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ЛЕКЦІЇ ² ВПРАВИ

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arccos a Àðêêîñèíóñ a<br />

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a v<br />

Äîâæèíà âåêòîðà a r<br />

v<br />

( ab ,<br />

) Ñêàëÿðíèé äîáóòîê<br />

v v r r<br />

⎡<br />

⎣ab , ⎤<br />

⎦<br />

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b Âåêòîðíèé äîáóòîê<br />

M(x, y) Òî÷êà M ç àáñöèñîþ x é îðäèíàòîþ y<br />

ρ(M 1 , M 2 ) ³äñòàíü ì³æ òî÷êàìè M 1 ³ M 2<br />

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Ìíîæèíà íàòóðàëüíèõ ÷èñåë<br />

Ζ<br />

Ìíîæèíà ö³ëèõ ÷èñåë<br />

Q<br />

Ìíîæèíà ðàö³îíàëüíèõ ÷èñåë<br />

R<br />

Ìíîæèíà ä³éñíèõ ÷èñåë<br />

£ Ìíîæèíà êîìïëåêñíèõ ÷èñåë<br />

Ïðîì³æîê<br />

[a, b] Çàêðèòèé ïðîì³æîê (ñåãìåíò): òî÷êè (÷èñëà)<br />

a ³ b íàëåæàòü ïðîì³æêó<br />

(a, b], [a, b) ϳââ³äêðèò³ ïðîì³æêè: (ï³â³íòåðâàë, ï³âñåãìåíò)<br />

òî÷êà a íå íàëåæèòü ïðîì³æêó, òî÷êà<br />

b íàëåæèòü ïðîì³æêó; â³äïîâ³äíî òî÷êà a<br />

íàëåæèòü, à òî÷êà b íå íàëåæèòü ïðîì³æêó<br />

(a, b), ]a, b[ ³äêðèòèé ïðîì³æîê (³íòåðâàë): òî÷êè a ³ b<br />

íå íàëåæàòü ïðîì³æêó<br />

i<br />

Óÿâíà îäèíèöÿ<br />

z, z Êîìïëåêñí³ ñïðÿæåí³ ÷èñëà<br />

Re z ijéñíà ÷àñòèíà êîìïëåêñíîãî ÷èñëà z<br />

Im z Óÿâíà ÷àñòèíà êîìïëåêñíîãî ÷èñëà z<br />

z<br />

Ìîäóëü êîìïëåêñíîãî ÷èñëà z<br />

Arg z Àðãóìåíò êîìïëåêñíîãî ÷èñëà z<br />

n! Äîáóòîê 1×2×3×...×n (÷èòàþòü n ôàêòîð³àë)<br />

P n<br />

×èñëî ïåðåñòàíîâîê ç n åëåìåíò³â<br />

m<br />

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×èñëî ñïîëó÷åíü ç n åëåìåíò³â ïî m åëåìåíò³â<br />

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×èñëî ðîçì³ùåíü ç n åëåìåíò³â ïî m åëåìåíò³â<br />

⎛<br />

ab ,<br />

⎞<br />

⎜ ⎟<br />

⎝ ⎠<br />

Êóò ì³æ âåêòîðàìè a ³ b<br />

∠<br />

Êóò<br />

·ABC Âåëè÷èíà êóòà ABC<br />

|| Ïàðàëåëüí³ñòü<br />

⊥<br />

Ïåðïåíäèêóëÿðí³ñòü<br />

∠(a, α) Êóò ì³æ ïðÿìîþ a ³ ïëîùèíîþ α<br />

∪ACB Äóãà ç ê³íöÿìè A ³ B<br />

Êóòîâà âåëè÷èíà äóãè ACB<br />

lim<br />

Ãðàíèöÿ<br />

o(α)<br />

ïðè α → 0 º âåëè÷èíà, ÿêà ïðÿìóº äî íóëÿ<br />

øâèäøå, í³æ α<br />

∆x<br />

Ïðèð³ñò àðãóìåíòó x<br />

∆y<br />

Ïðèð³ñò ôóíêö³¿ y<br />

(x – δ, x + δ) δ–îê³ë òî÷êè x<br />

f¢ ( x), df<br />

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Ïåðøà ïîõ³äíà ôóíêö³¿ f(x)<br />

n<br />

( n)<br />

df<br />

f ( x)<br />

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d n y<br />

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f<br />

z¢ x, f¢ x,<br />

×àñòèííà ïîõ³äíà ôóíêö³¿ z = f(x, y) ïî x<br />

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z¢¢ xy, f¢¢<br />

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ò<br />

b<br />

ò<br />

a<br />

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n=<br />

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Çì³øàíà ïîõ³äíà ôóíêö³¿ z = f(x, y) ïî x òà<br />

ó<br />

Íåâèçíà÷åíèé ³íòåãðàë<br />

Âèçíà÷åíèé ³íòåãðàë<br />

×èñëîâèé ðÿä<br />

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