Маслова Т.Н., Суходский А.М. Справочник школьника по математике. 5-11 кл
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650
Ïðåäìåòíûé óêàçàòåëü
651
ÑÎÄÅÐÆÀÍÈÅ
Ïðåäèñëîâèå .....................................................3
ÀËÃÅÁÐÀ
Ðàçäåë I. ×èñëà
§ 1. Íàòóðàëüíûå ÷èñëà ....................................5
1. Çàïèñü íàòóðàëüíûõ ÷èñåë .............................5
2. Àðèôìåòè÷åñêèå äåéñòâèÿ
íàä íàòóðàëüíûìè ÷èñëàìè ............................ 6
3. Äåëåíèå ñ îñòàòêîì ........................................ 7
4. Ðàçëîæåíèå íàòóðàëüíîãî ÷èñëà
íà ïðîñòûå ìíîæèòåëè ...................................8
5. Íàèáîëüøèé îáùèé äåëèòåëü íåñêîëüêèõ
íàòóðàëüíûõ ÷èñåë ........................................9
6. Íàèìåíüøåå îáùåå êðàòíîå íåñêîëüêèõ
íàòóðàëüíûõ ÷èñåë ...................................... 10
7. Ïðèçíàêè äåëèìîñòè ................................... 11
ñòàðøèé 79
ïîñëåäîâàòåëüíîñòè 283
ïðîïîðöèè êðàéíèé 45
ñðåäíèé 45
Ø
Øàð 526, 605
, âïèñàííûé â ìíîãîãðàííèê 530
, îïèñàííûé îêîëî ìíîãîãðàííèêà 530
Øàðîâîé ñåãìåíò 527, 606
ñåêòîð 527, 607
ñëîé 527, 607
Ý
Ýêñïîíåíòà 152
Ýêñòðåìóì 324
Ýëåìåíò îïðåäåëèòåëÿ 230
Ýëëèïñ 521
650
Ïðåäìåòíûé óêàçàòåëü
651
ÑÎÄÅÐÆÀÍÈÅ
Ïðåäèñëîâèå .....................................................3
ÀËÃÅÁÐÀ
Ðàçäåë I. ×èñëà
§ 1. Íàòóðàëüíûå ÷èñëà ....................................5
1. Çàïèñü íàòóðàëüíûõ ÷èñåë .............................5
2. Àðèôìåòè÷åñêèå äåéñòâèÿ
íàä íàòóðàëüíûìè ÷èñëàìè ............................ 6
3. Äåëåíèå ñ îñòàòêîì ........................................ 7
4. Ðàçëîæåíèå íàòóðàëüíîãî ÷èñëà
íà ïðîñòûå ìíîæèòåëè ...................................8
5. Íàèáîëüøèé îáùèé äåëèòåëü íåñêîëüêèõ
íàòóðàëüíûõ ÷èñåë ........................................9
6. Íàèìåíüøåå îáùåå êðàòíîå íåñêîëüêèõ
íàòóðàëüíûõ ÷èñåë ...................................... 10
7. Ïðèçíàêè äåëèìîñòè ................................... 11
ñòàðøèé 79
ïîñëåäîâàòåëüíîñòè 283
ïðîïîðöèè êðàéíèé 45
ñðåäíèé 45
Ø
Øàð 526, 605
, âïèñàííûé â ìíîãîãðàííèê 530
, îïèñàííûé îêîëî ìíîãîãðàííèêà 530
Øàðîâîé ñåãìåíò 527, 606
ñåêòîð 527, 607
ñëîé 527, 607
Ý
Ýêñïîíåíòà 152
Ýêñòðåìóì 324
Ýëåìåíò îïðåäåëèòåëÿ 230
Ýëëèïñ 521
Ñîäåðæàíèå
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Ñîäåðæàíèå
8. Óïîòðåáëåíèå áóêâ â àëãåáðå.
Ïåðåìåííûå ............................................... 13
§ 2. Ðàöèîíàëüíûå ÷èñëà ................................ 13
9. Îáûêíîâåííûå äðîáè. Ïðàâèëüíûå
è íåïðàâèëüíûå äðîáè. Ñìåøàííûå ÷èñëà ... 13
10. Ðàâåíñòâî äðîáåé. Îñíîâíîå ñâîéñòâî
äðîáè. Ñîêðàùåíèå äðîáåé ......................... 15
11. Ïðèâåäåíèå äðîáåé ê îáùåìó
çíàìåíàòåëþ ............................................. 16
12. Àðèôìåòè÷åñêèå äåéñòâèÿ íàä
îáûêíîâåííûìè äðîáÿìè ............................ 18
13. Äåñÿòè÷íûå äðîáè ..................................... 21
14. Àðèôìåòè÷åñêèå äåéñòâèÿ íàä
äåñÿòè÷íûìè äðîáÿìè ............................... 22
15. Ïðîöåíòû ................................................. 25
16. Îáðàùåíèå îáûêíîâåííîé äðîáè
â áåñêîíå÷íóþ äåñÿòè÷íóþ
ïåðèîäè÷åñêóþ äðîáü.................................. 26
17. Îáðàùåíèå áåñêîíå÷íîé äåñÿòè÷íîé
ïåðèîäè÷åñêîé äðîáè â îáûêíîâåííóþ
äðîáü ........................................................ 28
18. Êîîðäèíàòíàÿ ïðÿìàÿ ................................ 29
19. Ìíîæåñòâî ðàöèîíàëüíûõ ÷èñåë ................. 30
§ 3. Äåéñòâèòåëüíûå ÷èñëà .............................. 31
20. Èððàöèîíàëüíûå ÷èñëà .............................. 31
21. Ìíîæåñòâî äåéñòâèòåëüíûõ ÷èñåë.
×èñëîâàÿ ïðÿìàÿ ....................................... 32
22. ×èñëîâàÿ ïëîñêîñòü. Ïðÿìîóãîëüíàÿ
äåêàðòîâà ñèñòåìà êîîðäèíàò íà ïëîñêîñòè
è â ïðîñòðàíñòâå ........................................ 33
23. Ïîëÿðíàÿ ñèñòåìà êîîðäèíàò ....................... 35
24. Îáîçíà÷åíèÿ íåêîòîðûõ ÷èñëîâûõ
ìíîæåñòâ. Îñíîâíûå ïîíÿòèÿ, ñâÿçàííûå
ñ ìíîæåñòâàìè .......................................... 37
25. Ñðàâíåíèå äåéñòâèòåëüíûõ ÷èñåë ................ 38
26. Ñâîéñòâà ÷èñëîâûõ íåðàâåíñòâ .................... 39
27. ×èñëîâûå ïðîìåæóòêè ............................... 40
28. Ìîäóëü äåéñòâèòåëüíîãî ÷èñëà .................... 42
29. Ôîðìóëà ðàññòîÿíèÿ ìåæäó äâóìÿ òî÷êàìè
êîîðäèíàòíîé ïðÿìîé ................................ 42
30. Ïðàâèëà äåéñòâèé
íàä äåéñòâèòåëüíûìè ÷èñëàìè .................... 44
31. Ñâîéñòâà àðèôìåòè÷åñêèõ äåéñòâèé
íàä äåéñòâèòåëüíûìè ÷èñëàìè .................... 44
32. Ïðîïîðöèè ................................................ 45
33. Öåëàÿ ÷àñòü ÷èñëà.
Äðîáíàÿ ÷àñòü ÷èñëà .................................. 46
34. Ñòåïåíü ñ íàòóðàëüíûì ïîêàçàòåëåì ........... 46
35. Ñòåïåíü ñ íóëåâûì ïîêàçàòåëåì.
Ñòåïåíü ñ îòðèöàòåëüíûì ïîêàçàòåëåì ......... 47
36. Ñòàíäàðòíûé âèä ïîëîæèòåëüíîãî
äåéñòâèòåëüíîãî ÷èñëà ............................... 47
37. Îïðåäåëåíèå àðèôìåòè÷åñêîãî êîðíÿ.
Ñâîéñòâà àðèôìåòè÷åñêèõ êîðíåé ............... 48
38. Êîðåíü íå÷åòíîé ñòåïåíè
èç îòðèöàòåëüíîãî ÷èñëà ............................. 50
39. Ñòåïåíü ñ äðîáíûì ïîêàçàòåëåì .................. 50
40. Ñâîéñòâà ñòåïåíåé ñ ðàöèîíàëüíûìè
ïîêàçàòåëÿìè ............................................ 51
41. Ïðèáëèæåííûå çíà÷åíèÿ ÷èñåë.
Àáñîëþòíàÿ è îòíîñèòåëüíàÿ
ïîãðåøíîñòè .............................................. 52
Ñîäåðæàíèå
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8. Óïîòðåáëåíèå áóêâ â àëãåáðå.
Ïåðåìåííûå ............................................... 13
§ 2. Ðàöèîíàëüíûå ÷èñëà ................................ 13
9. Îáûêíîâåííûå äðîáè. Ïðàâèëüíûå
è íåïðàâèëüíûå äðîáè. Ñìåøàííûå ÷èñëà ... 13
10. Ðàâåíñòâî äðîáåé. Îñíîâíîå ñâîéñòâî
äðîáè. Ñîêðàùåíèå äðîáåé ......................... 15
11. Ïðèâåäåíèå äðîáåé ê îáùåìó
çíàìåíàòåëþ ............................................. 16
12. Àðèôìåòè÷åñêèå äåéñòâèÿ íàä
îáûêíîâåííûìè äðîáÿìè ............................ 18
13. Äåñÿòè÷íûå äðîáè ..................................... 21
14. Àðèôìåòè÷åñêèå äåéñòâèÿ íàä
äåñÿòè÷íûìè äðîáÿìè ............................... 22
15. Ïðîöåíòû ................................................. 25
16. Îáðàùåíèå îáûêíîâåííîé äðîáè
â áåñêîíå÷íóþ äåñÿòè÷íóþ
ïåðèîäè÷åñêóþ äðîáü.................................. 26
17. Îáðàùåíèå áåñêîíå÷íîé äåñÿòè÷íîé
ïåðèîäè÷åñêîé äðîáè â îáûêíîâåííóþ
äðîáü ........................................................ 28
18. Êîîðäèíàòíàÿ ïðÿìàÿ ................................ 29
19. Ìíîæåñòâî ðàöèîíàëüíûõ ÷èñåë ................. 30
§ 3. Äåéñòâèòåëüíûå ÷èñëà .............................. 31
20. Èððàöèîíàëüíûå ÷èñëà .............................. 31
21. Ìíîæåñòâî äåéñòâèòåëüíûõ ÷èñåë.
×èñëîâàÿ ïðÿìàÿ ....................................... 32
22. ×èñëîâàÿ ïëîñêîñòü. Ïðÿìîóãîëüíàÿ
äåêàðòîâà ñèñòåìà êîîðäèíàò íà ïëîñêîñòè
è â ïðîñòðàíñòâå ........................................ 33
23. Ïîëÿðíàÿ ñèñòåìà êîîðäèíàò ....................... 35
24. Îáîçíà÷åíèÿ íåêîòîðûõ ÷èñëîâûõ
ìíîæåñòâ. Îñíîâíûå ïîíÿòèÿ, ñâÿçàííûå
ñ ìíîæåñòâàìè .......................................... 37
25. Ñðàâíåíèå äåéñòâèòåëüíûõ ÷èñåë ................ 38
26. Ñâîéñòâà ÷èñëîâûõ íåðàâåíñòâ .................... 39
27. ×èñëîâûå ïðîìåæóòêè ............................... 40
28. Ìîäóëü äåéñòâèòåëüíîãî ÷èñëà .................... 42
29. Ôîðìóëà ðàññòîÿíèÿ ìåæäó äâóìÿ òî÷êàìè
êîîðäèíàòíîé ïðÿìîé ................................ 42
30. Ïðàâèëà äåéñòâèé
íàä äåéñòâèòåëüíûìè ÷èñëàìè .................... 44
31. Ñâîéñòâà àðèôìåòè÷åñêèõ äåéñòâèé
íàä äåéñòâèòåëüíûìè ÷èñëàìè .................... 44
32. Ïðîïîðöèè ................................................ 45
33. Öåëàÿ ÷àñòü ÷èñëà.
Äðîáíàÿ ÷àñòü ÷èñëà .................................. 46
34. Ñòåïåíü ñ íàòóðàëüíûì ïîêàçàòåëåì ........... 46
35. Ñòåïåíü ñ íóëåâûì ïîêàçàòåëåì.
Ñòåïåíü ñ îòðèöàòåëüíûì ïîêàçàòåëåì ......... 47
36. Ñòàíäàðòíûé âèä ïîëîæèòåëüíîãî
äåéñòâèòåëüíîãî ÷èñëà ............................... 47
37. Îïðåäåëåíèå àðèôìåòè÷åñêîãî êîðíÿ.
Ñâîéñòâà àðèôìåòè÷åñêèõ êîðíåé ............... 48
38. Êîðåíü íå÷åòíîé ñòåïåíè
èç îòðèöàòåëüíîãî ÷èñëà ............................. 50
39. Ñòåïåíü ñ äðîáíûì ïîêàçàòåëåì .................. 50
40. Ñâîéñòâà ñòåïåíåé ñ ðàöèîíàëüíûìè
ïîêàçàòåëÿìè ............................................ 51
41. Ïðèáëèæåííûå çíà÷åíèÿ ÷èñåë.
Àáñîëþòíàÿ è îòíîñèòåëüíàÿ
ïîãðåøíîñòè .............................................. 52
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42. Äåñÿòè÷íûå ïðèáëèæåíèÿ
äåéñòâèòåëüíîãî ÷èñëà ïî íåäîñòàòêó
è ïî èçáûòêó ............................................. 54
43. Ïîíÿòèå î ñòåïåíè ñ èððàöèîíàëüíûì
ïîêàçàòåëåì .............................................. 55
44. Ñâîéñòâà ñòåïåíåé ñ äåéñòâèòåëüíûìè
ïîêàçàòåëÿìè ............................................ 55
§ 4. Êîìïëåêñíûå ÷èñëà .................................. 56
45. Ïîíÿòèå î êîìïëåêñíîì ÷èñëå.................... 56
46. Àðèôìåòè÷åñêèå îïåðàöèè
íàä êîìïëåêñíûìè ÷èñëàìè ........................ 57
47. Àëãåáðàè÷åñêàÿ ôîðìà êîìïëåêñíîãî
÷èñëà ....................................................... 58
48. Äåéñòâèÿ íàä êîìïëåêñíûìè ÷èñëàìè,
çàäàííûìè â àëãåáðàè÷åñêîé ôîðìå ............ 59
49. Ãåîìåòðè÷åñêîå èçîáðàæåíèå êîìïëåêñíûõ
÷èñåë. Òðèãîíîìåòðè÷åñêàÿ ôîðìà
êîìïëåêñíîãî ÷èñëà ................................... 61
50. Äåéñòâèÿ íàä êîìïëåêñíûìè ÷èñëàìè,
çàäàííûìè â òðèãîíîìåòðè÷åñêîé ôîðìå ..... 63
Ðàçäåë II. Âûðàæåíèÿ
§ 5. Îñíîâíûå ïîíÿòèÿ .................................... 68
51. Âèäû àëãåáðàè÷åñêèõ âûðàæåíèé ............... 68
52. Äîïóñòèìûå çíà÷åíèÿ ïåðåìåííûõ.
Îáëàñòü îïðåäåëåíèÿ àëãåáðàè÷åñêîãî
âûðàæåíèÿ ............................................... 69
53. Ïîíÿòèå òîæäåñòâåííîãî ïðåîáðàçîâàíèÿ
âûðàæåíèÿ. Òîæäåñòâî .............................. 70
§ 6. Öåëûå ðàöèîíàëüíûå âûðàæåíèÿ .............. 71
54. Îäíî÷ëåíû è îïåðàöèè íàä íèìè ................ 71
55. Ìíîãî÷ëåíû. Ïðèâåäåíèå ìíîãî÷ëåíîâ
ê ñòàíäàðòíîìó âèäó .................................. 73
56. Ôîðìóëû ñîêðàùåííîãî óìíîæåíèÿ ............ 75
57. Ðàçëîæåíèå ìíîãî÷ëåíîâ íà ìíîæèòåëè ....... 76
58. Ìíîãî÷ëåíû îò îäíîé ïåðåìåííîé ............... 79
59. Äåëåíèå ìíîãî÷ëåíîâ. Ñõåìà Ãîðíåðà.
Òåîðåìà Áåçó ............................................. 80
60. Ðàçëîæåíèå êâàäðàòíîãî òðåõ÷ëåíà
íà ëèíåéíûå ìíîæèòåëè ............................ 84
61. Ðàçëîæåíèå íà ìíîæèòåëè
äâó÷ëåíà .................................................. 85
62. Âîçâåäåíèå äâó÷ëåíà â íàòóðàëüíóþ
ñòåïåíü (ôîðìóëà áèíîìà Íüþòîíà) ............. 85
§ 7. Äðîáíûå ðàöèîíàëüíûå âûðàæåíèÿ .......... 86
63. Ðàöèîíàëüíàÿ äðîáü è åå îñíîâíîå
ñâîéñòâî ................................................... 86
64. Ñîêðàùåíèå ðàöèîíàëüíûõ äðîáåé .............. 88
65. Ïðèâåäåíèå ðàöèîíàëüíûõ äðîáåé
ê îáùåìó çíàìåíàòåëþ............................... 89
66. Ñëîæåíèå è âû÷èòàíèå ðàöèîíàëüíûõ
äðîáåé ....................................................... 90
67. Óìíîæåíèå è äåëåíèå ðàöèîíàëüíûõ
äðîáåé ...................................................... 91
68. Âîçâåäåíèå ðàöèîíàëüíîé äðîáè
â öåëóþ ñòåïåíü ......................................... 93
69. Ïðåîáðàçîâàíèå ðàöèîíàëüíûõ
âûðàæåíèé................................................ 94
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42. Äåñÿòè÷íûå ïðèáëèæåíèÿ
äåéñòâèòåëüíîãî ÷èñëà ïî íåäîñòàòêó
è ïî èçáûòêó ............................................. 54
43. Ïîíÿòèå î ñòåïåíè ñ èððàöèîíàëüíûì
ïîêàçàòåëåì .............................................. 55
44. Ñâîéñòâà ñòåïåíåé ñ äåéñòâèòåëüíûìè
ïîêàçàòåëÿìè ............................................ 55
§ 4. Êîìïëåêñíûå ÷èñëà .................................. 56
45. Ïîíÿòèå î êîìïëåêñíîì ÷èñëå.................... 56
46. Àðèôìåòè÷åñêèå îïåðàöèè
íàä êîìïëåêñíûìè ÷èñëàìè ........................ 57
47. Àëãåáðàè÷åñêàÿ ôîðìà êîìïëåêñíîãî
÷èñëà ....................................................... 58
48. Äåéñòâèÿ íàä êîìïëåêñíûìè ÷èñëàìè,
çàäàííûìè â àëãåáðàè÷åñêîé ôîðìå ............ 59
49. Ãåîìåòðè÷åñêîå èçîáðàæåíèå êîìïëåêñíûõ
÷èñåë. Òðèãîíîìåòðè÷åñêàÿ ôîðìà
êîìïëåêñíîãî ÷èñëà ................................... 61
50. Äåéñòâèÿ íàä êîìïëåêñíûìè ÷èñëàìè,
çàäàííûìè â òðèãîíîìåòðè÷åñêîé ôîðìå ..... 63
Ðàçäåë II. Âûðàæåíèÿ
§ 5. Îñíîâíûå ïîíÿòèÿ .................................... 68
51. Âèäû àëãåáðàè÷åñêèõ âûðàæåíèé ............... 68
52. Äîïóñòèìûå çíà÷åíèÿ ïåðåìåííûõ.
Îáëàñòü îïðåäåëåíèÿ àëãåáðàè÷åñêîãî
âûðàæåíèÿ ............................................... 69
53. Ïîíÿòèå òîæäåñòâåííîãî ïðåîáðàçîâàíèÿ
âûðàæåíèÿ. Òîæäåñòâî .............................. 70
§ 6. Öåëûå ðàöèîíàëüíûå âûðàæåíèÿ .............. 71
54. Îäíî÷ëåíû è îïåðàöèè íàä íèìè ................ 71
55. Ìíîãî÷ëåíû. Ïðèâåäåíèå ìíîãî÷ëåíîâ
ê ñòàíäàðòíîìó âèäó .................................. 73
56. Ôîðìóëû ñîêðàùåííîãî óìíîæåíèÿ ............ 75
57. Ðàçëîæåíèå ìíîãî÷ëåíîâ íà ìíîæèòåëè ....... 76
58. Ìíîãî÷ëåíû îò îäíîé ïåðåìåííîé ............... 79
59. Äåëåíèå ìíîãî÷ëåíîâ. Ñõåìà Ãîðíåðà.
Òåîðåìà Áåçó ............................................. 80
60. Ðàçëîæåíèå êâàäðàòíîãî òðåõ÷ëåíà
íà ëèíåéíûå ìíîæèòåëè ............................ 84
61. Ðàçëîæåíèå íà ìíîæèòåëè
äâó÷ëåíà .................................................. 85
62. Âîçâåäåíèå äâó÷ëåíà â íàòóðàëüíóþ
ñòåïåíü (ôîðìóëà áèíîìà Íüþòîíà) ............. 85
§ 7. Äðîáíûå ðàöèîíàëüíûå âûðàæåíèÿ .......... 86
63. Ðàöèîíàëüíàÿ äðîáü è åå îñíîâíîå
ñâîéñòâî ................................................... 86
64. Ñîêðàùåíèå ðàöèîíàëüíûõ äðîáåé .............. 88
65. Ïðèâåäåíèå ðàöèîíàëüíûõ äðîáåé
ê îáùåìó çíàìåíàòåëþ............................... 89
66. Ñëîæåíèå è âû÷èòàíèå ðàöèîíàëüíûõ
äðîáåé ....................................................... 90
67. Óìíîæåíèå è äåëåíèå ðàöèîíàëüíûõ
äðîáåé ...................................................... 91
68. Âîçâåäåíèå ðàöèîíàëüíîé äðîáè
â öåëóþ ñòåïåíü ......................................... 93
69. Ïðåîáðàçîâàíèå ðàöèîíàëüíûõ
âûðàæåíèé................................................ 94
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§ 8. Èððàöèîíàëüíûå âûðàæåíèÿ ..................... 96
70. Ïðîñòåéøèå ïðåîáðàçîâàíèÿ
àðèôìåòè÷åñêèõ êîðíåé (ðàäèêàëîâ) ............ 96
71. Òîæäåñòâî
.
2
aa =
.................................. 98
72. Ïðåîáðàçîâàíèå èððàöèîíàëüíûõ
âûðàæåíèé ................................................ 99
§ 9. Ïðåîáðàçîâàíèå âûðàæåíèé, ñîäåðæàùèõ
ïåðåìåííóþ ïîä çíàêîì ëîãàðèôìà............. 100
73. Ïîíÿòèå òðàíñöåíäåíòíîãî âûðàæåíèÿ. ...... 100
74. Îïðåäåëåíèå ëîãàðèôìà ïîëîæèòåëüíîãî
÷èñëà ïî äàííîìó îñíîâàíèþ .................... 101
75. Ñâîéñòâà ëîãàðèôìîâ ............................... 101
76. Ëîãàðèôìèðîâàíèå è ïîòåíöèðîâàíèå ........ 103
77. Äåñÿòè÷íûé ëîãàðèôì. Õàðàêòåðèñòèêà
è ìàíòèññà äåñÿòè÷íîãî ëîãàðèôìà .......... 104
§ 10. Ôîðìóëû òðèãîíîìåòðèè
è èõ èñïîëüçîâàíèå äëÿ ïðåîáðàçîâàíèÿ
òðèãîíîìåòðè÷åñêèõ âûðàæåíèé .............. 106
78. Òðèãîíîìåòðè÷åñêèå âûðàæåíèÿ ............... 106
79. Ôîðìóëû ñëîæåíèÿ è âû÷èòàíèÿ
àðãóìåíòîâ .............................................. 106
80. Ôîðìóëû ïðèâåäåíèÿ ............................... 108
81. Ñîîòíîøåíèÿ ìåæäó òðèãîíîìåòðè÷åñ-
êèìè ôóíêöèÿìè îäíîãî è òîãî æå
àðãóìåíòà ................................................ 109
82. Ôîðìóëû äâîéíîãî óãëà............................ 111
83. Ôîðìóëû ïîíèæåíèÿ ñòåïåíè ................... 112
84. Âûðàæåíèå sin t, cos t è tg t
÷åðåç ç ............................................... 114
85. Ïðåîáðàçîâàíèå ñóììû òðèãîíîìåòðè÷åñêèõ
ôóíêöèé â ïðîèçâåäåíèå .......................... 115
86. Ïðåîáðàçîâàíèå ïðîèçâåäåíèÿ
òðèãîíîìåòðè÷åñêèõ ôóíêöèé â ñóììó....... 116
87. Ïðåîáðàçîâàíèå âûðàæåíèÿ
a cos t + b sin t ê âèäó A sin (t + a) ............. 117
88. Ïðåîáðàçîâàíèå âûðàæåíèé, ñîäåðæàùèõ
îáðàòíûå òðèãîíîìåòðè÷åñêèå ôóíêöèè ..... 118
Ðàçäåë III. Ôóíêöèè è ãðàôèêè
§ 11. Ñâîéñòâà ôóíêöèé ................................. 120
89. Îïðåäåëåíèå ôóíêöèè .............................. 120
90. Àíàëèòè÷åñêîå çàäàíèå ôóíêöèè.............. 121
91. Òàáëè÷íîå çàäàíèå ôóíêöèè ..................... 122
92. Ãðàôè÷åñêîå çàäàíèå ôóíêöèè .................. 122
93. Ãðàôèê ôóíêöèè, çàäàííîé
àíàëèòè÷åñêè .......................................... 124
94. ×åòíûå è íå÷åòíûå ôóíêöèè .................... 125
95. Ãðàôèêè ÷åòíîé è íå÷åòíîé ôóíêöèé ........ 126
96. Ïåðèîäè÷åñêèå ôóíêöèè .......................... 128
97. Âîçðàñòàþùèå è óáûâàþùèå ôóíêöèè ....... 129
§ 12. Âèäû ôóíêöèé ............................................... 130
98. Ïîñòîÿííàÿ ôóíêöèÿ ............................... 130
99. Ïðÿìàÿ ïðîïîðöèîíàëüíîñòü ..................... 131
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§ 8. Èððàöèîíàëüíûå âûðàæåíèÿ ..................... 96
70. Ïðîñòåéøèå ïðåîáðàçîâàíèÿ
àðèôìåòè÷åñêèõ êîðíåé (ðàäèêàëîâ) ............ 96
71. Òîæäåñòâî
.
2
aa =
.................................. 98
72. Ïðåîáðàçîâàíèå èððàöèîíàëüíûõ
âûðàæåíèé ................................................ 99
§ 9. Ïðåîáðàçîâàíèå âûðàæåíèé, ñîäåðæàùèõ
ïåðåìåííóþ ïîä çíàêîì ëîãàðèôìà............. 100
73. Ïîíÿòèå òðàíñöåíäåíòíîãî âûðàæåíèÿ. ...... 100
74. Îïðåäåëåíèå ëîãàðèôìà ïîëîæèòåëüíîãî
÷èñëà ïî äàííîìó îñíîâàíèþ .................... 101
75. Ñâîéñòâà ëîãàðèôìîâ ............................... 101
76. Ëîãàðèôìèðîâàíèå è ïîòåíöèðîâàíèå ........ 103
77. Äåñÿòè÷íûé ëîãàðèôì. Õàðàêòåðèñòèêà
è ìàíòèññà äåñÿòè÷íîãî ëîãàðèôìà .......... 104
§ 10. Ôîðìóëû òðèãîíîìåòðèè
è èõ èñïîëüçîâàíèå äëÿ ïðåîáðàçîâàíèÿ
òðèãîíîìåòðè÷åñêèõ âûðàæåíèé .............. 106
78. Òðèãîíîìåòðè÷åñêèå âûðàæåíèÿ ............... 106
79. Ôîðìóëû ñëîæåíèÿ è âû÷èòàíèÿ
àðãóìåíòîâ .............................................. 106
80. Ôîðìóëû ïðèâåäåíèÿ ............................... 108
81. Ñîîòíîøåíèÿ ìåæäó òðèãîíîìåòðè÷åñ-
êèìè ôóíêöèÿìè îäíîãî è òîãî æå
àðãóìåíòà ................................................ 109
82. Ôîðìóëû äâîéíîãî óãëà............................ 111
83. Ôîðìóëû ïîíèæåíèÿ ñòåïåíè ................... 112
84. Âûðàæåíèå sin t, cos t è tg t
÷åðåç ç ............................................... 114
85. Ïðåîáðàçîâàíèå ñóììû òðèãîíîìåòðè÷åñêèõ
ôóíêöèé â ïðîèçâåäåíèå .......................... 115
86. Ïðåîáðàçîâàíèå ïðîèçâåäåíèÿ
òðèãîíîìåòðè÷åñêèõ ôóíêöèé â ñóììó....... 116
87. Ïðåîáðàçîâàíèå âûðàæåíèÿ
a cos t + b sin t ê âèäó A sin (t + a) ............. 117
88. Ïðåîáðàçîâàíèå âûðàæåíèé, ñîäåðæàùèõ
îáðàòíûå òðèãîíîìåòðè÷åñêèå ôóíêöèè ..... 118
Ðàçäåë III. Ôóíêöèè è ãðàôèêè
§ 11. Ñâîéñòâà ôóíêöèé ................................. 120
89. Îïðåäåëåíèå ôóíêöèè .............................. 120
90. Àíàëèòè÷åñêîå çàäàíèå ôóíêöèè.............. 121
91. Òàáëè÷íîå çàäàíèå ôóíêöèè ..................... 122
92. Ãðàôè÷åñêîå çàäàíèå ôóíêöèè .................. 122
93. Ãðàôèê ôóíêöèè, çàäàííîé
àíàëèòè÷åñêè .......................................... 124
94. ×åòíûå è íå÷åòíûå ôóíêöèè .................... 125
95. Ãðàôèêè ÷åòíîé è íå÷åòíîé ôóíêöèé ........ 126
96. Ïåðèîäè÷åñêèå ôóíêöèè .......................... 128
97. Âîçðàñòàþùèå è óáûâàþùèå ôóíêöèè ....... 129
§ 12. Âèäû ôóíêöèé ............................................... 130
98. Ïîñòîÿííàÿ ôóíêöèÿ ............................... 130
99. Ïðÿìàÿ ïðîïîðöèîíàëüíîñòü ..................... 131
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100. Ëèíåéíàÿ ôóíêöèÿ ................................. 131
101. Âçàèìíîå ðàñïîëîæåíèå ãðàôèêîâ
ëèíåéíûõ ôóíêöèé ................................ 133
102. Îáðàòíàÿ ïðîïîðöèîíàëüíîñòü ................. 134
103. Ôóíêöèÿ y = x
2
................................................
136
104. Ôóíêöèÿ y = x
3
................................................
136
105. Ñòåïåííàÿ ôóíêöèÿ ñ íàòóðàëüíûì
ïîêàçàòåëåì ........................................... 137
106. Ñòåïåííàÿ ôóíêöèÿ ñ öåëûì
îòðèöàòåëüíûì ïîêàçàòåëåì ................... 139
107. Ôóíêöèÿ y = ......................................... 140
108. Ôóíêöèÿ ............................................... 141
109. Ôóíêöèÿ ............................................... 142
110. Ñòåïåííàÿ ôóíêöèÿ ñ ïîëîæèòåëüíûì
äðîáíûì ïîêàçàòåëåì ............................ 142
111. Ñòåïåííàÿ ôóíêöèÿ ñ îòðèöàòåëüíûì
äðîáíûì ïîêàçàòåëåì ............................ 143
112. Ôóíêöèÿ y = [x] ..................................... 144
113. Ôóíêöèÿ y = {x} ..................................... 144
114. Ïîêàçàòåëüíàÿ ôóíêöèÿ ......................... 145
115. Îáðàòíàÿ ôóíêöèÿ.
Ãðàôèê îáðàòíîé ôóíêöèè ...................... 146
116. Ëîãàðèôìè÷åñêàÿ ôóíêöèÿ ..................... 150
117. ×èñëî å. Ôóíêöèÿ ó = å
õ
.
Ôóíêöèÿ ÿ ................................... 151
118. Îïðåäåëåíèå òðèãîíîìåòðè÷åñêèõ
ôóíêöèé ............................................... 153
119. Çíàêè òðèãîíîìåòðè÷åñêèõ ôóíêöèé
ïî ÷åòâåðòÿì ......................................... 155
120. Èññëåäîâàíèå òðèãîíîìåòðè÷åñêèõ
ôóíêöèé íà ÷åòíîñòü, íå÷åòíîñòü .............. 155
121. Ïåðèîäè÷íîñòü òðèãîíîìåòðè÷åñêèõ
ôóíêöèé ............................................... 156
122. Ñâîéñòâà è ãðàôèê ôóíêöèè y = sin x ...... 157
123. Ñâîéñòâà è ãðàôèê ôóíêöèè y = cos x ...... 158
124. Ñâîéñòâà è ãðàôèê ôóíêöèè y = tg x ........ 159
125. Ñâîéñòâà è ãðàôèê ôóíêöèè y = ctg x ...... 161
126. Ôóíêöèÿ y = arcsin x .............................. 161
127. Ôóíêöèÿ y = arccos x ............................. 163
128. Ôóíêöèè y = arctg x, y = arcctg x ............. 164
129. Àðêñèíóñ, àðêêîñèíóñ,
àðêòàíãåíñ è àðêêîòàíãåíñ ...................... 165
§ 13. Ïðåîáðàçîâàíèÿ ãðàôèêîâ ..................... 168
130. Ïîñòðîåíèå ãðàôèêà
ôóíêöèè y = mf (x) ............................... 168
131. Ãðàôèêè ôóíêöèé ó = àõ
2
, ó = àõ
3
.......... 169
132. Ïîñòðîåíèå ãðàôèêà ôóíêöèè
y = f (x a) + b ...................................... 171
133. Ãðàôèê êâàäðàòè÷íîé ôóíêöèè ............... 172
134. Ñïîñîáû ïîñòðîåíèÿ ãðàôèêà
êâàäðàòè÷íîé ôóíêöèè ........................... 174
135. Ïîñòðîåíèå ãðàôèêà
ôóíêöèè y = f (kx) ................................. 177
Öx
n
Öx
Öx
3
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100. Ëèíåéíàÿ ôóíêöèÿ ................................. 131
101. Âçàèìíîå ðàñïîëîæåíèå ãðàôèêîâ
ëèíåéíûõ ôóíêöèé ................................ 133
102. Îáðàòíàÿ ïðîïîðöèîíàëüíîñòü ................. 134
103. Ôóíêöèÿ y = x
2
................................................
136
104. Ôóíêöèÿ y = x
3
................................................
136
105. Ñòåïåííàÿ ôóíêöèÿ ñ íàòóðàëüíûì
ïîêàçàòåëåì ........................................... 137
106. Ñòåïåííàÿ ôóíêöèÿ ñ öåëûì
îòðèöàòåëüíûì ïîêàçàòåëåì ................... 139
107. Ôóíêöèÿ y = ......................................... 140
108. Ôóíêöèÿ ............................................... 141
109. Ôóíêöèÿ ............................................... 142
110. Ñòåïåííàÿ ôóíêöèÿ ñ ïîëîæèòåëüíûì
äðîáíûì ïîêàçàòåëåì ............................ 142
111. Ñòåïåííàÿ ôóíêöèÿ ñ îòðèöàòåëüíûì
äðîáíûì ïîêàçàòåëåì ............................ 143
112. Ôóíêöèÿ y = [x] ..................................... 144
113. Ôóíêöèÿ y = {x} ..................................... 144
114. Ïîêàçàòåëüíàÿ ôóíêöèÿ ......................... 145
115. Îáðàòíàÿ ôóíêöèÿ.
Ãðàôèê îáðàòíîé ôóíêöèè ...................... 146
116. Ëîãàðèôìè÷åñêàÿ ôóíêöèÿ ..................... 150
117. ×èñëî å. Ôóíêöèÿ ó = å
õ
.
Ôóíêöèÿ ÿ ................................... 151
118. Îïðåäåëåíèå òðèãîíîìåòðè÷åñêèõ
ôóíêöèé ............................................... 153
119. Çíàêè òðèãîíîìåòðè÷åñêèõ ôóíêöèé
ïî ÷åòâåðòÿì ......................................... 155
120. Èññëåäîâàíèå òðèãîíîìåòðè÷åñêèõ
ôóíêöèé íà ÷åòíîñòü, íå÷åòíîñòü .............. 155
121. Ïåðèîäè÷íîñòü òðèãîíîìåòðè÷åñêèõ
ôóíêöèé ............................................... 156
122. Ñâîéñòâà è ãðàôèê ôóíêöèè y = sin x ...... 157
123. Ñâîéñòâà è ãðàôèê ôóíêöèè y = cos x ...... 158
124. Ñâîéñòâà è ãðàôèê ôóíêöèè y = tg x ........ 159
125. Ñâîéñòâà è ãðàôèê ôóíêöèè y = ctg x ...... 161
126. Ôóíêöèÿ y = arcsin x .............................. 161
127. Ôóíêöèÿ y = arccos x ............................. 163
128. Ôóíêöèè y = arctg x, y = arcctg x ............. 164
129. Àðêñèíóñ, àðêêîñèíóñ,
àðêòàíãåíñ è àðêêîòàíãåíñ ...................... 165
§ 13. Ïðåîáðàçîâàíèÿ ãðàôèêîâ ..................... 168
130. Ïîñòðîåíèå ãðàôèêà
ôóíêöèè y = mf (x) ............................... 168
131. Ãðàôèêè ôóíêöèé ó = àõ
2
, ó = àõ
3
.......... 169
132. Ïîñòðîåíèå ãðàôèêà ôóíêöèè
y = f (x a) + b ...................................... 171
133. Ãðàôèê êâàäðàòè÷íîé ôóíêöèè ............... 172
134. Ñïîñîáû ïîñòðîåíèÿ ãðàôèêà
êâàäðàòè÷íîé ôóíêöèè ........................... 174
135. Ïîñòðîåíèå ãðàôèêà
ôóíêöèè y = f (kx) ................................. 177
Öx
n
Öx
Öx
3
y = ln x