llïmites matematicas
DESCRIPTION
Ejercicios matematicas- limites y continuidad.TRANSCRIPT
-
Colegio San Agustn (Santander) Pgina 1
1. Calcula los siguientes lmites: [
] (El lmite tiende a + )
1.1 4
xLimx
Solucin: 0
1.2
2
3
1
22 xx
Limx
Solucin: 0
1.3 22
3
x
xLimx
Solucin: +
1.4 1
13
2
x
xLimx
Solucin: 0
1.5 23
62
3
xx
xxLimx
Solucin: +
1.6 1
12
3
x
xLimx
Solucin: +
1.7 x
Lim
332
1118
2
2
xx Solucin:
4
3
1.8 x
xLim
3
2 Solucin: 0
1.9
4
52
3
x
xLimx
Solucin: -
1.10 3
24 3
x
xLimx
Solucin: +
1.11 24
623
5
xx
xxLimx
Solucin: 0
1.12 x
xxLimx
2
Solucin: 1
1.13 134
35
2
xx
xLimx
Solucin:
1.14 1
142
2
x
xxLimx
Solucin: 4
1.15 23
23
82
523
xx
xxLimx
Solucin:
1.16
44
5232
2
x
xxLimx
Solucin: -
1.17 23
23
82
52
xx
xxLimx
Solucin:
1.18 62
24
5
3
xx
xxLimx
Solucin: -
Matemticas 1Bachillerato
Aplicadas a las Ciencias Sociales Lmites
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Colegio San Agustn (Santander) Pgina 2
2. Calcula los siguientes lmites: [
] (El lmite tiende a - )
2.1 x
Lim
xx
xx
26
132
Solucin: 0
2.2 x
Lim
142
1423
x
x Solucin: - 2
2.3 1
142
2
x
xxLimx
Solucin: 4
2.4 1
12
3
x
xLimx
Solucin: -
2.5 62
24
5
3
xx
xxLimx
Solucin:
2.6
x
xLim
2
3 Solucin: 0
2.7 23
23
92
635
xx
xxLimx
Solucin: -
2.8 xx
xLimx 83
522
2
Solucin:
2.9 x
xxLimx
2
Solucin:- 1
2.10 139
35
2
xx
xLimx
Solucin:
3. Calcula los siguientes lmites: [
]
3.1 2x
Lim2
62
2
xx
xx Solucin:
3
5
3.2 3
962
3
x
xxLimx
Solucin: 0
3.3 1
13
2
1
x
xLimx
Solucin:
3.4 xxx
xxLimx 23
623
2
2
Solucin:
3.5 1x
Lim 323
23
2783
132
xxx
xx Solucin: 3 3
3.6 1
122
1
x
xxLimx
Solucin: 0
3.7 x
xLimx 110
Solucin: 2
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Colegio San Agustn (Santander) Pgina 3
3.8 3x
Lim3
21
x
x Solucin:
4
1
3.9 0x
Lim416
39
x
x Solucin:
3
4
3.10 0x
Lim11
242
x
x Solucin: 1
3.11 x
xLimx
42
0 Solucin:
3.12 1
1
1
x
xLimx
Solucin: 2
3.13 xx
xLimx 110
Solucin: 1
3.14
5
5
5
x
xLimx
Solucin:
3.15 1
12
3
1
x
xLimx
Solucin:
3.16 823
2522
2
2
xx
xxLimx
Solucin:
3.17 2x
Lim2
62
2
xx
xx Solucin:
3
5
4. Calcula los siguientes lmites: [ ]
4.1 22
xxLimx
Solucin: 0
4.2
xxxLim
x12 Solucin:
4.3
122 xxxLim
x Solucin:
4.4
12xxLim
x Solucin: 0
4.5 x
Lim - Solucin: 2
3
5. Calcula los siguientes lmites: [ ]
5.1
2
3
5
x
x x
xLim Solucin:
5.2
23
2
22
17
17
x
x x
xLim Solucin:
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Colegio San Agustn (Santander) Pgina 4
5.3
23
15
15
x
x x
xLim Solucin:
5.4 1
1
2
2
2
12
xx
x x
xxLim Solucin:
5.5 1
1
2
3
1
13
xx
x x
xxLim Solucin: +
5.6 1
1
3
2 2
13
1
xx
x xx
xLim Solucin: 1
6 Calcula los siguientes lmites: [
]
6.1 0x
Limxx
xx
2
2 23 Solucin: no existe
6.2 2x
Lim2
652
2
xx
xx Solucin: no existe
6.3 0x
Lim2
2 86
x
xx Solucin: +
6.4 1x
Lim12
652
2
xx
xx Solucin: +
6.5 4x
Lim12
232
2
xx
xx Solucin: No existe
6.6 1x
Lim34
42
23
xx
xx Solucin: No existe
7 Calcula los siguientes lmites: (varias indeterminaciones)
7.1 1x
Lim1
2323
2
xxx
xx Solucin: no existe [
] y [
]
7.2 3x
Lim
3
1
9
22 x
x
x
x Solucin: no existe [ ] y [
]
7.3 1x
Lim1
3
2 6
42
xx
xx
x Solucin: e [ ] y [
]
7.4 2x
Lim2
2 42
23
xx
xx
x Solucin: e [ ] y [
]
7.5 3x
Lim3
22
44
12
xx
x
xx Solucin: e 8
21
[ ] y [
]
7.6 0x
Limx
x
xx3
2
15
13
Solucin: e 24 [ ] y [
]
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Colegio San Agustn (Santander) Pgina 5
7.7 1x
Lim1
12
1
32
x
x
xx Solucin: e 2
1
[ ] y [
]
7.8 x
Lim
12 2
52
21
x
x
x Solucin: 0 [ ] y [
]
7.9 x
Lim
12
53
24
x
x
x Solucin: + [ ] y [
]
7.10 x
Lim
1
23
22
x
x
x Solucin: e 2
5
[ ] y [
]
7.11 x
Lim
x
xx
x
93
742
2
Solucin: 0 [ ] y [
]
7.12 x
Lim
x
x
x2
2
2
2
1
Solucin: 1 [ ] y [
]
7.13 x
Lim 13 22 xxx Solucin: 2
3[ ] y [
]
7.14 3x
Lim935
323
xxx
x Solucin: no existe [
] y [
]
7.15 1x
Lim122
3
xx
xx Solucin: no existe [
] y [
]
7.16 x
Lim
1
34
23
x
x
x Solucin:
2
1
e [ ] y [
]
7.17 2x
Lim
2
1
4
32 x
x
x
x Solucin: no existe [ ] y [
]
7.18 x
Lim
1
3
1
32
32
x
x
x
x Solucin: -3 [ ] y [
]
7.19 1x
Lim1
1
22
3
x
x
x Solucin: e 4
1
[ ] y [
]
7.20 x
Lim
12
12
32
x
x
x
x Solucin: -2 [ ] y [
]
7.21 2
231
2
2
0 1
1 xx
x x
xLim
Solucin: [ ] y [
]