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Unformatted text preview: Answers to Odd-Numbered Exercises 505 Review Exercises (Chapter 3) _ W . e 49 1 1 11V— (1+1?) cosmeuye {1+y2)2 5mm: 5 — sinZ - 5. zz = 6:12; 21,, = 41.13:” = 6; 11111 = 4; zzy = 0 7 Letting :r' = «.xe + 3F, 3": = (—wsinr)/r fy = (—ysinr)/r f“ = (—1-2 sinr 4 marcosr + 1112 sin r}/r3 fyy = (—1”2 sinr —- garcosr + y2 sin r)/r3 fey : (Fwyr cosr + my sinr)/r3 9. Both are e” + zye’” + 63:22. 11. Check that f,” + f“, : 0. 15. 1 — 1:2/2 + my 15. (0,0); saddle point 17. (ﬂ, 0); saddle point 19. Use the second derivative test; [0, 0) is a local maximum; (—1,0) is a saddle point; (2, 0] is a local minumum. 21. Saddle points at (11,0),11 = integer. 23. 1 1 1 1 25. (E'EIE) 27. 2,1/2 29. maximum 1, minimum c051 31. 2WJ—1ifb22,lb|ifb52 33. 31/5/41 35. Use the second derivative test. 37. n / d where n has components as follows: 11 = bomlagbg + 0.119.353 - nigh - a3b1, (1111251 + 620.353 — agbg - agbz, {1111351 + (12:13.53 - 0&53 — 0%53] and d = ((1% + 11% + (1%)2 - ((1151 + 62332 + £143,333)2 39. (fmllfyyl e (fey)2 = (ﬁll-555) - {—611}2 = 0 at (0,0) 41. maxmum 2, minimum #2 Chapter 4' Vector—Valued Functions 4.1 Acceleration 1. 6 + 312;(0,6,61) 3. (4c053t5in2t+9(1 —t2)3 +1)%; (—2c052t,e-6t,0) 5. (et # 5“, cost —- sint, —3t2) 7. [#3129 sint + cost) — 13(2 cost — 51111)]1 + [332(28t + e“) + 133(26‘ — e")]i + [e‘(cost — sin t) — e_t{- 5th + cost)]k 9. m(0,6,0) 11. —-247r3( cos (Zn-H5), sin [21rt/5))/25 ...
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