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Ãëàâíàÿ Ñëó÷àéíàÿ ñòðàíèöà Êîíòàêòû | Ìû ïîìîæåì â íàïèñàíèè âàøåé ðàáîòû! | |
äåéñòâèòåëüíîãî ïåðåìåííîãî
|
|
Íàéòè ãîäîãðàôû âåêòîð–ôóíêöèé
5.507. 
=(2 t –1) i +(–3t+2) j +4 tk, t Î R.
5.508. = 
t Î[0,1].
5.509. =4 cht × i – j +3 sht × k, t Î R.
5.510. =3 t × i +(2 t – t 2) j, t Î R.
5.511. =cos t × i +sin t×j + t × k, t Î R.
5.512. =2cos3 t × i +2sin3 t×j, t Î[0,2p].
5.513. = t × i + t 2 j + t 3 k, t Î R.
5.514. =cos2 t × i +sin t× cos t × j +sin t × k, t Î[0,2p].
5.515. =5cos t × i +4sin t × j +2 k, t Î[0,2p].
5.516. =(sht –1) i + ch 2 t × j +3 k, t Î R.
5.517. Äàíî óðàâíåíèå äâèæåíèÿ =3 ti –4 tj. Îïðåäåëèòü òðàåêòîðèþ è ñêîðîñòü äâèæåíèÿ.
5.518. Äàíî óðàâíåíèå äâèæåíèÿ =3 ti +(4 t – t 2) j. Îïðåäåëèòü òðàåêòîðèþ è ñêîðîñòü äâèæåíèÿ. Ïîñòðîèòü âåêòîðû ñêîðîñòè äëÿ ìîìåíòîâ t =0, t = 1, t = 2, t = 3.
5.519. Äàíî óðàâíåíèå äâèæåíèÿ =2(t –sin t) i +2(1–cos t) j. Îïðåäåëèòü òðàåêòîðèþ è ñêîðîñòü äâèæåíèÿ. Ïîñòðîèòü âåêòîðû ñêîðîñòè äëÿ ìîìåíòîâ t = p/2, t = p.
5.520. Íàéòè ïðîèçâîäíûå âåêòîð-ôóíêöèé:
à) =sin t × i +cos2 t × j +sin t cos t × k.
á) = t cos t × i + t sin t × j + tk.
â) =(t +cos t)× i + t × j +sin t × k.
5.521. Íàéòè ïðîèçâîäíûå âåêòîð-ôóíêöèé:
à) =e t × i +cos t × j +(t 2+1) k â òî÷êå (1,1,1).
á) = t 3× i +(t +1)2 j + 
k ïðè t = –2.
Äëÿ êàæäîé èç ñëåäóþùèõ êðèâûõ íàïèñàòü óðàâíåíèå êàñàòåëüíîé è óðàâíåíèå íîðìàëüíîé ïëîñêîñòè â äàííîé òî÷êå:
5.522. x =4sin2 t, y =4sin t cos t, z =2cos2 t ïðè t =p/4.
5.523. x =(1/2) t 2, y =(1/3) t 3, z =(1/4) t 4 ïðè t =2.
5.524. x = a ch t, y =ash t, z =a t ïðè t =0.
5.525. x 2+ y 2=10, y 2+ z 2=25 â òî÷êå M 0(1,3,4).
5.526. 2 x 2+3 y 2+ z 2=9, 3 x 2+ y 2– z 2=0 â òî÷êå M 0(1,–1,2).
5.527. Íàéòè âòîðûå ïðîèçâîäíûå âåêòîð-ôóíêöèé:
à) =cos t × i + etj +(t 2+1) k;
á) = t × i + t cos t × j + t sin t × k;
ïðè ïðîèçâîëüíîì t è ïðè t =0.
5.528. Äàíî óðàâíåíèå äâèæåíèÿ =2(t –sin t) i +2(1–cos t) j. Îïðåäåëèòü óñêîðåíèå äâèæåíèÿ. Ïîñòðîèòü âåêòîðû óñêîðåíèÿ äëÿ ìîìåíòîâ t = p/2, t = p.
Âû÷èñëèòü êðèâèçíó äàííîé êðèâîé:
5.529. y = x 2 â íà÷àëå êîîðäèíàò è â òî÷êå M (1,1).
5.530. x 2+9 y 2=9 â âåðøèíàõ ýëëèïñà A (3,0) è B (0,1).
5.531. x 2– xy + y 2=1 â òî÷êå M (1,1).
5.532. x = t 2, y = t –(t 3/3) ïðè t =1.
5.533. y =0,5 t 2, y=(1/3) t 3 â òî÷êå M (1/2,1/3).
5.534. r = a (1–cosj) â ëþáîé òî÷êå è ïðè j=p.
5.535. r 2= a 2sin2j ïðè j=p/4.
Íàéòè ðàäèóñû êðèâèçíû (â ëþáîé òî÷êå) äàííûõ êðèâûõ:
5.536. y =  .
| 5.537.  .
|
| 5.538. x 2/3+ y 2/3= a 2/3. | 5.539. x = a cos t, y = b sin t. |
| 5.540. x = a (t –sin t), y = a (1–cos t). | 5.541. r 2= a 2cos2j. |
| 5.542. r = a j. |
Âû÷èñëèòü êîîðäèíàòû öåíòðîâ êðèâèçíû è íàïèñàòü óðàâíåíèÿ îêðóæíîñòåé êðèâèçíû äàííûõ êðèâûõ â óêàçàííûõ òî÷êàõ:
5.543. y =  â òî÷êå M (0, a).
| 5.544. y =  â òî÷êå M (0,1).
|
Íàéòè ýâîëþòû êðèâûõ:
| 5.545. y = x 3. | 5.546. x 2– y 2= a 2. |
Îòâåòû
5.1. 15 x 2+6 x –4. 5.2. 
. 5.3. (1/sin2 x)–1. 5.4. –2/ x 3. 5.5. 
.
5.6. 5cos x –3sin x. 5.7. 5tg2 x. 5.8. – ex /(ex +1)2. 5.9. 
.
5.10. 5 x 4–12 x 2+2. 5.11. 
+2 x –2 x 3. 5.12. –(15 x 2)/ a. 5.13. –p/ x 2.
5.14. 2 x –1/3–5 x 3/2–3 x –4. 5.15. 
. 5.16. 
.
5.17. x 6 ex (x +7). 5.18. xex. 5.19. 
. 5.20. 
. 5.21. ex (cos x –sin x). 5.22. x 2 ex. 5.23. ex (arcsin x + 
. 5.24. 
. 5.25. 3 x 2ln x.
5.26. 
. 5.27. 
. 5.28. sh x + x ch x. 5.29. 
. 5.30. –th2 x. 5.31. 
. 5.32. 
.
5.33. 
. 5.34. 
.
5.35. 
. 5.36. 
. 5.37. 
.
5.38. 
. 5.39. 
. 5.40. 
.
5.41. (3/2)sin2 x (cos x –2). 5.42. sec2(x/5). 5.43. 
.
5.44. 
. 5.45. e cos x (cos x –sin2 x). 5.46. 
. 5.47. 
. 5.48. 
. 5.49. 
.
5.50. 
. 5.51. 
. 5.52. 
. 5.53. 
. 5.54. 
. 5.55. 
.
5.56. 
. 5.57. arctg 
. 5.58. 
. 5.59. 
. 5.60. 
. 5.61. 
.
5.62. 
. 5.63. sin53 x ×cos33 x. 5.64. 
.
5.65. 
. 5.66. 
.
5.67. 
. 5.68. 
. 5.69. 
.
5.70. 
. 5.71. 
.
5.72. 
. 5.73. 
. 5.74. 
. 5.75. 
.
5.76. 
. 5.77. 
.
5.78. 
. 5.79. 
. 5.80. 
. 5.81. 
. 5.82. 
. 5.83. 
.
5.84. 
. 5.85. 
.
5.86. 
. 5.87. 
. 5.88. 
.
5.89. 
. 5.90. 2sin x × (x sin x cos x 2+cos x sin x 2).
5.91. 
. 5.92. 
. 5.93. 
.
5.94. 
. 5.95. 
. 5.96. 
.
5.97. 
. 5.98. 
. 5.99. 
. 5.100. –cos2 x. 5.101. 
. 5.102. 
. 5.103. 
. 5.104. 
. 5.105. 
. 5.106. 
.
5.107. 
. 5.108. 
. 5.109. 
.
5.110. 
. 5.111. 
. 5.112. ex sin x cos3 x × ×(1+ctg x ––3tg x). 5.113. 
. 5.114. 
.
5.115. 
. 5.116. 
[2 x (ex + e – x )–(ex – e – x )]. 5.117. 
. 5.118. 
. 5.119. 
.
5.120. 
. 5.121. 6sh22 x ch2 x. 5.122. eax(achb x +bshb x).
5.123. 6th22 x (1– –th22 x). 5.124. 2ñth2 x. 5.125. 
.
5.126. 
. 5.127. 1/cos2 x. 5.128. 1/sin x. 5.129. 2/(1– x 2).
5.130. x Arth x. 5.131. sin x; 0; sin1; 
; sin(p/8); sin 
.
5.132. 
; 2; íå ñóù.; íå ñóù. 5.133. (6+x)/(3+x2); 3/4. 5.134. sin1. 5.135. 
; 
. 5.141. 1) 0; 2) 6; 3) –4; 4) k1=2, k2=4. 5.142. (1,1); (–1,–1). 5.143. 1) (0,0); 2) 
. 5.144. íå ìîæåò. 5.145. a1=arctg(1/7), a2=arctg(1/13). 5.146. a1=p/2, a2=arctg(3/4).
5.147. arctg3. 5.148. y =12 x –16; x +12 y –98=0; ïîäêàñàòåëüíàÿ ðàâíà 2/3; ïîäíîðìàëü ðàâíà 96. 5.149. ïðè x =0 è ïðè x =2/3. 5.150. 1) (2,4); 2) (–3/2;9/4); 3) (–1,1) è (1/4,1/16). 5.151. a) t 1=0, t 2=8; á) t 1=0, t 2=4, t 3=8.
5.152. 181,5×103 ýðã. 5.153. w=13 ðàä/ñåê. 5.154. w=2p ðàä/ñåê.
5.155. w=(2 at – b) ðàä/ñåê; ñêîðîñòü îáðàòèòñÿ â íóëü ïðè t = b /(2 a) ñåê. 5.156. 23A. 5.157. tgj=0,8; j=0,675. 5.158. Ìàññà âñåãî ñòåðæíÿ ñîñòàâëÿåò 360ã, ïëîòíîñòü â òî÷êå M ðàâíà 5 x (ã/ñì), ïëîòíîñòü â òî÷êå À ðàâíà 0 à â òî÷êå B – 60ã/ñì. 5.159. –0,0015 ì/ñåê2. 5.160. –1,8 ì/ñåê2.
5.161. 
. 5.162. 
.
5.163. 
. 5.164. 
.
5.165. 
. 5.166. 
.
5.167. 
.
5.168. 
.
5.169. 
.
5.170. 
. 5.171. 
. 5.172. 
. 6.173. 
.
5.174. 
. 6.175. – (1– x 2)arccos x 
. 5.176. 
.
5.177. 
.
5.178. 
.
5.179. 
.
5.180. 
.
5.181. 
.
5.182. 
.
5.183. – (b 2 x)/(a 2 y). 5.184. 
. 5.185. 
. 5.186. 
.
5.187. 
. 5.188. y /(y – x). 5.189. x / y 
.
5.190. 
. 5.191. 
.
5.192. 
. 5.193. 
. 5.194. 
.
5.195. 
. 5.196. 
. 5.197. 
.
5.198. 
. 5.199. 
. 5.200. 
.
5.201. 
. 5.202. 
. 5.203. 
.
5.204. 
. 5.206. 0. 5.207. 1/2. 5.208. 0. 5.209. 
. 5.210. 
. 5.211. 
. 5.212. 
. 5.213. 
. 5.214. 
. 5.215. tg t. 5.216. – b / a. 5.217. (– b / a)tg t. 5.218. –tg3 t. 5.219. 
.
5.220. –2 e 3 t . 5.221. tg t. 5.222. 
. 5.223. 1. 5.224. 1. 5.225. ¥.
5.227. D y =0,0501; dy =0,05; | dy –D y |=0,0001; 
.
5.228. D y =0,0332; dy =0,0333; | dy –D y |=0,0001; 
.
5.229. D y = - 0,0099; dy = – 0,01; | dy –D y | = 0,0001; 
.
5.230. D y»0,007(ì). 5.231. dy =(–2/ x 3) dx. 5.232. 
.
5.233. 
. 5.234. 
. 5.235. dy =sin2 xdx.
5.236. dy = ex (cos x –sin x) dx. 5.237. 
.
5.238. 
. 5.239. ds =2 xdx. 5.242. 2,03. 5.243. 1,22. 5.244. 0,849. 5.245. 0,9954. 5.246. 0,88. 5.247. 1,0035. 5.248. 0,5005.
5.249. 0,01. 5.250. 2,999. 5.251. arctg1,02»0,795. 5.252. 0,355.
5.253. arctg0,97»0,770. 5.255. íåïðåðûâíà è äèôôåðåíöèðóåìà. 5.256. ïðè x = k p, ãäå k – ïðîèçâîëüíîå öåëîå ÷èñëî. 5.257. Íåïðåðûâíà, íî íåäèôôåðåíöèðóåìà. 5.258. f ¢(0)=0. 5.259. Íåïðåðûâíà, íî íåäèôôåðåíöèðóåìà. 5.260. Íåïðåðûâíà, íî íåäèôôåðåíöèðóåìà. 5.261. Äà; íåò.
5.266. y ²=56 x 6+210 x 4. 5.267. 
. 5.268. y ²=2cos2 x.
5.269. 
. 5.270. 
. 5.271. y ²=2arctg x + 
.
5.272. y ²= 
. 5.273. 
. 5.274. 
.
5.275. y ²=ln x. 5.276. 
. 5.277. y ²= 
(3 x +2 x 3).
5.278. 
. 5.279. 
.
5.280. 
. 5.281. 
. 5.282. 
.
5.283. 
. 5.284. 
. 5.285. 
. 5.286. 
. 5.287. 
. 5.288. 
.
5.292. 
. 5.295. 
. 5.296. 
.
5.297. 
. 5.298. 
.
5.299. 
. 5.301. 
. 5.302. –ctg3 t.
5.303. 
. 5.304. 
. 5.305. 
.
5.308. y (n)=(–3) n × e –3 x . 5.309. y (n)= 
.
5.310. y (n)=2 n –1sin 
. 5.311. y (n)= ex (x + n). 5.312. y (n)=2 x ln n 2.
5.313. 
. 5.314. 
.
5.315. y (n)= 
. 5.316. 
. 5.317. y (n)=(–1) n × n! 
. 5.318. y (n)=(–1) n × n! 
.
5.319. y (n)=4 n –1 
. 5.320. 
. 5.321. +¥. 5.322. d 2 y = –25cos5 dx 2. 5.323. d 2 y =– 
.
5.324. d 2 y = – 
. 5.325. 
.
5.326. 
. 5.327. d 3 z = – e – x (x 2–6 x +6) dx 3.
5.328. d nu =3×2 n sin 
. 5.329. a) íåò; á) íåò. 5.330. Äà.  òî÷êàõ, Î[0,1], äëÿ êîòîðûõ tg(p/ x)=p/ x. 5.331. x1= 
; x2= 
; –1<x1<0; 0<x2<1. 5.332. Íåò, ò.ê. f’ (2) íå ñóùåñòâóåò. 5.333. Íåò, y (0), y ¢(0) íå ñóùåñòâóþò, 0Î[–1;1]. 5.336. 3 êîðíÿ, ïðèíàäëåæàùèõ ñîîòâåòñòâåííî èíòåðâàëàì (1;2), (2;3), (3;4). 5.337. sin3 x 2–sin3 x 1= 3(x 2– x 1)cos3x, ãäå x 1<x< x 2. 5.338. a (1–ln a)– b (1–ln b)=(b – a)lnx, ãäå a <x< b. 5.339. arcsin(2(x 0+D x)) – arcsin2 x 0= 
ãäå x 0<x< x 0+D x. 5.340. Óñëîâèÿ òåîðåìû Ëàãðàíæà, âûïîëíÿþòñÿ; x= –1, ò.ê. –2<x<1 è f ¢(x)= –2. 5.341. x=0. 5.342. (2;4).
5.346. 1,27<ln(1+ e)<1,37. 5.347. 0,947<arctg1,5<1,025. 5.348. a) x=14/9; á) x=p/4. 5.349. Íåò, ò.ê. f ¢(0) =j¢(0)=0. 5.351. 15 ( x-2)2+ +11(x-2)3+2(x-2)4. 5.352. –1–(x +1)–(x +1)2–(x +1) n +(–1) n +1 
ãäå 0<Q<1.
5.353. 
ãäå 0<Q<1.
5.354. 
ãäå 0<Q<1. 5.355. 0,4002<ln(1+0,5)<0,4080.
5.356. £0,00002. 5.357. 
. 5.358. 0,78;d<0.01. 5.359. e»1+ 
. 5.360. 
. 5.361. 0. 5.362. 1. 5.363. a/b. 5.364. 1/3. 5.365. –1/2. 5.366. 2. 5.367. 
. 5.368. 2. 5.369. 1. 5.370. 1. 5.371. 1. 5.372. 0. 5.373. a. 5.374. –1. 5.375. 0. 5.376. 1. 5.377. ¥. 5.378. 1. 5.379. 1. 5.380. e. 5.381. 1. 5.382. e 2. 5.383. 1. 5.384. 1. 5.385. 1. 5.386. 1. 5.387. e 2/p. 5.388. e –2/p. 5.389. Óáûâàåò íà (–¥,–6), âîçðàñòàåò íà (–6,¥). 5.390. Âîçðàñòàåò íà (–¥,5), óáûâàåò íà (5,¥). 5.391. Âîçðàñòàåò íà (-¥,-7), (–7,¥). 5.392. Óáûâàåò íà (0,1), âîçðàñòàåò íà (1,¥). 5.393. âîçðàñòàåò íà (0,1/64), óáûâàåò íà (1/64,¥). 5.394. Óáûâàåò íà (–¥,¥). 5.395. âîçðàñòàåò íà (0, 
), óáûâàåò íà (,¥). 5.396. âîçðàñòàåò íà (–¥,1/5), óáûâàåò íà (1/5,¥). 5.397. y max= y (–2)=35, y min= y (4)=–73. 5.398. y min= y (–4)= –27. 5.399. Ýêñòðåìóìîâ íåò. 5.400. y max= y (–1/3)=13/4, y min= y (4)=0.
5.401. y max= y (0)=0, y min= y (64)= –32. 5.402. y max= 
.
5.403. Ýêñòðåìóìîâ íåò. 5.404. y max= y (–4)=8 e –4, y min= y (2)=–4 e 2.
5.405. y min= y (0)=0, y max= y (2/3)= 
»0,39. 5.406. y min= y (1/ e)=–1/ e.
5.407. y max= y (–p+2p n)=3, y min= y (±p/3+2p n)= –3/2, y max= y (2p n)= –1, n Î z.
5.408. 
.
5.409. 
y (–3)= y (3)=20.
5.410. 
. 5.411. 
y (–2)=–1/4, 
. 5.412. 
= y (1)=0, 
= y (e)= e.
5.413. 
. 5.414. min y íå ñóùåñòâóåò, 
= y (p)=–1. 5.415. 
íå ñóùåñòâóåò. 5.416. 13/2 è –13/2. 5.417. Êâàäðàò ñî ñòîðîíîé 7,5ñì. 5.418.  ñå÷åíèè äîëæåí áûòü êâàäðàò ñî ñòîðîíîé 
. 5.419. arctg 
. 5.420. Îñíîâàíèå îêíà 
. 5.421. Äëèíà áðåâíà (à 2/3+ b 2/3)3/2ì. 5.422. 2,4ì. 5.423. ×åðåç 
÷àñà»1÷àñ 38ìèí. 5.424.  3êì îò ëàãåðÿ.
5.425. 
. 5.426. p 2/ p 1. 5.427. Äëèíà áàëêè 
ì, ñòîðîíà ïîïåðå÷íîãî ñå÷åíèÿ 
ì. 5.428. (–¥,2) – âûïóêëûé, (2,¥) – âîãíóòûé, Ì (2,12) – òî÷êà ïåðåãèáà. 5.429. (–¥,¥) – âîãíóòûé 5.430. (–¥,–3) – âûïóêëûé, (–3,¥) – âîãíóòûé, òî÷åê ïåðåãèáà íåò. 5.431. (–¥,–6);(0,6) – âîãíóòûé, (–6,0);(6,¥) – âûïóêëûé, M 1(–6,–9/2); M 2(6,9/2); O (0,0)– òî÷êè ïåðåãèáà. 5.432. (-¥,- 
); (0, ) – âîãíóòûé, (
,0); (,¥) – âûïóêëûé, M 1(,0); M 2(,0); O (0;0) – òî÷êè ïåðåãèáà. 5.433. ((4 k +1)p/2, (4 k +3)p/2) – âîãíóòûé, ((4 k +3)p/2, (4 k +5)p/2) – âûïóêëûé, k Î z, ((2 k +1)p/2, 0) – òî÷êè ïåðåãèáà. 5.434. (2 k p,(2 k +1)p) – âîãíóòûé, ((2 k –1)p,2 k p) – âûïóêëûé, k Îz, x = k p – òî÷êè ïåðåãèáà. 5.435. (0, e –3/2) – âûïóêëûé, (e –3/2,¥) – âîãíóòûé, M 
– òî÷êà ïåðåãèáà. 5.436. (–¥,0) – âîãíóòûé, (0,¥) – âûïóêëûé, Î (0,0) – òî÷êà ïåðåãèáà. 5.437. (–¥,–3); (–1,¥) – âîãíóòûé, (–3,–1) – âûïóêëûé, M 1(–3,10 e –3); M2(–1,2/ e) – òî÷êè ïåðåãèáà. 5.438. [0,¥) – âûïóêëûé, òî÷åê ïåðåãèáà íåò. 5.439. (–¥,0) – âûïóêëûé, (0,¥) – âîãíóòûé, òî÷åê ïåðåãèáà íåò. 5.440. x = –5, y =0. 5.441. x =4, y =0.
5.442. x =3, y =2. 5.443. x =0, y = x. 5.444. y =1. 5.445. x = 
2, y = – x.
5.446. y = x. 5.447. x = –2, y = x –7. 5.448. x =6, y = x +3, y = – x –3. 5.449. y =3 x, y = x. 5.450. y = –2. 5.451. y =4 x. 5.452. x = 1. 5.453. y = 
, y = 
. 5.454. y = – x. 5.455. x =0, y = x +1. 5.456. x =1, x =2, y =2 x +6. 5.457. x = 2. 5.458. y min= y(
) = 
; (
), 
– òî÷êè ïåðåãèáà. 5.459. y max= =y(0) = 3; y min= y(±1) = 2, 
– òî÷êè ïåðåãèáà. 5.460. y min= =y(±1) = 2, x =0 – àñèìïòîòà. 5.461. y max= y (–1)=0, y min= y (5)=12; x =2, 
– àñèìïòîòû. 5.462. y min= y (0)= 
, 
– òî÷êè ïåðåãèáà; y =1 – àñèìïòîòà. 5.463. y min= y (1)=0; y max= y (5)=2/27; x =5± 
– òî÷êè ïåðåãèáà. Àñèìïòîòû x = –1, y = 0. 5.464. y max= y (3,5)=-6,25, x = 1, x = 6, y = 0 – àñèìïòîòû. 5.465. y min= y (2)=0, x = 1, y = x – àñèìïòîòû. 5.466. (0;0) – òî÷êà ïåðåãèáà, x = 3, y = 0 – àñèìïòîòû. 5.467. y min= y (0)= 0, y max= y (
) = = . 5.468. y min= y (1) = 
; y max= y (–1) = 
; (
); (0,0) – òî÷êè ïåðåãèáà; y = x - àñèìïòîòà. 5.469. (0,0); 
– òî÷êè ïåðåãèáà; y = x- àñèìïòîòà. 5.470. 
; (–1,–1) – òî÷êè ïåðåãèáà; x =0, y =1 - àñèìïòîòû.
5.471. y max= y (0)=1; y min= y (±1)=0. 5.472. y = x – àñèìïòîòû. 5.473. y max= = y (1)= e, 
– òî÷êè ïåðåãèáà; y =0 – ëåâàÿ àñèìïòîòà. 5.474. y min= y (-3) = 
; y max= y (1) = 2, x = −2± 
– òî÷êè ïåðåãèáà. Àñèìïòîòû x = –1, y = 0. 5.475. y min= y (2,5)= − 0,5, 
- òîêà ïåðåãèáà, y =0 – ëåâàÿ àñèìïòîòà. 5.476. y max= y (1)= 
; y min= y (–1)= 
; (0,0); 
– òî÷êè ïåðåãèáà; y =0 – àñèìïòîòà. 5.477. y max= y (1)=1/ e; 
– òî÷êè ïåðåãèáà; x =0 – ëåâàÿ àñèìïòîòà, y =0 – àñèìïòîòà. 5.478. (1, e 2) – òî÷êà ïåðåãèáà, x =0 – ïðàâàÿ àñèìïòîòà, y =2 x +3 – àñèìïòîòà. 5.479. y max= y ()= 
e –3/2; y min= y () = 
, (0,0); 
, 
– òî÷êè ïåðåãèáà, y =0 – àñèìïòîòà.
5.480. y max= y (e)=1/ e; 
– òî÷êà ïåðåãèáà; x =0, y =0 – ïðàâûå àñèìïòîòû. 5.481. y max= y (1/ e)= – e; x =1 – àñèìïòîòà, x =0, y =0 – ïðàâûå àñèìïòîòû. 5.482. y min= y ()= 
; 
– òî÷êà ïåðåãèáà. 5.483. y max = y (–1– 
)= –1– +ln(2+ 
); x = ± 2 − àñèìïòîòû.
5.484. y max= y (0)=ln4; x = ± 2 – àñèìïòîòû. 5.485. (0,0) – òî÷êà ïåðåãèáà; x =±1 – àñèìïòîòû. 5.486. y min= y (1)=1; x =0 – àñèìïòîòà. 5.487. y min= y (–1) = =−p/2; y max= y (1)=p/2; (0,0) – òî÷êà ïåðåãèáà, y =0 – àñèìïòîòà. 5.488. y min= = y (0)=0; y = –p x /2–1 – ëåâàÿ àñèìïòîòà, y =p x /2–1 – ïðàâàÿ àñèìïòîòà. 5.489. y min= y (1/ e)= 
»0,69; y ®1 ïðè x ®+0, ò.å. M (+0,1) – êîíöåâàÿ òî÷êà. 5.490. y min= y (
+2p k)= 
; y max= y (p/4+2p k)= 
; 
– òî÷êè ïåðåãèáà, k Î z. 5.491. y min= y (p/4+2p k)= 
; y max= y 
; x = 
+ k p – àñèìïòîòû, k Î z. 5.492. x min= –1/ e ïðè t = –1, y (–1) = = – e; y max=1/ e ïðè t =1; x (1)= e. 
– òî÷êè ïåðåãèáà; x =0, y =0 – àñèìïòîòû. 5.493. y min= –1 ïðè t =1, y (1)=3; y min= –1 ïðè t = –1, x (–1)=3; ïàðàáîëà ñ âåðøèíîé â íà÷àëå êîîðäèíàò, îñü êîòîðîé – ïðÿìàÿ y = x (x >0, y >0). 5.494. Àñòðîèäà. 5.495. Àñèìïòîòà x + y +1=0; (0,0) – òî÷êà ñàìîïåðåñå÷åíèÿ, êàñàòåëüíûìè â ýòîé òî÷êå ñëóæàò îñè êîîðäèíàò.  ïåðâîì êâàäðàíòå – çàìêíóòàÿ ïåòëÿ. 5.496. (1,2) – òî÷êà âîçâðàòà (ïðè t =1); àñèìïòîò íåò. y min = y(–3) = –2 (ïðè t = –2). 5.497. y min = y(1) = 0 (ïðè t =1); y max= y(0) =1 (ïðè t = –1). Àñèìïòîò íåò. Ãðàôèê – ïàðàáîëà, ðàñïîëîæåííàÿ â ïåðâîì êâàäðàíòå. Îñü ñèììåòðèè: y = x. 5.498. r2= a 2sin2j ïðè 0£j£p/2, p£j£3p/2. 5.499. ×åòûðåõëåïåñòêîâàÿ ðîçà (0,0) – äâîéíàÿ òî÷êà ñàìîïðèêîñíîâåíèÿ. 5.500. 
. 5.501. Ôóíêöèÿ óáûâàåò. (0,3) – òî÷êà ïåðåãèáà. 5.502. y min=1. 5.503. y min=2. 5.504. y max= = –11. 5.505. Ôóíêöèÿ âîçðàñòàåò; (0,0) – òî÷êà ïåðåãèáà. 5.506. Ôóíêöèÿ âîçðàñòàåò; (0,4) – òî÷êà ïåðåãèáà. 5.507. Ïðÿìàÿ 
. 5.508.  ïëîñêîñòè xOy äóãà îêðóæíîñòè x 2+ y 2=2 ìåæäó òî÷êàìè (1,1) è (0, ), ïðîáåãàåìàÿ ïðîòèâ ÷àñîâîé ñòðåëêè. 5.509. Ïðàâàÿ âåòâü ãèïåðáîëû 
y = –1, ïðîáåãàåìàÿ ñíèçó ââåðõ, åñëè ñìîòðåòü îò íà÷àëà êîîðäèíàò. 5.510.  ïëîñêîñòè xOy ïàðàáîëà y= 
, ïðîáåãàåìàÿ ñëåâà íàïðàâî. 5.511. Âèíòîâàÿ ëèíèÿ x =cos t, y =sin t, z = t. 5.512. Àñòðîèäà x 2/3+ y 2/3=22/3, z =0. 5.513. Ëèíèÿ ïåðåñå÷åíèÿ öèëèíäðîâ y = x 2, z = x 3, ïðîáåãàåìàÿ ñíèçó ââåðõ. 5.514. Êðèâàÿ Âèâèàíè – ëèíèÿ ïåðåñå÷åíèÿ ñôåðû è êðóãîâîãî öèëèíäðà: x 2+ y 2+ z 2=1, x 2+ y 2= x. 5.515. Ýëëèïñ 
, z =2. 5.516. Äâàæäû ïðîáåãàåìàÿ ïàðàáîëà y = x 2+ x, z =3. 5.517. Ïðÿìàÿ 4 x +3 y =0, z =0; 
3 i –4 j. 5.518. Ïàðàáîëà (â ïëîñêîñòè xOy) y= 
; 
=3 i +(4–2 t) j, 
=3 i +4 j, 
3 i +2 j, 
, 
.
Äàòà ïóáëèêîâàíèÿ: 2015-02-22; Ïðî÷èòàíî: 448 | Íàðóøåíèå àâòîðñêîãî ïðàâà ñòðàíèöû | Ìû ïîìîæåì â íàïèñàíèè âàøåé ðàáîòû!
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