

22 1

nn 3 nlim2n 1 2

++++


++++ minusminusminusminus minusminusminusminus

79

4n2

2n

3n 4lim


minusminusminusminus + minus+ minus+ minus+ minus

80

2 1

n

n 5n 9lim

n 10


++++



++++

81

5

n

1lim 1

n



++++

822n

2n 3lim

n



++++

83

3n

n

1lim 1

nrarr+infinrarr+infinrarr+infinrarr+infin


84

4

n

4lim 1



85

2n 3

n

1lim 1

3n 2



++++


86n

1lim 1

5n



++++

872n

1lim 1


++++

88

1

n

3lim 1

n 3

++++



89

3

3

3n

n 3lim

n 7rarr+infinrarr+infinrarr+infinrarr+infin

++++

minusminusminusminus 90 5

n

3n 1lim


minusminusminusminus ++++

91

n 2

n

n 3lim

n 7

++++


++++ ++++

92

2n n

3n 2

n

5n 3lim

5n 4

++++




++++

93

n

n

n 5lim



94

2n 1

n

2 3nlim

5 3n



minusminusminusminus minusminusminusminus

95

4n 3

n

4n 2lim

4n 3

++++



96

n3

3 2n

n 2n 1lim

n nrarr+infinrarr+infinrarr+infinrarr+infin


++++

97

n 2

n

1lim 1

n

++++



98

5 3x

x 12

2x

16x 5x 3lim

7x 4x

++++



+ minus+ minus+ minus+ minus ++++

99

2

4x

x 8x 5lim

2x 3rarr+infinrarr+infinrarr+infinrarr+infin

++++

++++

1002

xlim x(3x 9x 6)rarr+infinrarr+infinrarr+infinrarr+infin




1

2 0 3 12

4 10

e 5

6

7 2 8

9 10 0 11

512e 12 1

2

13

12e

14 15 a

2a 16 1 17 2 18 1

19 2 20

21 22 0 23 0 24 0

25

26 0 27 1 28 13 29

30 1

31 a 12a

32 0 33 2 34 154

35 1 36 1

37 5

18

38 13

8

39 718

40 10

3

41 75

42 25

43 28

3 44

283

45 10

3 46 1

2 47 2

2 48 1

49 2 50 45

51 217 52 2 53 1

5 54 1

3

55 3ln 2 56 1 3 57 2 4 58 1log 2 59 3loge 60 0

61 711

62 3

4 63 2 64 3 2

465

32

66 16

67 68 9e

69 5 4 70 6 71

61

2 72 0

73 4 74 3 52 75

62

76 3

2 77 0 78 1

79

80 0 81

e 82

83

3

e

84

1

e

85

23e 86

15e

87 1 88 89

10e 90

215e

91 4e

92

715e

93 1 94 2

e 95 e 96 1e

97 98 8 99 2 100 1



412

x 2

x 5 5x 5lim

x 2 x x 6rarr minusrarr minusrarr minusrarr minus



422

x 2

x 1 10x 5lim

x 2 x x 6rarrrarrrarrrarr



43

2x 63 x 2

2x 2

x 3x 5lim

2x 3x 1

++++

++++



+ ++ ++ ++ +

44

2x 63 x 2

2x 2

x 3x 5lim

2x 3x 1

++++

++++



+ ++ ++ ++ +

45

2

2x 1

2x x 3lim



+ minus minus ++ minus minus ++ minus minus ++ minus minus + 46

xlim x x x xrarr+infinrarr+infinrarr+infinrarr+infin


47

x

2x 1 2x 1lim




48

(((( ))))(((( ))))x

lim x x 1 x 1rarrinfinrarrinfinrarrinfinrarrinfin


49

3 2

3 2x 3

x 5x 3x 9lim

x 7x 15x 9rarrminusrarrminusrarrminusrarrminus


+ + ++ + ++ + ++ + +

50

4 3 2

4 3 2x 2

x 4x 5x 4x 4lim

x 4x 4xrarrminusrarrminusrarrminusrarrminus

+ + + ++ + + ++ + + ++ + + +

+ ++ ++ ++ +

51

4 3

3 2x 2

x 2x x 2lim




52

4 2

4 3x 1

x 6x 8x 3lim




53

(((( ))))2

2h 0

ln 5 h ln 5lim

hrarrrarrrarrrarr


54(((( ))))

h 0

ln 3 h ln 3lim

hrarrrarrrarrrarr


55 (((( ))))x 3

xlim ln x 3 ln

x 3++++rarrrarrrarrrarr

minus +minus +minus +minus + minusminusminusminus

56

2

x 0

x 1 xln ln

1 x xlim

3x++++rarrrarrrarrrarr

minusminusminusminus ++++ minusminusminusminus

57 (((( ))))(((( ))))3 5 5

xlim x 1 2x 2x 2x 3xrarr+infinrarr+infinrarr+infinrarr+infin


58 (((( )))) (((( ))))(((( ))))2 2

xlim log x 2x 6 log 2x 3x 5rarr+infinrarr+infinrarr+infinrarr+infin

minus + minus + minusminus + minus + minusminus + minus + minusminus + minus + minus

59x

3lim x log 1


++++

60

2 2

n

n 2 n 2nlim


+ ++ ++ ++ +minusminusminusminus minus +minus +minus +minus +

617n n 5n 6 n 3

lim11n n 4 n 10

minus + + minusminus + + minusminus + + minusminus + + minus


62 (((( ))))2

nlim 2n 4n 3n 2rarr+infinrarr+infinrarr+infinrarr+infin

minus minus +minus minus +minus minus +minus minus +

63 (((( ))))2 2

nlim n 4n 1 n 8n 1rarr+infinrarr+infinrarr+infinrarr+infin

+ + minus + ++ + minus + ++ + minus + ++ + minus + +

64 (((( ))))2 2

nlim 2n 3n 3 2n 7rarr+infinrarr+infinrarr+infinrarr+infin


65

3 2 3

n

n 3n 2 n 1

lim n 2rarr+infinrarr+infinrarr+infinrarr+infin

minus + minus +minus + minus +minus + minus +minus + minus +

++++

66 2n

1 2 3 n

lim 3n 1rarr+infinrarr+infinrarr+infinrarr+infin

+ + + ++ + + ++ + + ++ + + +


67

28n 5n n 3n 2

lim6n n 2n 5



23n 3n 13

3n

n 2n 5lim

n 5n 2

+ ++ ++ ++ +


+ ++ ++ ++ +

+ ++ ++ ++ +



69

2n 1

5n 2

nn

1 1 1

lim 1 2 4 2


++++


+ + + ++ + + ++ + + ++ + + +

70(((( )))) (((( ))))

(((( )))) (((( ))))

3 3

n

3n 1 3n 1lim




71

24

6 3n

n 3n 1lim


+ ++ ++ ++ +


72

2

5n

3n 5n 4lim




3 2n

8n n 2 nlim




74(((( )))) (((( ))))

32n

2n 1 5n 3lim


+ ++ ++ ++ +


75

2

2n

3n 2n nlim


+ ++ ++ ++ +


22 2n 1

2n

3n 2n 5lim

4n n 6

++++





77n

n 9lim



78

22 1

nn 3 nlim2n 1 2

++++



79

4n2

2n

3n 4lim



80

2 1

n

n 5n 9lim

n 10


++++



++++

81

5

n

1lim 1

n



++++

822n

2n 3lim

n



++++

83

3n

n

1lim 1



84

4

n

4lim 1



85

2n 3

n

1lim 1

3n 2



++++


86n

1lim 1

5n



++++

872n

1lim 1


++++

88

1

n

3lim 1

n 3

++++



89

3

3

3n

n 3lim


++++


n

3n 1lim



91

n 2

n

n 3lim

n 7

++++


++++ ++++

92

2n n

3n 2

n

5n 3lim

5n 4

++++




++++

93

n

n

n 5lim



94

2n 1

n

2 3nlim

5 3n




95

4n 3

n

4n 2lim

4n 3

++++



96

n3

3 2n

n 2n 1lim



++++

97

n 2

n

1lim 1

n

++++



98

5 3x

x 12

2x

16x 5x 3lim

7x 4x

++++




99

2

4x

x 8x 5lim


++++

++++

1002





1

2 0 3 12

4 10

e 5

6

7 2 8

9 10 0 11

512e 12 1

2

13

12e

14 15 a

2a 16 1 17 2 18 1

19 2 20

21 22 0 23 0 24 0

25

26 0 27 1 28 13 29

30 1

31 a 12a

32 0 33 2 34 154

35 1 36 1

37 5

18

38 13

8

39 718

40 10

3

41 75

42 25

43 28

3 44

283

45 10

3 46 1

2 47 2

2 48 1

49 2 50 45

51 217 52 2 53 1

5 54 1

3

55 3ln 2 56 1 3 57 2 4 58 1log 2 59 3loge 60 0

61 711

62 3

4 63 2 64 3 2

465

32

66 16

67 68 9e

69 5 4 70 6 71

61

2 72 0

73 4 74 3 52 75

62

76 3

2 77 0 78 1

79

80 0 81

e 82

83

3

e

84

1

e

85

23e 86

15e

87 1 88 89

10e 90

215e

91 4e

92

715e

93 1 94 2

e 95 e 96 1e

97 98 8 99 2 100 1



69

2n 1

5n 2

nn

1 1 1

lim 1 2 4 2


++++


+ + + ++ + + ++ + + ++ + + +

70(((( )))) (((( ))))

(((( )))) (((( ))))

3 3

n

3n 1 3n 1lim




71

24

6 3n

n 3n 1lim


+ ++ ++ ++ +


72

2

5n

3n 5n 4lim




3 2n

8n n 2 nlim




74(((( )))) (((( ))))

32n

2n 1 5n 3lim


+ ++ ++ ++ +


75

2

2n

3n 2n nlim


+ ++ ++ ++ +


22 2n 1

2n

3n 2n 5lim

4n n 6

++++





77n

n 9lim



78

22 1

nn 3 nlim2n 1 2

++++



79

4n2

2n

3n 4lim



80

2 1

n

n 5n 9lim

n 10


++++



++++

81

5

n

1lim 1

n



++++

822n

2n 3lim

n



++++

83

3n

n

1lim 1



84

4

n

4lim 1



85

2n 3

n

1lim 1

3n 2



++++


86n

1lim 1

5n



++++

872n

1lim 1


++++

88

1

n

3lim 1

n 3

++++



89

3

3

3n

n 3lim


++++


n

3n 1lim



91

n 2

n

n 3lim

n 7

++++


++++ ++++

92

2n n

3n 2

n

5n 3lim

5n 4

++++




++++

93

n

n

n 5lim



94

2n 1

n

2 3nlim

5 3n




95

4n 3

n

4n 2lim

4n 3

++++



96

n3

3 2n

n 2n 1lim



++++

97

n 2

n

1lim 1

n

++++



98

5 3x

x 12

2x

16x 5x 3lim

7x 4x

++++




99

2

4x

x 8x 5lim


++++

++++

1002





1

2 0 3 12

4 10

e 5

6

7 2 8

9 10 0 11

512e 12 1

2

13

12e

14 15 a

2a 16 1 17 2 18 1

19 2 20

21 22 0 23 0 24 0

25

26 0 27 1 28 13 29

30 1

31 a 12a

32 0 33 2 34 154

35 1 36 1

37 5

18

38 13

8

39 718

40 10

3

41 75

42 25

43 28

3 44

283

45 10

3 46 1

2 47 2

2 48 1

49 2 50 45

51 217 52 2 53 1

5 54 1

3

55 3ln 2 56 1 3 57 2 4 58 1log 2 59 3loge 60 0

61 711

62 3

4 63 2 64 3 2

465

32

66 16

67 68 9e

69 5 4 70 6 71

61

2 72 0

73 4 74 3 52 75

62

76 3

2 77 0 78 1

79

80 0 81

e 82

83

3

e

84

1

e

85

23e 86

15e

87 1 88 89

10e 90

215e

91 4e

92

715e

93 1 94 2

e 95 e 96 1e

97 98 8 99 2 100 1



1

2 0 3 12

4 10

e 5

6

7 2 8

9 10 0 11

512e 12 1

2

13

12e

14 15 a

2a 16 1 17 2 18 1

19 2 20

21 22 0 23 0 24 0

25

26 0 27 1 28 13 29

30 1

31 a 12a

32 0 33 2 34 154

35 1 36 1

37 5

18

38 13

8

39 718

40 10

3

41 75

42 25

43 28

3 44

283

45 10

3 46 1

2 47 2

2 48 1

49 2 50 45

51 217 52 2 53 1

5 54 1

3

55 3ln 2 56 1 3 57 2 4 58 1log 2 59 3loge 60 0

61 711

62 3

4 63 2 64 3 2

465

32

66 16

67 68 9e

69 5 4 70 6 71

61

2 72 0

73 4 74 3 52 75

62

76 3

2 77 0 78 1

79

80 0 81

e 82

83

3

e

84

1

e

85

23e 86

15e

87 1 88 89

10e 90

215e

91 4e

92

715e

93 1 94 2

e 95 e 96 1e

97 98 8 99 2 100 1

Soluciones ejercicios limites 2 bach

Documents

Transcript of Soluciones ejercicios limites 2 bach