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7.9. Ïîõ³äí³ âèùèõ ïîðÿäê³â ............................ 221<br />
7.9.1. Îçíà÷åííÿ .................................................. 221<br />
7.9.2. Ïðèêëàäè .................................................. 221<br />
7.10. Äèôåðåíö³àë ôóíêö³¿ .................................. 225<br />
7.10.1. Îçíà÷åííÿ .................................................. 225<br />
7.10.2. ²íâàð³àíòí³ñòü ôîðìè ïåðøîãî<br />
äèôåðåíö³àëà .............................................. 226<br />
7.10.3. Çàñòîñóâàííÿ äèôåðåíö³àëà äëÿ íàáëèæåíèõ<br />
îá÷èñëåíü çíà÷åíü ôóíêö³é............. 226<br />
7.10.4. Äèôåðåíö³àëè âèùèõ ïîðÿäê³â ................... 227<br />
7.11. Çàñòîñóâàííÿ ïîõ³äíî¿ â åêîíîì³ö³ .............. 227<br />
7.11.1. Äåÿê³ òåðì³íè â åêîíîì³ö³, ÿê³ ïîâ’ÿçàí³<br />
ç ïîíÿòòÿì ïîõ³äíî¿ ............................. 227<br />
7.11.2. Ïîíÿòòÿ åëàñòè÷íîñò³ ôóíêö³¿ .................... 228<br />
7.12. Êëàñè÷í³ çàñòîñóâàííÿ ïîõ³äíî¿ â ìàòåìàòèö³<br />
òà åêîíîì³ö³ ................................... 229<br />
7.12.1. Çàñòîñóâàííÿ ïîõ³äíî¿ â ìàòåìàòèö³ ........... 229<br />
7.12.2. Çàñòîñóâàííÿ ïîõ³äíî¿ â åêîíîì³ö³ ............. 232<br />
7.13. Åêñòðåìóì ôóíêö³¿ ³ îñíîâí³ òåîðåìè<br />
äèôåðåíö³àëüíîãî ÷èñëåííÿ ........................ 236<br />
7.13.1. Îçíà÷åííÿ åêñòðåìóìó ôóíêö³¿ ................... 236<br />
7.13.2. Îñíîâí³ òåîðåìè äèôåðåíö³àëüíîãî<br />
÷èñëåííÿ .................................................... 237<br />
7.14. Ðîçêðèòòÿ íåâèçíà÷åíîñòåé ......................... 241<br />
7.14.1. Ïðàâèëî Ëîï³òàëÿ ...................................... 241<br />
7.14.2. Çàñòîñóâàííÿ ïðàâèëà Ëîï³òàëÿ<br />
äëÿ ðîçêðèòòÿ íåâèçíà÷åíîñòåé<br />
0/0 òà ∞/∞ ................................................ 241<br />
7.14.3. Ðîçêðèòòÿ íåâèçíà÷åíîñòåé 0 ⋅∞<br />
òà ∞ –∞ ..................................................... 243<br />
7.14.4. Ðîçêðèòòÿ íåâèçíà÷åíîñòåé 1 ∞ , ∞ 0 òà 0 0 ...... 244<br />
Âïðàâè .................................................................. 246<br />
7.15. Ôîðìóëà Òåéëîðà ....................................... 246<br />
7.15.1. Ôîðìóëà Òåéëîðà äëÿ ìíîãî÷ëåíà .............. 246<br />
7.15.2. Ôîðìóëà á³íîìà Íüþòîíà ........................... 248<br />
7.15.3. Ôîðìóëà Òåéëîðà äëÿ ôóíêö³¿ ................... 249<br />
7.16. Íåîáõ³äí³ òà äîñòàòí³ óìîâè ³ñíóâàííÿ<br />
åêñòðåìóìó ôóíêö³¿ .................................... 252<br />
7.16.1. Íåîáõ³äíà óìîâà ³ñíóâàííÿ åêñòðåìóìó<br />
ôóíêö³¿ ...................................................... 252<br />
7.16.2. Äîñòàòí³ óìîâè åêñòðåìóìó ôóíêö³¿ ........... 253<br />
7.17. Çàñòîñóâàííÿ äèôåðåíö³àëüíîãî ÷èñëåííÿ<br />
äëÿ äîñë³äæåííÿ ôóíêö³¿.......................... 255<br />
7.17.1. Âèçíà÷åííÿ ïðîì³æê³â ìîíîòîííîñò³<br />
ôóíêö³¿ ...................................................... 255<br />
7.17.2. Çíàõîäæåííÿ íàéá³ëüøîãî ³ íàéìåíøîãî<br />
çíà÷åííÿ íåïåðåðâíî¿ ôóíêö³¿ .................... 255<br />
7.17.3. Îïóêëîñò³ êðèâî¿ ³ òî÷êè ïåðåãèíó ............ 255<br />
7.18. Àcèìïòîòè ................................................. 256<br />
7.18.1. Îçíà÷åííÿ .................................................. 256<br />
7.18.2. Âåðòèêàëüí³ àñèìïòîòè............................... 256<br />
7.18.3. Íåâåðòèêàëüí³ àñèìïòîòè ........................... 256<br />
7.19. Çàãàëüíà ñõåìà äîñë³äæåííÿ ôóíêö³¿<br />
³ ïîáóäîâà ¿¿ ãðàô³êà ................................. 257<br />
ÒÅÌÀ 8. ÍÅÂÈÇÍÀ×ÅÍÈÉ ²ÍÒÅÃÐÀË ² ÉÎÃÎ ×ÈÑËÅÍÍß<br />
8.1. Ïåðâ³ñíà ³ íåâèçíà÷åíèé ³íòåãðàë ............... 259<br />
8.1.1. Ïðîáëåìí³ çàäà÷³ ....................................... 259<br />
8.2. Âëàñòèâîñò³ íåâèçíà÷åíèõ ³íòåãðàë³â<br />
òà ¿õíÿ îñíîâíà òàáëèöÿ ............................ 264<br />
8.2.1. Âëàñòèâîñò³ ³ ¿õ äîâåäåííÿ ......................... 264<br />
8.2.2. Îñíîâíà òàáëèöÿ íåâèçíà÷åíèõ<br />
³íòåãðàë³â .................................................. 266<br />
8.3. Îñíîâí³ ìåòîäè ³íòåãðóâàííÿ ...................... 267<br />
8.3.1. Ìåòîä áåçïîñåðåäíüîãî ³íòåãðóâàííÿ ........... 267<br />
Âïðàâè .................................................................. 267<br />
8.3.2. Ìåòîä ï³äñòàíîâêè ..................................... 268<br />
Âïðàâè .................................................................. 271<br />
8.3.3. Ìåòîä ³íòåãðóâàííÿ ÷àñòèíàìè ................... 272<br />
Âïðàâè .................................................................. 274<br />
8.4. ²íòåãðóâàííÿ ðàö³îíàëüíèõ ôóíêö³é ........... 275<br />
8.4.1. Îñíîâí³ ïîíÿòòÿ ïðî ðàö³îíàëüí³<br />
ôóíêö³¿ ...................................................... 275<br />
8.4.2. ²íòåãðóâàííÿ ìíîãî÷ëåí³â ........................... 275<br />
8.4.3. ²íòåãðóâàííÿ äðîáîâî-ðàö³îíàëüíèõ<br />
ôóíêö³é ..................................................... 275<br />
Âïðàâè .................................................................. 279<br />
8 9
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