bludova_t_v_praktikum_z_vishoi_matematiki
.pdfРозділ 3. ВСТУП ДО МАТЕМАТИЧНОГО АНАЛІЗУ
Задача 3. 1. За даними табл. 3.1 знайти границю:
lim |
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A x4 |
B x3 |
C x2 |
D x F |
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1 |
1 |
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1 |
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1 |
1 |
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A x4 |
B x3 |
C |
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x2 |
D x F |
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x x0 |
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2 |
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2 |
2 |
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2 |
2 |
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Таблиця 3.1 |
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Номер |
х0 |
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А1 |
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В1 |
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С1 |
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D1 |
F1 |
А2 |
В2 |
С2 |
D2 |
F2 |
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варіанта |
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1 |
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0 |
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1 |
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– 100 |
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0 |
1 |
0 |
200 |
0 |
15 |
0 |
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2 |
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5 |
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1 |
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0 |
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3 |
– 1 |
2 |
0 |
3 |
1 |
1 |
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3 |
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2 |
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0 |
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– 7 |
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4 |
0 |
0 |
105 |
7 |
2 |
– 5 |
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4 |
2 |
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0 |
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0 |
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1 |
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– 4 |
1 |
0 |
0 |
0 |
2 |
1 |
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5 |
3 |
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0 |
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0 |
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1 |
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0 |
– 9 |
0 |
0 |
1 |
– 2 |
– 3 |
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6 |
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1 |
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4 |
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0 |
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3 |
5 |
7 |
0 |
0 |
– 1 |
– 1 |
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7 |
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9 |
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– 1 |
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8 |
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0 |
6 |
0 |
2 |
15 |
0 |
11 |
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8 |
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0 |
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21 |
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10 |
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0 |
– 17 |
25 |
0 |
7 |
– 8 |
– 3 |
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9 |
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0 |
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1 |
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– 3 |
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3 |
– 1 |
0 |
2 |
3 |
0 |
1 |
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10 |
– 1 |
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0 |
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1 |
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1 |
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– 1 |
– 1 |
0 |
1 |
1 |
1 |
1 |
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11 |
0,4 |
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0 |
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5 |
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– 2 |
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5 |
– 2 |
5 |
– 2 |
– 5 |
2 |
0 |
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12 |
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100 |
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10 |
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17 |
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0 |
– 1 |
20 |
– 3 |
4 |
– 1 |
– 1 |
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13 |
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12 |
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3 |
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– 1 |
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0 |
7 |
4 |
– 2 |
–17 |
0 |
3 |
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14 |
– 1 |
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0 |
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0 |
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1 |
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– 1 |
– 2 |
0 |
1 |
0 |
0 |
1 |
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15 |
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0 |
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92 |
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3 |
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– 4 |
0 |
4 |
0 |
25 |
2 |
1 |
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16 |
– 1 |
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0 |
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0 |
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1 |
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0 |
– 1 |
0 |
0 |
1 |
3 |
2 |
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17 |
2 |
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0 |
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2 |
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– 2 |
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1 |
1 |
0 |
1 |
– 1 |
3 |
– 3 |
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18 |
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2 |
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3 |
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– 1 |
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0 |
1 |
1 |
7 |
4 |
5 |
2 |
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19 |
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0 |
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– 9 |
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5 |
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6 |
0 |
0 |
3 |
– 4 |
5 |
1 |
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20 |
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27 |
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2 |
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3 |
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– 1 |
– 1 |
9 |
– 2 |
4 |
6 |
9 |
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21 |
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0 |
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0 |
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1 |
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– 1 |
1 |
0 |
2 |
0 |
3 |
– 1 |
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22 |
– 3 |
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0 |
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1 |
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5 |
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3 |
– 9 |
0 |
1 |
8 |
21 |
18 |
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70
Продовження табл. 3.1
Номер |
х0 |
А1 |
В1 |
С1 |
D1 |
F1 |
А2 |
В2 |
С2 |
D2 |
F2 |
варіанта |
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23 |
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8 |
0 |
2 |
3 |
7 |
4 |
1 |
– 1 |
12 |
9 |
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24 |
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0 |
0 |
1 |
– 1 |
3 |
0 |
0 |
5 |
– 2 |
4 |
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25 |
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0 |
2 |
0 |
7 |
9 |
0 |
1 |
2 |
– 10 |
12 |
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26 |
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17 |
0 |
– 3 |
4 |
29 |
1 |
21 |
18 |
2 |
– 3 |
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27 |
2 |
0 |
0 |
1 |
– 5 |
6 |
0 |
0 |
1 |
12 |
20 |
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28 |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
– 2 |
0 |
0 |
0 |
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29 |
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10 |
0 |
2 |
7 |
1 |
5 |
3 |
2 |
0 |
1 |
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30 |
1 |
0 |
0 |
– 1 |
2 |
– 1 |
0 |
1 |
– 1 |
– 1 |
1 |
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31 |
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0 |
1 |
27 |
3 |
9 |
7 |
21 |
11 |
0 |
9 |
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32 |
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5 |
2 |
3 |
9 |
6 |
1 |
2 |
4 |
8 |
1 |
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33 |
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0 |
0 |
1 |
0 |
1 |
0 |
2 |
6 |
3 |
4 |
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34 |
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8 |
2 |
4 |
1 |
3 |
0 |
4 |
2 |
8 |
1 |
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35 |
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49 |
– 70 |
– 3 |
20 |
4 |
16 |
2 |
5 |
1 |
7 |
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36 |
1 |
0 |
1 |
– 3 |
3 |
– 1 |
0 |
1 |
2 |
– 1 |
– 2 |
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37 |
– 3 |
0 |
1 |
9 |
27 |
27 |
0 |
1 |
3 |
– 4 |
– 12 |
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38 |
– 1 |
0 |
0 |
2 |
1 |
– 1 |
0 |
0 |
1 |
– 6 |
7 |
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39 |
1 |
0 |
1 |
0 |
0 |
– 1 |
0 |
0 |
0 |
1 |
– 1 |
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40 |
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0 |
6 |
0 |
– 2 |
1 |
0 |
1 |
0 |
– 2 |
5 |
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41 |
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10 |
1 |
3 |
1 |
1 |
2 |
– 4 |
6 |
– 3 |
1 |
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42 |
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0 |
7 |
2 |
3 |
6 |
0 |
4 |
9 |
8 |
5 |
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43 |
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– 3 |
1 |
12 |
1 |
5 |
1 |
6 |
11 |
2 |
8 |
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44 |
1 |
1 |
0 |
0 |
– 2 |
1 |
0 |
1 |
0 |
– 2 |
1 |
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45 |
1 |
0 |
0 |
1 |
4 |
– 5 |
0 |
0 |
1 |
0 |
– 1 |
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46 |
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7 |
2 |
– 3 |
– 6 |
3 |
1 |
– 2 |
4 |
5 |
7 |
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47 |
2/3 |
0 |
0 |
9 |
– 12 |
4 |
0 |
27 |
0 |
0 |
– 8 |
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48 |
– 2 |
0 |
1 |
1 |
– 4 |
– 4 |
0 |
0 |
0 |
2 |
4 |
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71
Продовження табл. 3.1
Номер |
х0 |
А1 |
В1 |
С1 |
D1 |
F1 |
А2 |
В2 |
С2 |
D2 |
F2 |
варіанта |
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49 |
2/5 |
0 |
5 |
– 2 |
5 |
– 2 |
5 |
– 2 |
– 5 |
2 |
0 |
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50 |
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13 |
7 |
4 |
1 |
3 |
1 |
0 |
2 |
7 |
8 |
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51 |
2 |
0 |
5 |
0 |
0 |
40 |
0 |
– 1 |
–3 |
4 |
12 |
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52 |
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23 |
2 |
1 |
3 |
– 1 |
1 |
2 |
4 |
2 |
7 |
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53 |
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17 |
3 |
1 |
0 |
1 |
2 |
1 |
4 |
5 |
7 |
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54 |
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0 |
2 |
17 |
3 |
1 |
2 |
5 |
6 |
8 |
3 |
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55 |
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21 |
0 |
1 |
3 |
7 |
0 |
8 |
7 |
9 |
6 |
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56 |
1 |
1 |
– 1 |
3 |
– 2 |
– 1 |
0 |
0 |
1 |
5 |
– 6 |
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57 |
– 5 |
1 |
7 |
10 |
1 |
5 |
0 |
0 |
1 |
– 1 |
– 30 |
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58 |
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12 |
3 |
2 |
1 |
7 |
7 |
– 2 |
– 4 |
5 |
6 |
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59 |
3 |
2 |
– 5 |
– 3 |
1 |
– 3 |
0 |
0 |
1 |
4 |
– 21 |
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60 |
|
17 |
– 21 |
3 |
2 |
7 |
1 |
– 3 |
– 1 |
5 |
4 |
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61 |
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0 |
16 |
7 |
9 |
12 |
0 |
8 |
9 |
6 |
1 |
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62 |
|
5 |
2 |
21 |
3 |
1 |
2 |
3 |
9 |
6 |
8 |
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63 |
– 1 |
0 |
1 |
0 |
– 8 |
7 |
0 |
0 |
1 |
6 |
– 7 |
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64 |
2 |
0 |
3 |
– 4 |
– 5 |
2 |
0 |
0 |
2 |
– 1 |
– 6 |
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65 |
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– 10 |
– 1 |
6 |
5 |
0 |
1 |
– 2 |
– 14 |
2 |
7 |
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66 |
|
25 |
– 3 |
4 |
7 |
1 |
5 |
– 4 |
5 |
– 1 |
1 |
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67 |
|
11 |
– 5 |
– 9 |
3 |
2 |
5 |
– 3 |
– 1 |
2 |
1 |
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68 |
|
12 |
7 |
3 |
2 |
7 |
4 |
5 |
– 3 |
– 8 |
6 |
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69 |
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0 |
3 |
2 |
8 |
6 |
5 |
2 |
3 |
1 |
7 |
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70 |
|
51 |
20 |
– 17 |
3 |
10 |
0 |
7 |
21 |
3 |
– 10 |
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71 |
5 |
2 |
– 10 |
– 1 |
6 |
5 |
0 |
1 |
– 2 |
– 14 |
– 5 |
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72 |
– 4 |
0 |
2 |
9 |
3 |
– 4 |
0 |
7 |
33 |
18 |
– 8 |
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73 |
1 |
0 |
3 |
– 4 |
3 |
– 2 |
0 |
0 |
2 |
5 |
– 7 |
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72
Закінчення табл. 3.1
Номер |
х0 |
А1 |
В1 |
С1 |
D1 |
F1 |
А2 |
В2 |
С2 |
D2 |
F2 |
варіанта |
|||||||||||
|
|
|
|
|
|
|
|
|
|
|
|
74 |
– 3 |
2 |
7 |
3 |
1 |
3 |
0 |
0 |
1 |
10 |
21 |
|
|
|
|
|
|
|
|
|
|
|
|
75 |
|
0 |
2 |
7 |
5 |
3 |
1 |
9 |
8 |
6 |
12 |
|
|
|
|
|
|
|
|
|
|
|
|
76 |
|
27 |
3 |
2 |
6 |
9 |
0 |
8 |
6 |
12 |
3 |
|
|
|
|
|
|
|
|
|
|
|
|
77 |
|
19 |
21 |
3 |
4 |
7 |
1 |
12 |
16 |
4 |
2 |
|
|
|
|
|
|
|
|
|
|
|
|
78 |
|
53 |
27 |
11 |
20 |
0 |
0 |
19 |
1 |
0 |
3 |
|
|
|
|
|
|
|
|
|
|
|
|
79 |
|
0 |
11 |
1 |
2 |
3 |
11 |
0 |
1 |
3 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
80 |
7 |
1 |
– 5 |
– 14 |
– 1 |
7 |
0 |
0 |
2 |
– 9 |
– 35 |
|
|
|
|
|
|
|
|
|
|
|
|
81 |
– 0,5 |
0 |
0 |
6 |
19 |
8 |
0 |
0 |
10 |
13 |
4 |
|
|
|
|
|
|
|
|
|
|
|
|
82 |
– 3 |
1 |
5 |
6 |
3 |
9 |
2 |
6 |
1 |
4 |
3 |
|
|
|
|
|
|
|
|
|
|
|
|
83 |
|
2 |
5 |
3 |
1 |
4 |
1 |
2 |
0 |
1 |
2 |
|
|
|
|
|
|
|
|
|
|
|
|
84 |
|
7 |
1 |
3 |
2 |
1 |
2 |
15 |
3 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
85 |
|
12 |
4 |
1 |
5 |
7 |
4 |
3 |
0 |
9 |
10 |
|
|
|
|
|
|
|
|
|
|
|
|
86 |
|
0 |
2 |
8 |
13 |
17 |
15 |
0 |
13 |
11 |
0 |
|
|
|
|
|
|
|
|
|
|
|
|
87 |
|
19 |
11 |
5 |
3 |
1 |
0 |
19 |
2 |
11 |
0 |
|
|
|
|
|
|
|
|
|
|
|
|
88 |
|
23 |
21 |
29 |
17 |
1 |
1 |
17 |
29 |
23 |
21 |
|
|
|
|
|
|
|
|
|
|
|
|
89 |
– 1/3 |
0 |
0 |
21 |
25 |
5 |
0 |
0 |
6 |
5 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
90 |
2 |
3 |
– 6 |
1 |
– 3 |
2 |
1 |
4 |
– 14 |
– 2 |
4 |
|
|
|
|
|
|
|
|
|
|
|
|
91 |
|
29 |
13 |
2 |
7 |
1 |
10 |
3 |
4 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
92 |
|
0 |
5 |
7 |
9 |
17 |
0 |
2 |
3 |
4 |
8 |
|
|
|
|
|
|
|
|
|
|
|
|
93 |
|
12 |
4 |
5 |
6 |
0 |
4 |
6 |
3 |
5 |
7 |
|
|
|
|
|
|
|
|
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|
94 |
– 1 |
2 |
3 |
1 |
– 3 |
– 3 |
3 |
3 |
– 1 |
0 |
1 |
|
|
|
|
|
|
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|
|
|
95 |
2 |
2 |
– 4 |
3 |
8 |
4 |
0 |
0 |
7 |
– 13 |
– 2 |
|
|
|
|
|
|
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|
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|
96 |
|
7 |
3 |
12 |
4 |
5 |
1 |
2 |
13 |
9 |
8 |
|
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|
|
|
|
|
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|
|
97 |
|
0 |
16 |
17 |
0 |
1 |
0 |
8 |
11 |
14 |
5 |
|
|
|
|
|
|
|
|
|
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|
98 |
|
25 |
11 |
6 |
7 |
0 |
10 |
0 |
12 |
4 |
3 |
|
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|
99 |
0,5 |
0 |
0 |
10 |
– 3 |
– 1 |
0 |
0 |
8 |
2 |
– 3 |
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|
100 |
5 |
0 |
1 |
– 2 |
– 16 |
5 |
0 |
2 |
11 |
8 |
– 15 |
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73
Задача 3.1-1. За даними табл. 3.1-1 знайти границю lim f (x) .
x g(x)
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Таблиця 3.1-1 |
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|
Номер |
|
f (x) |
g (x) |
|
варіанта |
||||
|
|
|
||
|
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|
|
1 |
0 |
tg x – sin x |
x3 |
|
2 |
0 |
1 x 1 x |
4x |
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|
|
3 |
0 |
1 – cos x |
x2 |
|
4 |
0 |
1 x 1 |
x |
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|
5 |
0 |
1 + sin x – cos x |
1 – sin x – cos x |
|
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6 |
0 |
3 1 x 2 1 |
x2 |
|
7 |
0 |
tg x |
3 (1 cosx) 2 |
|
8 |
– 8 |
1 x 3 |
2 3 x |
|
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|
9 |
0 |
tg x – cos x + 1 |
х |
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10 |
0 |
3 1 x 3 1 x |
х |
|
11 |
0 |
sin2x |
1 xsin x cos x |
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|
12 |
9 |
9 – x |
x 3 |
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13 |
0 |
sin 3x |
x 2 2 |
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|
14 |
– 4 |
x 12 4 x |
x2 + 2x – 8 |
|
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|
15 |
0 |
1 – cos 3x |
x2 |
|
16 |
2 |
x3 – 2x2 – x + 2 |
3 x2 3 3 x 1 |
|
17 |
0 |
tg 3x – sin 3x |
27 x3 |
|
18 |
0 |
x2 1 1 |
x2 4 2 |
|
19 |
2 |
x2 – 4 |
sin (x – 2) |
|
20 |
0,5 |
arcsin (1 – 2x) |
4x2 – 1 |
|
21 |
/2 |
sin x – sin2 x |
cos2 x |
74
|
|
|
|
Продовження табл. 3.1-1 |
|||||
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Номер |
|
|
f (x) |
g (x) |
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||
варіанта |
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22 |
0 |
1 – cos m x |
|
x2 |
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|
||
23 |
2 |
sin (x – 2) |
x2 – 4 |
|
|||||
24 |
– /4 |
sin + sin 5 |
cos + cos 5 |
||||||
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25 |
0 |
1 – cos 2x + tg2x |
x sin x |
|
|||||
26 |
– 1 |
x2 3 2x |
x + 1 |
|
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|
|||
27 |
0 |
cos (x + 3) – cos (x – 3) |
|
x |
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||
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||
28 |
1 |
3 x 1 |
3 x2 23 x 3 |
||||||
29 |
0 |
tg x – sin x |
|
x3 |
|
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|
||
30 |
1 |
4 x 1 |
3 |
x 1 |
|
||||
31 |
/4 |
2 2cos x |
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sin x |
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4 |
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32 |
0 |
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x |
3 8 x 3 8 x |
||||
33 |
0 |
tg x – sin x |
sin3x |
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|
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34 |
0 |
1 x x2 1 |
|
x |
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35 |
0 |
tg 2x – tg x |
sin 2x – sin x |
||||||
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36 |
2 |
x2 5 3 |
x3 – 8 |
|
|||||
37 |
2 |
x2 3 x2 3 3 |
3 x2 2x |
|
|||||
38 |
/2 |
1 – sin x |
1 + cos 2x |
||||||
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||||
39 |
0 |
|
2 tg 6x |
1 cos 4x |
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40 |
0 |
x x |
2 |
x x |
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x |
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2 |
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41 |
0 |
sin |
|
sin4x |
2x |
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2 |
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||||||
42 |
4 |
|
x – 4 |
2x 1 3 |
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43 |
2 |
sin 2x – 2 tg x |
cos x – 1 |
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75
Продовження табл. 3.1-1
Номер |
|
|
f (x) |
|
|
g (x) |
варіанта |
|
|
|
|||
|
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||
44 |
1 |
sin (x – 1) |
2 |
5 x2 |
||
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||
45 |
0 |
2 |
x 4 |
sin 2x |
||
|
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|
|||
46 |
3 |
x2 7 4 |
x2 – 5x + 6 |
|||
47 |
0 |
tg 3x – sin 3x |
|
27 x3 |
||
48 |
0 |
x2 1 1 |
x2 4 2 |
|||
49 |
2 |
x3 – 2x2 – x + 2 |
3 x2 3 3 x 1 |
|||
50 |
0 |
1 – cos 2x |
sin 2x |
|||
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|
|||
51 |
4 |
x x 6 |
x 5 x 6 |
|||
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52 |
0 |
1 3x4 1 2x |
x2 + x+ 2x3 |
|||
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||
53 |
1 |
3 x 1 |
|
3 x2 23 x 3 |
||
54 |
0 |
(x2 + 3x – 1) tgx |
x2 + 2x |
|||
55 |
1 |
(x2 – 4x + 3) sin (x – 1) |
(x – 1)2 |
|||
56 |
– 1 |
2x 3 1 |
5 x 2 |
|||
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57 |
0 |
|
1 |
2x 1 |
|
sin x |
|
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||
58 |
3 |
x3 9 2x |
|
x – 3 |
||
59 |
0 |
sin x – tg x |
|
x3 |
||
60 |
|
|
tg x |
|
sin 2x |
|
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|
|||
61 |
/4 |
sin x – cos x |
cos 2x |
|||
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62 |
0 |
|
x |
|
1 3x 1 |
|
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||
63 |
a |
ax x |
|
x – a |
||
|
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64 |
1 |
3 |
x 1 |
|
|
x 1 |
|
|
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|
||
65 |
0 |
3 1 mx 1 |
|
x |
||
76
Продовження табл. 3.1-1
Номер |
|
|
f (x) |
|
g (x) |
|||
варіанта |
|
|
||||||
|
|
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66 |
0 |
1 x |
1 x |
x |
|
|||
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||
67 |
|
1 tgx |
1 tgx |
sin 2x |
||||
|
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|
|||
68 |
|
1 cos x |
sin x |
|||||
|
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|
||
69 |
7 |
2 |
x 3 |
x2 – 49 |
||||
|
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|
|||
70 |
/4 |
sin2x – cos2x – 1 |
cosx – sinx |
|||||
|
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|
|||
71 |
0 |
1 – cos2x + tg2x |
xsinx |
|||||
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|
|||
72 |
0 |
1 x sin x cos x |
sin2x |
|||||
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||
73 |
|
cos |
x |
|
|
x – |
||
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|||||||
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2 |
|
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|
|
74 |
– 1 |
cos (x + 1) |
3 x 1 |
|||||
75 |
/2 |
1 cos 2x |
|
2x |
||||
|
|
|
|
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|
|||
76 |
4 |
x – 4 |
|
x 1 |
7 x |
|||
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|
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|
|||||
77 |
– 1 |
x 10 8 x |
x + 1 |
|||||
|
|
|
|
|||||
78 |
0 |
x2 1 1 |
x2 16 4 |
|||||
79 |
|
sin2x – sin2 |
x – |
|||||
|
|
|
|
|
|
|||
80 |
|
sin2x |
|
1 cos2 |
x 2 |
|||
|
|
|
|
|||||
81 |
0 |
2x 1 1 |
3x 4 2 |
|||||
|
|
|
|
|
|
|||
82 |
0 |
|
tg2x |
|
sin5x |
|||
|
|
|
|
|||||
83 |
|
cos2x – cos2 |
x – |
|||||
|
|
|
|
|
||||
84 |
0 |
3 1 x 2 1 |
x2 |
|
||||
|
|
|
|
|||||
85 |
1 |
sin (1 – x) |
x 1 |
|||||
|
|
|
|
|||||
86 |
0 |
1 – cosx |
x 1 x 1 |
|||||
77
|
|
|
Закінчення табл. 3.1-1 |
|
|
|
|
|
|
Номер |
|
f (x) |
|
g (x) |
варіанта |
|
|||
|
|
|
|
|
|
|
|
|
|
87 |
0 |
x |
|
4 1 2x 1 |
88 |
/4 |
tg x |
|
x – /4 |
|
|
|
|
|
89 |
0 |
3sinx + sin2x |
|
sin2x – sin3x |
|
|
|
|
|
90 |
0 |
sin2x – 2sinx |
|
(cos2x – 2cosx)x2 |
|
|
|
|
|
91 |
0 |
1 – cos4x |
|
(1 + cos4x)x2 |
|
|
|
|
|
92 |
1 |
3 5x 3 23 x |
|
3x 1 2 |
|
|
|
|
|
93 |
0 |
3 x x |
|
3 x 1 1 |
94 |
0 |
x3 |
|
1 3 x3 1 |
|
|
|
|
|
95 |
0 |
3 (1 cos x)2 |
|
tg x |
|
|
|
|
|
96 |
– 8 |
2 3 x |
|
1 x 3 |
|
|
|
|
|
97 |
2 |
3 x2 3 3 x 1 |
|
x3 – 2x2 – x + 2 |
98 |
/2 |
cos2x |
|
sin x – sin2x |
|
|
|
|
|
99 |
0 |
x sin x |
|
1 – cos 2x + tg2x |
|
|
|
|
|
100 |
0 |
sin 2x – sin x |
|
tg 2x – tg x |
|
|
|
|
|
Задача 3.1-2. За даними табл. 3.1-2 знайти границюlim (x) ( x) . |
||||
|
|
|
x |
|
|
|
|
Таблиця 3.1-2 |
|
|
|
|
|
|
Номер |
|
(x) |
(x) |
|
варіанта |
||||
|
|
|
||
|
|
|
|
|
1 |
0 |
1 – 2x |
1/x |
|
|
|
|
|
|
2 |
|
(x + 1)/x |
x |
|
|
|
|
|
|
3 |
|
(x + 3)x |
5x – 2 |
|
|
|
|
|
|
4 |
|
(2x + 1)/(2x + 3) |
x + 1 |
|
|
|
|
|
|
5 |
|
(2x + 3)/(5x – 1) |
x + 3 |
|
|
|
|
|
|
78
|
|
Продовження табл. 3.1-2 |
||||
|
|
|
|
|
|
|
Номер |
|
(x) |
(x) |
|
|
|
варіанта |
|
|
||||
|
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||
|
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|
6 |
|
(x2 + 2)/(x2 + 1) |
x2 |
|
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|
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|
7 |
|
(5x2 + 1)/5x2 |
x |
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|
8 |
|
(x2 + 1)/(x2 – 1) |
x2 |
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|
9 |
|
(2x + 7)/(x – 1) |
x |
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|
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|
|
10 |
|
(3x – 4)/(3x + 2) |
(x + 1)/3 |
|
||
|
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|
|
11 |
|
(x + 1)/(2x – 1) |
x |
|
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|
12 |
|
(2x + 1)/(x – 1) |
x |
|
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|
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|
|
|
13 |
0 |
1 + sin2x |
1/sin x |
|
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|
14 |
|
1 + 1/x2 |
x |
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|
|
15 |
0 |
2x + 1 |
5/x |
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||
16 |
/4 |
tg x |
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||
1/sin x |
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4 |
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17 |
|
(5x3 + x2 – 1)/(5x3 – x2 + 1) |
x2 |
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||
18 |
0 |
1 – 4x |
(1 – x)/x |
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||
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19 |
|
(7x – 1)/(7x + 3) |
5x |
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20 |
0 |
cos x |
ctg2x |
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21 |
/4 |
sin 2x |
tg22x |
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22 |
0 |
1 + tg x |
ctg x |
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23 |
0 |
1 + 2x |
1/x |
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24 |
0 |
1 + 3 tg2x |
ctg2x |
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25 |
|
(2x – 1)/(2x + 1) |
2x |
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26 |
0 |
1 + sin x |
cosec x |
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27 |
|
(x2 – 2x + 1)/(x2 – 4x + 2) |
x |
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28 |
0 |
sin x |
tg x |
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29 |
|
1 + 3/x |
x |
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30 |
0 |
x |
x |
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79