Реферат: Шпаргалки по высшей математике
до<img src="/cache/referats/8147/image002.gif" v:shapes="_x0000_i1025">
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Интегрированиепо частям
<img src="/cache/referats/8147/image070.gif" v:shapes="_x0000_i1059">
Простейшиедроби
<img src="/cache/referats/8147/image072.gif" v:shapes="_x0000_i1060">
<img src="/cache/referats/8147/image074.gif" v:shapes="_x0000_i1061">
Для<img src="/cache/referats/8147/image076.gif" v:shapes="_x0000_i1062">
<img src="/cache/referats/8147/image078.gif" v:shapes="_x0000_i1063">
Интегрированиетригонометрических выражений:
1)<span Times New Roman"">
<img src="/cache/referats/8147/image080.gif" v:shapes="_x0000_i1064"><img src="/cache/referats/8147/image082.gif" v:shapes="_x0000_i1065"><img src="/cache/referats/8147/image084.gif" v:shapes="_x0000_i1066">; <img src="/cache/referats/8147/image086.gif" v:shapes="_x0000_i1067">
2)<span Times New Roman"">
Обе степени четные (sinи cos)<img src="/cache/referats/8147/image088.gif" v:shapes="_x0000_i1068"><img src="/cache/referats/8147/image090.gif" v:shapes="_x0000_i1069">
<img src="/cache/referats/8147/image092.gif" v:shapes="_x0000_i1070">; <img src="/cache/referats/8147/image094.gif" v:shapes="_x0000_i1071">
Одна– нечетная:
<img src="/cache/referats/8147/image096.gif" v:shapes="_x0000_i1072">
<img src="/cache/referats/8147/image098.gif" v:shapes="_x0000_i1073">
<img src="/cache/referats/8147/image100.gif" v:shapes="_x0000_i1074">; <img src="/cache/referats/8147/image102.gif" v:shapes="_x0000_i1075">
3)<span Times New Roman"">
<img src="/cache/referats/8147/image104.gif" v:shapes="_x0000_i1076"><img src="/cache/referats/8147/image106.gif" v:shapes="_x0000_i1077">
<img src="/cache/referats/8147/image108.gif" v:shapes="_x0000_i1078">
4)<span Times New Roman"">
Для <img src="/cache/referats/8147/image110.gif" v:shapes="_x0000_i1079"><img src="/cache/referats/8147/image112.gif" v:shapes="_x0000_i1080">
Иррациональныефункции(дроби)
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<span Times New Roman",«serif»;mso-fareast-font-family:«Times New Roman»;mso-ansi-language: EN-US;mso-fareast-language:RU;mso-bidi-language:AR-SA"><img src="/cache/referats/8147/image138.gif" v:shapes="_x0000_i1093">
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<span Times New Roman",«serif»; mso-fareast-font-family:«Times New Roman»;mso-ansi-language:RU;mso-fareast-language: RU;mso-bidi-language:AR-SA"><img src="/cache/referats/8147/image227.gif" v:shapes="_x0000_i1139">
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<span Times New Roman",«serif»; mso-fareast-font-family:«Times New Roman»;mso-ansi-language:RU;mso-fareast-language: RU;mso-bidi-language:AR-SA">Ряд– сума <img src="/cache/referats/8147/image313.gif" v:shapes="_x0000_i1183">an– общий член ряда.
Частичная сумма<img src="/cache/referats/8147/image315.gif" v:shapes="_x0000_i1184">
Рядназывается сходящимся, если существует <img src="/cache/referats/8147/image317.gif" v:shapes="_x0000_i1185">
Рядназывается расходящимся, если не существует <img src="/cache/referats/8147/image319.gif" v:shapes="_x0000_i1186">
Сходимость/расходимостьрядов:
Если<img src="/cache/referats/8147/image321.gif" v:shapes="_x0000_i1187"> ряд расходится.
Ряды сположительными членами.
<img src="/cache/referats/8147/image323.gif" v:shapes="_x0000_i1188">
<img src="/cache/referats/8147/image325.gif" v:shapes="_x0000_i1189">
<img src="/cache/referats/8147/image327.gif" v:shapes="_x0000_i1190">
<img src="/cache/referats/8147/image329.gif" v:shapes="_x0000_i1191">
Если сходится (2) <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">Þ
сходится (1)Если расходится (1) <span Times New Roman";mso-hansi-font-family: «Times New Roman»;mso-char-type:symbol;mso-symbol-font-family:Symbol">Þ
расходится (2)ПризнакДаламбера
<img src="/cache/referats/8147/image331.gif" v:shapes="_x0000_i1192">
Ряд сходится
Ряд расходится
Нужны доп. исследования
Интегральныйпризнак Коши
<img src="/cache/referats/8147/image333.gif" v:shapes="_x0000_i1193"> определена при <img src="/cache/referats/8147/image335.gif" v:shapes="_x0000_i1194"><img src="/cache/referats/8147/image337.gif" v:shapes="_x0000_i1195"> монотонно убывает при <img src="/cache/referats/8147/image339.gif" v:shapes="_x0000_i1196">
<img src="/cache/referats/8147/image341.gif" v:shapes="_x0000_i1197">(1) и (2) сходятся/расходятся одновременно.
Обобщенныегармонические ряды
<img src="/cache/referats/8147/image343.gif" v:shapes="_x0000_i1198">
Сходитсяпри <img src="/cache/referats/8147/image345.gif" v:shapes="_x0000_i1199">
Расходитсяпри <img src="/cache/referats/8147/image347.gif" v:shapes="_x0000_i1200">
Предельнаятеорема сравнения.
<img src="/cache/referats/8147/image349.gif" v:shapes="_x0000_i1201"> ряды (1) и (2)сходятся/расходятся одновременно.
Рядыс произвольными членами.
<img src="/cache/referats/8147/image351.gif" v:shapes="_x0000_i1202">
Если (2) сходятся: (1) – абсолютно сходящийся
(2) расход., (1) – сход.: (1) – условно сходящийся
Теоремаоб абсолютной сходимости:
Если(2) – сходится, то (1) – тоже сходится (обратное неверно)
Знакочередующиеся ряды.
<img src="/cache/referats/8147/image353.gif" v:shapes="_x0000_i1203">
Признак Лейбница (только для (*))
(*) сходится, если:
1)<span Times New Roman"">
<img src="/cache/referats/8147/image355.gif" v:shapes="_x0000_i1204">2)<span Times New Roman"">
<img src="/cache/referats/8147/image357.gif" v:shapes="_x0000_i1205">