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Soluciones ejercicios limites 2 bach ciencias de la salud
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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
minusminusminusminus
minusminusminusminus
8 (((( ))))3
xlim 3x xrarrminusinfinrarrminusinfinrarrminusinfinrarrminusinfin
minus +minus +minus +minus + 9
3 2
2x
x 2x xlim
2x 6xrarr+infinrarr+infinrarr+infinrarr+infin
minus +minus +minus +minus +
minusminusminusminus
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
rarr minusrarr minusrarr minusrarr minus
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++++
minusminusminusminus
rarrrarrrarrrarr
minusminusminusminus
minusminusminusminus
14
5 2
2x
3x xlim
2x 1rarrminusinfinrarrminusinfinrarrminusinfinrarrminusinfin
minus +minus +minus +minus +
minusminusminusminus 15
x a
x alim
x ararrrarrrarrrarr
minusminusminusminus
minusminusminusminus
16
2
2x
x 1 1lim
x 2 4rarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
+ minus+ minus+ minus+ minus
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
++++
+ minus+ minus+ minus+ minus
20x
x 2lim
x 3 1rarr+infinrarr+infinrarr+infinrarr+infin
++++
+ minus+ minus+ minus+ minus
21(((( ))))(((( ))))
3
4x 3
x 1lim
x 3rarrminusrarrminusrarrminusrarrminus
++++
++++
22x 0
3 x 3lim
xrarrrarrrarrrarr
+ minus+ minus+ minus+ minus 23
x 1
x xlim
2xrarrrarrrarrrarr
minusminusminusminus
24x 1
x xlim
2xrarrminusrarrminusrarrminusrarrminus
minusminusminusminus
25x 0
x xlim
2xrarrrarrrarrrarr
minusminusminusminus
26x
x xlim
2xrarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
27x
x xlim
2xrarrminusinfinrarrminusinfinrarrminusinfinrarrminusinfin
minusminusminusminus
28
2
2x 0x 1lim
x 2 x 1 1rarrrarrrarrrarr
minusminusminusminus
minus minus minusminus minus minusminus minus minusminus minus minus
29
2
2x 1x 1lim
x 2 x 1 1rarrrarrrarrrarr
minusminusminusminus
minus minus minusminus minus minusminus minus minusminus minus minus
30
2
2xx 1lim
x 2 x 1 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
minus minus minusminus minus minusminus minus minusminus minus minus
31(((( ))))2
2 2x a
x a 1 x alim
x ararrrarrrarrrarr
minus + +minus + +minus + +minus + +
minusminusminusminus
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 +minus +minus +minus +
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 minusminus minus minusminus minus minusminus minus minus
+ minus ++ minus ++ minus ++ minus +
37
2
2x 2
x 3x 1 2x 1limx 2x 8rarrrarrrarrrarr
+ minus minus ++ minus minus ++ minus minus ++ minus minus +
+ minus+ minus+ minus+ minus
38
2
2x 2
2x 3x 2 3x 2limx 3x 2rarrrarrrarrrarr
+ + minus ++ + minus ++ + minus ++ + minus +
minus +minus +minus +minus +
39
2
2x 2
x x 3 2x 1lim
2x 5x 2rarrrarrrarrrarr
+ + minus ++ + minus ++ + minus ++ + minus +
minus +minus +minus +minus +
40
2
2x 1
2x x 3lim
x 4x 1 3x 1rarrrarrrarrrarr
+ minus+ minus+ minus+ minus
+ minus minus ++ minus minus ++ minus minus ++ minus minus +
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 24
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
+ minus+ minus+ minus+ minusminusminusminusminus
minus + minusminus + minusminus + minusminus + minus
43
2x 63 x 2
2x 2
x 3x 5lim
2x 3x 1
++++
++++
rarr minusrarr minusrarr minusrarr minus
minus +minus +minus +minus +
+ ++ ++ ++ +
44
2x 63 x 2
2x 2
x 3x 5lim
2x 3x 1
++++
++++
rarr minusrarr minusrarr minusrarr minus
minus +minus +minus +minus +
+ ++ ++ ++ +
45
2
2x 1
2x x 3lim
x 4x 1 3x 1rarrrarrrarrrarr
+ minus+ minus+ minus+ minus
+ 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
x 1 x 1rarr+infinrarr+infinrarr+infinrarr+infin
+ minus minus+ minus minus+ minus minus+ minus minus
+ minus minus+ minus minus+ minus minus+ minus minus
48
(((( ))))(((( ))))x
lim x x 1 x 1rarrinfinrarrinfinrarrinfinrarrinfin
+ minus minus+ minus minus+ minus minus+ minus minus
49
3 2
3 2x 3
x 5x 3x 9lim
x 7x 15x 9rarrminusrarrminusrarrminusrarrminus
+ + minus+ + minus+ + minus+ + minus
+ + ++ + ++ + ++ + +
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
minus + minusminus + minusminus + minusminus + minus
+ minus minus+ minus minus+ minus minus+ minus minus
52
4 2
4 3x 1
x 6x 8x 3lim
x 2x 2x 1rarrrarrrarrrarr
minus + minusminus + minusminus + minusminus + minus
minus + minusminus + minusminus + minusminus + minus
53
(((( ))))2
2h 0
ln 5 h ln 5lim
hrarrrarrrarrrarr
+ minus+ minus+ minus+ minus
54(((( ))))
h 0
ln 3 h ln 3lim
hrarrrarrrarrrarr
+ minus+ minus+ minus+ minus
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
+ minus minus ++ minus minus ++ minus minus ++ minus minus +
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
xrarr+infinrarr+infinrarr+infinrarr+infin
++++
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
minus +minus +minus +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
+ minus minus ++ minus minus ++ minus minus ++ minus minus +
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
+ + + ++ + + ++ + + ++ + + +
minusminusminusminus
67
28n 5n n 3n 2
lim6n n 2n 5
minus + +minus + +minus + +minus + +
minus +minus +minus +minus + 68
23n 3n 13
3n
n 2n 5lim
n 5n 2
+ ++ ++ ++ +
rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
+ ++ ++ ++ +
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 34
69
2n 1
5n 2
nn
1 1 1
lim 1 2 4 2
minusminusminusminus
++++
rarr+infinrarr+infinrarr+infinrarr+infin
+ + + ++ + + ++ + + ++ + + +
70(((( )))) (((( ))))
(((( )))) (((( ))))
3 3
n
3n 1 3n 1lim
3n 1 3n 1rarr+infinrarr+infinrarr+infinrarr+infin
+ minus minus+ minus minus+ minus minus+ minus minus
+ minus+ minus+ minus+ minus
71
24
6 3n
n 3n 1lim
2n n 5rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minus +minus +minus +minus +
72
2
5n
3n 5n 4lim
n 6 n 7rarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
minus + +minus + +minus + +minus + + 73
3 2n
8n n 2 nlim
4n n 2rarr+infinrarr+infinrarr+infinrarr+infin
minus +minus +minus +minus +
+ minus+ minus+ minus+ minus
74(((( )))) (((( ))))
32n
2n 1 5n 3lim
4n 3rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minusminusminusminus
75
2
2n
3n 2n nlim
2n 5n 2rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minus + +minus + +minus + +minus + + 76
22 2n 1
2n
3n 2n 5lim
4n n 6
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
+ minus+ minus+ minus+ minus
77n
n 9lim
2n 7rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus
78
22 1
nn 3 nlim2n 1 2
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus minusminusminusminus
79
4n2
2n
3n 4lim
2n n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus + minus+ minus+ minus+ minus
80
2 1
n
n 5n 9lim
n 10
minusminusminusminus
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minus +minus +minus +minus +
++++
81
5
n
1lim 1
n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
822n
2n 3lim
n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
83
3n
n
1lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
84
4
n
4lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
85
2n 3
n
1lim 1
3n 2
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
minusminusminusminus
86n
1lim 1
5n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
872n
1lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
++++
88
1
n
3lim 1
n 3
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus
89
3
3
3n
n 3lim
n 7rarr+infinrarr+infinrarr+infinrarr+infin
++++
minusminusminusminus 90 5
n
3n 1lim
3n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus ++++
91
n 2
n
n 3lim
n 7
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ ++++
92
2n n
3n 2
n
5n 3lim
5n 4
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
++++
93
n
n
n 5lim
n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus ++++
94
2n 1
n
2 3nlim
5 3n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus minusminusminusminus
95
4n 3
n
4n 2lim
4n 3
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus minusminusminusminus
96
n3
3 2n
n 2n 1lim
n nrarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
++++
97
n 2
n
1lim 1
n
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
98
5 3x
x 12
2x
16x 5x 3lim
7x 4x
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
+ 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
minus minusminus minusminus minusminus minus
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 44
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
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 24
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
+ minus+ minus+ minus+ minusminusminusminusminus
minus + minusminus + minusminus + minusminus + minus
43
2x 63 x 2
2x 2
x 3x 5lim
2x 3x 1
++++
++++
rarr minusrarr minusrarr minusrarr minus
minus +minus +minus +minus +
+ ++ ++ ++ +
44
2x 63 x 2
2x 2
x 3x 5lim
2x 3x 1
++++
++++
rarr minusrarr minusrarr minusrarr minus
minus +minus +minus +minus +
+ ++ ++ ++ +
45
2
2x 1
2x x 3lim
x 4x 1 3x 1rarrrarrrarrrarr
+ minus+ minus+ minus+ minus
+ 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
x 1 x 1rarr+infinrarr+infinrarr+infinrarr+infin
+ minus minus+ minus minus+ minus minus+ minus minus
+ minus minus+ minus minus+ minus minus+ minus minus
48
(((( ))))(((( ))))x
lim x x 1 x 1rarrinfinrarrinfinrarrinfinrarrinfin
+ minus minus+ minus minus+ minus minus+ minus minus
49
3 2
3 2x 3
x 5x 3x 9lim
x 7x 15x 9rarrminusrarrminusrarrminusrarrminus
+ + minus+ + minus+ + minus+ + minus
+ + ++ + ++ + ++ + +
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
minus + minusminus + minusminus + minusminus + minus
+ minus minus+ minus minus+ minus minus+ minus minus
52
4 2
4 3x 1
x 6x 8x 3lim
x 2x 2x 1rarrrarrrarrrarr
minus + minusminus + minusminus + minusminus + minus
minus + minusminus + minusminus + minusminus + minus
53
(((( ))))2
2h 0
ln 5 h ln 5lim
hrarrrarrrarrrarr
+ minus+ minus+ minus+ minus
54(((( ))))
h 0
ln 3 h ln 3lim
hrarrrarrrarrrarr
+ minus+ minus+ minus+ minus
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
+ minus minus ++ minus minus ++ minus minus ++ minus minus +
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
xrarr+infinrarr+infinrarr+infinrarr+infin
++++
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
minus +minus +minus +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
+ minus minus ++ minus minus ++ minus minus ++ minus minus +
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
+ + + ++ + + ++ + + ++ + + +
minusminusminusminus
67
28n 5n n 3n 2
lim6n n 2n 5
minus + +minus + +minus + +minus + +
minus +minus +minus +minus + 68
23n 3n 13
3n
n 2n 5lim
n 5n 2
+ ++ ++ ++ +
rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
+ ++ ++ ++ +
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 34
69
2n 1
5n 2
nn
1 1 1
lim 1 2 4 2
minusminusminusminus
++++
rarr+infinrarr+infinrarr+infinrarr+infin
+ + + ++ + + ++ + + ++ + + +
70(((( )))) (((( ))))
(((( )))) (((( ))))
3 3
n
3n 1 3n 1lim
3n 1 3n 1rarr+infinrarr+infinrarr+infinrarr+infin
+ minus minus+ minus minus+ minus minus+ minus minus
+ minus+ minus+ minus+ minus
71
24
6 3n
n 3n 1lim
2n n 5rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minus +minus +minus +minus +
72
2
5n
3n 5n 4lim
n 6 n 7rarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
minus + +minus + +minus + +minus + + 73
3 2n
8n n 2 nlim
4n n 2rarr+infinrarr+infinrarr+infinrarr+infin
minus +minus +minus +minus +
+ minus+ minus+ minus+ minus
74(((( )))) (((( ))))
32n
2n 1 5n 3lim
4n 3rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minusminusminusminus
75
2
2n
3n 2n nlim
2n 5n 2rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minus + +minus + +minus + +minus + + 76
22 2n 1
2n
3n 2n 5lim
4n n 6
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
+ minus+ minus+ minus+ minus
77n
n 9lim
2n 7rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus
78
22 1
nn 3 nlim2n 1 2
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus minusminusminusminus
79
4n2
2n
3n 4lim
2n n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus + minus+ minus+ minus+ minus
80
2 1
n
n 5n 9lim
n 10
minusminusminusminus
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minus +minus +minus +minus +
++++
81
5
n
1lim 1
n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
822n
2n 3lim
n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
83
3n
n
1lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
84
4
n
4lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
85
2n 3
n
1lim 1
3n 2
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
minusminusminusminus
86n
1lim 1
5n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
872n
1lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
++++
88
1
n
3lim 1
n 3
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus
89
3
3
3n
n 3lim
n 7rarr+infinrarr+infinrarr+infinrarr+infin
++++
minusminusminusminus 90 5
n
3n 1lim
3n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus ++++
91
n 2
n
n 3lim
n 7
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ ++++
92
2n n
3n 2
n
5n 3lim
5n 4
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
++++
93
n
n
n 5lim
n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus ++++
94
2n 1
n
2 3nlim
5 3n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus minusminusminusminus
95
4n 3
n
4n 2lim
4n 3
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus minusminusminusminus
96
n3
3 2n
n 2n 1lim
n nrarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
++++
97
n 2
n
1lim 1
n
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
98
5 3x
x 12
2x
16x 5x 3lim
7x 4x
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
+ 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
minus minusminus minusminus minusminus minus
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 44
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
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 34
69
2n 1
5n 2
nn
1 1 1
lim 1 2 4 2
minusminusminusminus
++++
rarr+infinrarr+infinrarr+infinrarr+infin
+ + + ++ + + ++ + + ++ + + +
70(((( )))) (((( ))))
(((( )))) (((( ))))
3 3
n
3n 1 3n 1lim
3n 1 3n 1rarr+infinrarr+infinrarr+infinrarr+infin
+ minus minus+ minus minus+ minus minus+ minus minus
+ minus+ minus+ minus+ minus
71
24
6 3n
n 3n 1lim
2n n 5rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minus +minus +minus +minus +
72
2
5n
3n 5n 4lim
n 6 n 7rarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
minus + +minus + +minus + +minus + + 73
3 2n
8n n 2 nlim
4n n 2rarr+infinrarr+infinrarr+infinrarr+infin
minus +minus +minus +minus +
+ minus+ minus+ minus+ minus
74(((( )))) (((( ))))
32n
2n 1 5n 3lim
4n 3rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minusminusminusminus
75
2
2n
3n 2n nlim
2n 5n 2rarr+infinrarr+infinrarr+infinrarr+infin
+ ++ ++ ++ +
minus + +minus + +minus + +minus + + 76
22 2n 1
2n
3n 2n 5lim
4n n 6
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
+ minus+ minus+ minus+ minus
77n
n 9lim
2n 7rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus
78
22 1
nn 3 nlim2n 1 2
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus minusminusminusminus
79
4n2
2n
3n 4lim
2n n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus + minus+ minus+ minus+ minus
80
2 1
n
n 5n 9lim
n 10
minusminusminusminus
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minus +minus +minus +minus +
++++
81
5
n
1lim 1
n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
822n
2n 3lim
n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
83
3n
n
1lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
84
4
n
4lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
85
2n 3
n
1lim 1
3n 2
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
minusminusminusminus
86n
1lim 1
5n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
++++
872n
1lim 1
nrarr+infinrarr+infinrarr+infinrarr+infin
++++
88
1
n
3lim 1
n 3
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ minusminusminusminus
89
3
3
3n
n 3lim
n 7rarr+infinrarr+infinrarr+infinrarr+infin
++++
minusminusminusminus 90 5
n
3n 1lim
3n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus ++++
91
n 2
n
n 3lim
n 7
++++
rarr+infinrarr+infinrarr+infinrarr+infin
++++ ++++
92
2n n
3n 2
n
5n 3lim
5n 4
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
++++
93
n
n
n 5lim
n 1rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus ++++
94
2n 1
n
2 3nlim
5 3n
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus minusminusminusminus
95
4n 3
n
4n 2lim
4n 3
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus minusminusminusminus
96
n3
3 2n
n 2n 1lim
n nrarr+infinrarr+infinrarr+infinrarr+infin
+ minus+ minus+ minus+ minus
++++
97
n 2
n
1lim 1
n
++++
rarr+infinrarr+infinrarr+infinrarr+infin
minusminusminusminus
98
5 3x
x 12
2x
16x 5x 3lim
7x 4x
++++
minusminusminusminus
rarr+infinrarr+infinrarr+infinrarr+infin
+ 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
minus minusminus minusminus minusminus minus
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 44
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
7172019 Soluciones ejercicios limites 2 bach
httpslidepdfcomreaderfullsoluciones-ejercicios-limites-2-bach 44
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
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