- Page 1 and 2:
̲ͲÑÒÅÐÑÒÂÎ ÎѲÒ
- Page 3 and 4:
2.4. Ðàíã ìàòðèö³ ......
- Page 5 and 6:
7.9. Ïîõ³äí³ âèùèõ ïî
- Page 7 and 8:
10.2. Ãðàíèöÿ ³ íåïåð
- Page 9 and 10:
Ïåðåäìîâà Ç óñ³õ ñî
- Page 11 and 12:
äåòüñÿ” âèêîðèñòî
- Page 13 and 14:
1 îòðèìàºìî äð³á m = 2
- Page 15 and 16:
1.2.7. Ìîäóëü ä³éñíîã
- Page 17 and 18:
Òåìà 2 Îñíîâè àëãåá
- Page 19 and 20:
Öÿ ñèñòåìà ð³âíÿíü
- Page 21 and 22:
2 0 . Ó ÿêîñò³ åëåìåí
- Page 23 and 24:
Äîâ³ëüíèé åëåìåíò
- Page 25 and 26:
Ïðèêëàä 2.2.2. Çíàéòè
- Page 27 and 28:
a a ... a a ... a a a ... a a ... a
- Page 29 and 30:
Òîä³ a 12 12 ∆ 1 =∆+ m =∆
- Page 31 and 32:
Äâ³ ìàòðèö³ À ³ Â íà
- Page 33 and 34:
3 0 . Îá÷èñëèòè àëãåá
- Page 35 and 36:
ÒÅÌÀ 3 ÑÈÑÒÅÌÈ Ë²Í²
- Page 37 and 38:
Ïðè ðîçâ’ÿçàíí³ ñè
- Page 39 and 40: äå æa11 a12 ... a ö 1n a21 a22
- Page 41 and 42: Ðîçâ’ÿçàííÿ. Øëÿõî
- Page 43 and 44: 3.3. Êîðèñòóþ÷èñü ïð
- Page 45 and 46: Äëÿ äàíî¿ òî÷êè Ì â
- Page 47 and 48: Îòæå, êîîðäèíàòè òî
- Page 49 and 50: ìèì îáìåæåííÿì, îáó
- Page 51 and 52: Ïðèêëàä 4.2.6. Ñêëàñò
- Page 53 and 54: Ïðèêëàä 4.2.14. Çíàéòè
- Page 55 and 56: ð³âíÿííÿìè ïåðøîãî
- Page 57 and 58: ßêùî k çàäàíå ÷èñëî,
- Page 59 and 60: 3) ∆ =0 ³ ∆ x = 0, ∆ y = 0.
- Page 61 and 62: ÿêèé íàðîäèâñÿ â ëþ
- Page 63 and 64: º àíàë³òè÷íå ð³âíÿ
- Page 65 and 66: 4.5. ÏÎÍßÒÒß ÏÐΠвÂÍ
- Page 67 and 68: Ç ðîçãëÿíóòîãî ïðè
- Page 69 and 70: ⎧1 ⎫ Ïðèêëàä 5.1.10. Ï
- Page 71 and 72: 5.1.5. Îñíîâí³ òåîðåì
- Page 73 and 74: Îòðèìàëè, ùî ð³çíèö
- Page 75 and 76:  òàê³é çàãàëüí³é ï
- Page 77 and 78: n n 1 ⎛⎛1+ 5⎞ ⎛1− 5⎞
- Page 79 and 80: 1. Àíàë³òè÷íèé ñïîñ
- Page 81 and 82: òâ³, ïðè òåõí³÷íèõ
- Page 83 and 84: 4. Äëÿ ïîáóäîâè ãðàô
- Page 85 and 86: Ðîçâ’ÿçàííÿ. Íåõàé
- Page 87 and 88: Öÿ ôóíêö³ÿ ÿâëÿº ñî
- Page 89: Çã³äíî ç îçíà÷åííÿ
- Page 93 and 94: Îçíà÷åííÿ 6.3.5 Ôóíêö
- Page 95 and 96: 6.3.6. Ãëîáàëüí³ âëàñ
- Page 97 and 98: Ñïðàâåäëèâ³ñòü ôîð
- Page 99 and 100: 6.23. Îá÷èñëèòè ãðàíè
- Page 101 and 102: Çà ïåð³îä ÷àñó â³ä t
- Page 103 and 104: Ïðèêëàä 7.3.2. Ïîêàçà
- Page 105 and 106: Â ÿêîñò³ ïðèêëàäà ð
- Page 107 and 108: Òåîðåìà 7.6.2 (ïðî äèô
- Page 109 and 110: Òàáëèöÿ ïîõ³äíèõ ñ
- Page 111 and 112: 7.13. r(ϕ) =ϕ sin ϕ + cos ϕ; î
- Page 113 and 114: 7.9.8. Çíàõîäèìî y′: Ò
- Page 115 and 116: Ôóíêö³ÿ ïðîïîçèö³¿
- Page 117 and 118: Îñê³ëüêè â êðèòè÷í
- Page 119 and 120: ïðè ∆x =1 i x=1000: (∆y)⏐x
- Page 121 and 122: Íàñë³äîê 3. ßêùî íà
- Page 123 and 124: 7.14.9. = ln x 1/ x = 1/ x 1 − =
- Page 125 and 126: Çàóâàæåííÿ. Ðîçêëà
- Page 127 and 128: Îö³íèìî n ( ) n+ 1 θx n+ 1
- Page 129 and 130: Çâ³äñè ó êð - ó äîò
- Page 131 and 132: Ð î ç â ’ ÿ ç à í í ÿ.
- Page 133 and 134: âè áóäåòå âèâ÷àòè ó
- Page 135 and 136: 8.3. ⎛ ∫ ⎜sin x+ ⎝ 3 ⎞ dx
- Page 137 and 138: 8.12. ∫ sin( ax + b) dx ; 8.13.
- Page 139 and 140: Ïåðøèé òèï äîäàíê³
- Page 141 and 142:
8.5. ²ÍÒÅÃÐÓÂÀÍÍß ÄÅ
- Page 143 and 144:
6 4 1 1 1 5 1 3 = ∫t − dt+ ∫t
- Page 145 and 146:
[ñ, b] ñåãìåíòà [a, b] ¿
- Page 147 and 148:
9.2.1. Îçíà÷åííÿ òà óì
- Page 149 and 150:
4. ßêùî ôóíêö³ÿ ó = f(
- Page 151 and 152:
9.4. ÎÑÍÎÂÍÀ ÔÎÐÌÓËÀ
- Page 153 and 154:
â³äíîñò³ äî ôîðìóë
- Page 155 and 156:
Îçíà÷åííÿ 9.6.1. Íåâë
- Page 157 and 158:
³ îñê³ëüêè +∞ ∫ 1 ðî
- Page 159 and 160:
Ïðèêëàä 9.6.12 (òåîðåò
- Page 161 and 162:
Ïðèêëàä 9.7.2. Îá÷èñë
- Page 163 and 164:
Îñê³ëüêè ôóíêö³ÿ ó
- Page 165 and 166:
Ãðàíèöÿ ö³º¿ ñóìè ï
- Page 167 and 168:
Ð î ç â ’ ÿ ç à í í ÿ.
- Page 169 and 170:
Òîä³ ìîæíà ïîêàçàò
- Page 171 and 172:
4 3 ∆Ψ = 10 − 10 = 9000 . Îò
- Page 173 and 174:
ïàäຠç íàö³îíàëüí
- Page 175 and 176:
Çàóâàæåííÿ 2. Àíàëî
- Page 177 and 178:
10.2. ÃÐÀÍÈÖß ² ÍÅÏÅÐ
- Page 179 and 180:
Öå ð³âíÿííÿ ïðÿìî¿,
- Page 181 and 182:
Öåé æàðò³âëèâèé åê
- Page 183 and 184:
äàòêîâ³é âàðòîñò³
- Page 185 and 186:
Îçíà÷åííÿ 10.4.2 Äèôå
- Page 187 and 188:
∂u äå ( i = 1, 2, K , n) ∂x
- Page 189 and 190:
Àíàëîã³÷íî ( 0, 0 ) ( 0,
- Page 191 and 192:
Çàóâàæèìî, ùî ïîíÿò
- Page 193 and 194:
Òîä³: 1) ÿêùî a a a a > 0,
- Page 195 and 196:
ÂÏÐÀÂÈ Äîñë³äèòè í
- Page 197 and 198:
Òàêèì ÷èíîì, ìè âèç
- Page 199 and 200:
Ðèñ. 10.21 ³äîìèé Îìó
- Page 201 and 202:
ßñíî, ùî âàð³àíò ë³
- Page 203 and 204:
11.1.3. Ïðî â³ëüíå ïàä
- Page 205 and 206:
ñòå, òî ìè çìîæåìî é
- Page 207 and 208:
êîîðäèíàò (ðèñ. 11.4).
- Page 209 and 210:
ÂÏÐÀÂÈ Ðîçâ’ÿçàòè
- Page 211 and 212:
ÂÏÐÀÂÈ Ðîçâ’ÿçàòè
- Page 213 and 214:
Äàë³ âàð³þºìî ñòàë
- Page 215 and 216:
11.6.2. ˳í³éí³ îäíîð³
- Page 217 and 218:
Òîä³ ( ) ( ) y2 x ≡λy1 x ,
- Page 219 and 220:
2x Çàãàëüíèé ðîçâ’ÿ
- Page 221 and 222:
y′ ÷.í. = e x (2Ax +Ax 2 ), y
- Page 223 and 224:
x = + + + . 2 2 5 y x c1 c2x c3 x
- Page 225 and 226:
Ô(t) =7⋅ 10 6 +3⋅ 10 6 e -0,1t
- Page 227 and 228:
S n 1 1 1 = + + K + 1⋅2 2⋅ 3 n
- Page 229 and 230:
Îñê³ëüêè ðÿä (12.2.7) ç
- Page 231 and 232:
Çàóâàæåííÿ. Ðÿäè ç
- Page 233 and 234:
íà çàâæäè íå ïîðîæí
- Page 235 and 236:
ÂÏÐÀÂÈ Âèçíà÷èòè ³
- Page 237 and 238:
12.5.6. Äîâåäåííÿ ôîðì
- Page 239 and 240:
êö³þ, êîòðó íàé÷àñò
- Page 241 and 242:
Âèðàç âèäó a+bi=z, äå à
- Page 243 and 244:
òî z z r (cos ϕ + isin ϕ ) r (c
- Page 245 and 246:
13.16. z =− 2+ 2 3i ; 13.17. z =
- Page 247 and 248:
14.2.4. Êîðåí³ òà ¿õí³
- Page 249 and 250:
y ⎛ π ⎞ x tg α= k , k ; ctg (
- Page 251 and 252:
1 2 tg α+ ctg α= = sin αcos α s
- Page 253 and 254:
14.4. ÅËÅÌÅÍÒÈ ÂÈÙί
- Page 255 and 256:
14.5. ÃÐÀÔ²ÊÈ ÄÅßÊÈÕ
- Page 257 and 258:
14.5.11. y = arctg x (ðèñ. 14.19
- Page 259 and 260:
14.7. ÍÀÁËÈÆÅÍÅ ÇÍÀ×Å
- Page 261:
Ê36 Êåðåêåøà Ï. Â. Ëå