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5.1.4. Íåñê³í÷åííî âåëèê³ òà ìàë³ ïîñë³äîâíîñò³ .... 136<br />
5.1.5. Îñíîâí³ òåîðåìè ïðî íåñê³í÷åííî ìàë³<br />
ïîñë³äîâíîñò³ ............................................... 140<br />
5.2. Ãðàíèöÿ ÷èñëîâî¿ ïîñë³äîâíîñò³.................... 142<br />
5.2.1. Ïîíÿòòÿ çá³æíî¿ ïîñë³äîâíîñò³ ..................... 142<br />
5.2.2. Îñíîâí³ òåîðåìè ïðî ãðàíèö³ ....................... 143<br />
5.2.3. Ãðàíè÷íèé ïåðåõ³ä â íåð³âíîñòÿõ................. 145<br />
5.2.4. Ãðàíèö³ ìîíîòîííèõ ïîñë³äîâíîñòåé ............. 147<br />
5.2.5. ×èñëî å ....................................................... 149<br />
5.2.6. Ïîíÿòòÿ ïðî åêñïîíåíö³àëüíó ôóíêö³þ<br />
òà íàòóðàëüíèé ëîãàðèôì ............................ 151<br />
Âïðàâè .................................................................. 151<br />
ÒÅÌÀ 6. ÃÐÀÍÈÖß ÔÓÍÊÖ²¯<br />
6.1. Ôóíêö³ÿ îäí³º¿ çì³ííî¿ ................................ 154<br />
6.1.1. Îçíà÷åííÿ ................................................... 154<br />
6.1.2. Ñïîñîáè çàäàííÿ ôóíêö³¿ ............................. 155<br />
6.1.3. Åëåìåíòàðí³ ôóíêö³¿ òà ¿õ êëàñèô³êàö³ÿ ...... 161<br />
6.1.4. Äåÿê³ âàæëèâ³ êëàñè ôóíêö³é ..................... 162<br />
6.1.5. Ïîáóäîâà ãðàô³ê³â ôóíêö³é ìåòîäîì<br />
ïåðåòâîðåíü.................................................. 163<br />
Âïðàâè .................................................................. 164<br />
6.1.6. Äåÿê³ ôóíêö³îíàëüí³ çàëåæíîñò³,<br />
ÿê³ âèêîðèñòîâóþòüñÿ â åêîíîì³ö³ ............... 165<br />
Âïðàâè .................................................................. 168<br />
6.2. Ïîíÿòòÿ ïðî ãðàíèöþ ôóíêö³¿ ..................... 169<br />
6.2.1. Ïðîáëåìí³ ïðèêëàäè ³ îçíà÷åííÿ ................. 169<br />
6.2.2. Ïîð³âíÿííÿ íåñê³í÷åííî ìàëèõ âåëè÷èí....... 177<br />
6.2.3. Äâ³ âàæëèâ³ ãðàíèö³ .................................... 178<br />
6.3. Íåïåðåðâí³ñòü ôóíêö³¿.................................. 182<br />
6.3.1. Íåïåðåðâí³ñòü ôóíêö³¿ â òî÷ö³..................... 182<br />
6.3.2. Àðèôìåòè÷í³ îïåðàö³¿ íàä íåïåðåðâíèìè<br />
ôóíêö³ÿìè ................................................... 184<br />
6.3.3. Òî÷êè ðîçðèâó ôóíêö³¿ òà ¿õ êëàñèô³êàö³ÿ<br />
.............................................................. 184<br />
6.3.4. Ïîíÿòòÿ ïðî îäíîñòîðîííþ íåïåðåðâí³ñòü..... 186<br />
6.3.5. Ëîêàëüí³ âëàñòèâîñò³ íåïåðåðâíèõ ôóíêö³é .. 187<br />
6.3.6. Ãëîáàëüí³ âëàñòèâîñò³ íåïåðåðâíèõ ôóíêö³é,<br />
ÿê³ çàäàí³ íà ñåãìåíò³........................... 188<br />
6.3.7. Íåïåðåðâí³ ³ ðîçðèâí³ ôóíêö³¿ â ïðèðîä³<br />
òà åêîíîì³ö³ ................................................ 189<br />
6.3.8. Äåÿê³ âàæëèâ³ ãðàíèö³ ................................ 190<br />
Âïðàâè .................................................................. 193<br />
ÒÅÌÀ 7. ÄÈÔÅÐÅÍÖ²ÀËÜÍÅ ×ÈÑËÅÍÍß ÔÓÍÊÖ²¯ ÎÄͲª¯<br />
Ç̲ÍÍί<br />
7.1. Çàäà÷³, ÿê³ ïðèâîäÿòü äî ïîíÿòòÿ ïîõ³äíî¿ ... 197<br />
7.1.1. Çàäà÷à ïðî äîòè÷íó äî êðèâî¿ ..................... 197<br />
7.1.2. Çàäà÷à ïðî øâèäê³ñòü ðóõó ......................... 199<br />
7.1.3. Çàäà÷à ïðî ïðîäóêòèâí³ñòü ïðàö³ ................. 199<br />
7.2. Ïîõ³äíà ....................................................... 200<br />
7.2.1. Àáñòðàêòíå îçíà÷åííÿ ïîõ³äíî¿ .................... 200<br />
7.2.2. Ãåîìåòðè÷íèé çì³ñò ïîõ³äíî¿........................ 201<br />
7.2.3. Ìåõàí³÷íèé çì³ñò ïîõ³äíî¿ ........................... 201<br />
7.2.4. Åêîíîì³÷íèé çì³ñò ïîõ³äíî¿ ......................... 201<br />
7.3. Çàëåæí³ñòü ì³æ íåïåðåâí³ñòþ ³ äèôåðåíö³éîâí³ñòþ<br />
ôóíêö³¿ ...................................... 202<br />
7.4. Ïîõ³äí³ åëåìåíòàðíèõ ôóíêö³é .................... 205<br />
7.4.1. Ïîõ³äíà ñòàëî¿ ôóíêö³¿<br />
y = f(x) = C = const, x = (a, b) ........................ 205<br />
7.4.2. Ïîõ³äíà ëîãàðèôì³÷íî¿ ôóíêö³¿<br />
y = log a x, a > 0, a ≠ 1, x∈ (0, ∞)........................ 205<br />
7.4.3. Ïîõ³äíà ïîêàçíèêîâî¿ ôóíêö³¿ y = a x ,<br />
x ∈ R, a > 0, a ≠ 1 .......................................... 206<br />
7.4.4. Ïîõ³äíà ñòåïåíåâî¿ ôóíêö³¿ y = x α ................ 207<br />
7.4.5. Ïîõ³äíà ôóíêö³¿ y = sin x, x∈R ..................... 208<br />
7.4.6. Ïîõ³äíà ôóíêö³¿ y = cos x, x∈R .................... 208<br />
7.5. Ïîõ³äíà îáåðíåíî¿ ôóíêö³¿ ........................... 209<br />
7.5.1. Ïîõ³äí³ îáåðíåíèõ òðèãîíîìåòðè÷íèõ<br />
ôóíêö³é ....................................................... 210<br />
7.6. Îñíîâí³ ïðàâèëà äèôåðåíö³þâàííÿ ôóíêö³é<br />
.............................................................. 211<br />
7.7. Ïðèêëàäè çàñòîñóâàííÿ îñíîâíèõ ïðàâèë<br />
äèôåðåíöþâàííÿ ôóíêö³é ............................. 213<br />
7.8. Ïîõ³äíà ñêëàäåíî¿ ôóíêö³¿ ........................... 214<br />
7.8.1. Òåîðåìà (ïðî ïîõ³äíó ñêëàäåíî¿ ôóíêö³¿) ..... 214<br />
7.8.2. Òàáëèöÿ ïîõ³äíèõ ñêëàäåíèõ ôóíêö³é .......... 215<br />
Âïðàâè .................................................................. 219<br />
6 7
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