Математика. Курзина В.М - 75 стр.

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75
49.
x
x
x
+
4
1
1lim . 50.
x
x
x
x
3
3
13
lim
+
. 51.
x
x
x
x
3
6
lim
+
.
52.
x
x
x
4
1
1lim
+
. 53.
x
x
x
x
3
3
lim
+
. 54.
2/
8
lim
x
x
x
x
+
.
55.
x
x
x
+
3
8
1lim . 56.
2/
4
34
lim
x
x
x
x
+
. 57.
x
x
x
x
3
2
2
1
9
lim
+
+
.
58.
2/
2
2
94
lim
x
x
x
x
+
. 59.
x
x
x
x
8
2
2
2
6
lim
+
. 60.
x
x
x
7
4
1lim
+
.
61.
2
/
cos
4/cos4/sin
lim
x
xx
x
π
. 62.
)1ln(
6sin
lim
0
+
x
x
x
. 63.
x
x
x
21
31
lim
.
64.
xx
xx
x
sin
sin
lim
0
+
. 65.
xx
xx
x
34
69
lim
. 66.
x
x
x
sin
lim
0
. 67.
2
/
sin
18
lim
0
x
x
x
.
68.
xx
x
x
x
ln
1
lim
1
. 69.
4
/
4ln)4ln(
lim
3
x
x
x
+
. 70.
2
/
cos
4/cos4/sin
lim
x
xx
x
π
.
71.
)1/(1
2
01
44
1
lim
+
x
x
x
x
. 72.
.
3
27
lim
)3/(1
3
03
x
x
x
x
+
73.
.
2
8
lim
)2/(8
3
02
x
x
x
x
+
+
+
75.
3
3
0
4
tg
lim
x
x
x
. 76.
x
x
x
arcsin
4/sin
lim
0
. 77.
x
x
x
6arcsin
2arcsin
lim
2
2
0
.
78.
4
0
4sin
lim
x
x
x
. 79.
x
xx
x
3arcsin
3tg4tg
lim
0
+
. 80.
x
e
x
x
9
1
lim
2
3
0
.
81.
x
x
x
8arctg
4/sin
lim
0
. 82. ]ln)5(ln(3[lim xxx
x
+
. 83.
)22sin(
)2ln(
lim
1
+
x
x
x
.
84.
)8/cos(
)3ln(
lim
4
x
x
x
π
. 85.
)42sin(
)2arcsin(
lim
2
x
x
x
. 86.
x
x
x
7
)51ln(
lim
0
.
                                                           75


                        x                                            3x                                         3x
         ⎛  1 ⎞                                         ⎛ 3x + 1 ⎞                                ⎛ x + 6⎞
49. lim ⎜1 + ⎟ .                               50. lim ⎜         ⎟ .                     51. lim ⎜       ⎟ .
    x →∞ ⎝  4x ⎠                                   x →∞ ⎝ 3 x ⎠                              x →∞ ⎝   x ⎠

                     4x                                              3x                                         x/2
         ⎛ 1⎞                                           ⎛ x + 3⎞                                  ⎛ x + 8⎞
52. lim ⎜1 + ⎟ .                               53. lim ⎜       ⎟ .                       54. lim ⎜       ⎟             .
    x →∞ ⎝  x⎠                                     x →∞ ⎝ x ⎠                                x →∞ ⎝ x ⎠


                      x                                               x/2                                            3x
         ⎛  8⎞                                          ⎛ 4x + 3 ⎞                                ⎛ x2 + 9 ⎞
55. lim ⎜1 + ⎟ .                               56. lim ⎜         ⎟          .            57. lim ⎜⎜ 2      ⎟ .
    x →∞ ⎝  3x ⎠                                   x →∞ ⎝ 4 x ⎠                              x →∞ x + 1 ⎟
                                                                                                  ⎝        ⎠

                               x/2                                        8x                                      7x
         ⎛ 4x2 + 9 ⎞                                    ⎛ x2 − 6 ⎞                                 ⎛ 4⎞
58. lim ⎜⎜         ⎟⎟                .         59. lim ⎜⎜ 2      ⎟ .                      60. lim ⎜1 + ⎟ .
    x →∞     x 2                                   x →∞ x + 2 ⎟                               x →∞ ⎝  x⎠
         ⎝          ⎠                                   ⎝        ⎠

         sin x / 4 − cos x / 4                           sin 6 x                                    1 − 3x
61. lim                        .                62. lim            .                       63. lim          .
    x →π       cos x / 2                            x→0 ln( x + 1)                             x →∞ 1 − 2 x



        x + sin x                                  9x − 6x                  sin x                    8x − 1
64. lim           .                       65. lim x        .        66. lim       .         67. lim           .
    x→0 x − sin x                             x →∞ 4 − 3 x              x →0 x                  x→0 sin x / 2



          xx −1                                   ln( x + 4) − ln 4                           sin x / 4 − cos x / 4
68. lim          .                       69. lim                    .                70. lim                        .
     x →1 x ln x                             x→−3        x/4                             x →π       cos x / 2

                            1 /( x −1)                             1 /( 3− x )                                 8 /( 2+ x )
           ⎛ x2 − 1 ⎞                                 ⎛ x3 − 27 ⎞                              ⎛ x3 + 8 ⎞
71. lim ⎜⎜          ⎟                    . 72. lim ⎜⎜           ⎟                .   73. lim ⎜⎜         ⎟                    .
    x →1+ 0 4 x − 4 ⎟                         x →3 + 0   x − 3  ⎟                       x →−2−0 x + 2 ⎟
           ⎝        ⎠                                 ⎝         ⎠                              ⎝        ⎠

        tg 3 x                                       sin x / 4                                  arcsin 2 2 x
75. lim 3 .                                 76. lim            .                        77. lim              .
    x→0 4 x                                     x →0 arcsin x                               x→0 arcsin 2 6 x


                                                                                                           2
       sin 4 x                                     tg 4 x + tg3 x                                1 − e 3x
78. lim 4 .                                79. lim                .                     80. lim           .
    x→0 x                                      x →0 arcsin 3 x                              x →0    9x

          sin x / 4                                                                                 ln( x + 2)
81. lim             .                      82. lim[3 x(ln( x + 5) − ln x] .             83. lim                  .
     x →0 arctg8 x                              x →∞                                           x→1 sin( 2 x − 2)



          ln( x − 3)                                arcsin( x − 2)                                  ln(1 − 5 x)
84. lim               .                     85. lim                .                     86. lim                .
     x→4 cos( πx / 8)                            x→2 sin( 2 x − 4)                             x →0     7x