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Äàþ÷è c ð³çí³ çíà÷åííÿ ³ ùîðàç áóäóþ÷è ë³í³þ ç çàäàíèì<br />
ð³âíåì, ìè îäåðæèìî ñ³ìåéñòâî ë³í³é ð³âíÿ. Öå ñ³ìåéñòâî<br />
íàî÷íî îïèñóº ôóíêö³þ z = f(x, y). Íàïðèêëàä, ñ³ìåéñòâîì<br />
ë³í³é ð³âíÿ ïàðàáîëî¿äà îáåðòàííÿ áóäå ñ³ìåéñòâî ê³ë<br />
(ðèñ. 10.5).<br />
Ðèñ. 10.6<br />
Ðèñ. 10.5<br />
˳í³ÿìè ð³âíÿ ïîçíà÷àþòü ãëèáèíó ìîð³â ³ âèñîòó ã³ð íà<br />
ãåîãðàô³÷íèõ êàðòàõ. Ñèíîïòèêè ïóáë³êóþòü êàðòè ç³ çîáðàæåííÿì<br />
³çîòåðì òà ³çîáàð, ÿê³ â³äïîâ³äíî áóäóòü ë³í³ÿìè<br />
ð³âíÿ òåìïåðàòóðè òà òèñêó.  åêîíîì³ö³ ïðèêëàäîì<br />
ë³í³é ð³âíÿ ñëóæàòü ³çîêâàíòè, öå ë³í³¿ âçäîâæ ÿêèõ âèðîáíè÷à<br />
ôóíêö³ÿ äîð³âíþº êîíñòàíò³.<br />
Ïðè äîñë³äæåíí³ åêîëîã³÷íèõ ïðîáëåì òåæ ââîäÿòü ïîíÿòòÿ<br />
ë³í³¿ ð³âíÿ.<br />
Ïðèêëàä 10.1.8. ³äçíà÷àþ÷è â³ä öåíòðó ìóðàøíèêà òî-<br />
÷êè ç îäí³º¿ ³ ò³ºþ æå ù³ëüí³ñòþ ìóðàõ (ê³ëüê³ñòü ìóðàõ,<br />
ùî ïðèõîäÿòüñÿ íà îäèíèöþ ïëîù³), îäåðæèìî ë³í³¿ ð³âíÿ<br />
ïîçà ìóðàøíèêîì (ðèñ. 10.6).<br />
Ö³ ë³í³¿ áóäóòü â³äð³çíÿòèñÿ â³ä ê³ë, ÿêùî ïðîñò³ð íàâêîëî<br />
ìóðàøíèêà íåîäíîð³äíèé çà ðîçïîä³ëîì êîðìó äëÿ ìóðàõ.<br />
Àíàëîã³÷í³ ë³í³¿ îïèñóþòü ñòðóêòóðó òâàðèííèõ ³ ðîñëèííèõ<br />
àðåàë³â.<br />
ÂÏÐÀÂÈ<br />
10.1. Çíàéòè îáëàñòü âèçíà÷åííÿ ôóíêö³¿<br />
2 2<br />
( )<br />
z= ln 1 −x − y .<br />
10.2. Çíàéòè îáëàñòü âèçíà÷åííÿ ôóíêö³¿<br />
2 2<br />
( )<br />
z= arcsin x + y − 3 .<br />
10.3. Çîáðàçèòè ãðàô³÷íî ôóíêö³þ<br />
2 2<br />
z = c 1 − x − y .<br />
2 2<br />
a b<br />
10.4. Çîáðàçèòè ãðàô³÷íî ôóíêö³þ<br />
2 2<br />
x y<br />
z = +<br />
2 2<br />
.<br />
a b<br />
10.5. Ë³í³¿ ð³âíÿ ù³ëüíîñò³ ìóðàõ òàê³:<br />
x y<br />
16 25<br />
2 2<br />
2<br />
+ = c .<br />
Óêàçàòè íàïðÿìîê ì³ñöü, äå º íàéá³ëüøà ê³ëüê³ñòü æèâèëüíèõ<br />
ðå÷îâèí äëÿ ìóðàõ.<br />
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