BRIEF CALCULUS Ch11- Differential Equations

1. Determine iwhether i iis ia isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: A 2. Determine iwhether i iis ia isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: A 3. Determine iwhether i iis ia isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: A 4. Determine iwhether i iis ia isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: A 5. Which iof ithe ifollowing iis ia isolution iof ithe idifferential iequation i ? A) B) C) D) E) Ans: A 6. Which iof ithe ifollowing iis ia isolution iof ithe idifferential iequation i ? A) B) C) D) E) Ans: C 7. Find ithe iparticular isolution iof ithe idifferential iequation i ithat isatisfies ithe iinitial icondition iy i= i8 iwhen ix i= i3, iwhere i iis ithe igeneral isolution. i A) B) C) D) E) Ans: B 8. Use iintegration ito ifind ia igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: C 9. Use iintegration ito ifind ia igeneral isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: D 10. Determine iwhether ithe ifunction i iis ia isolution iof ithe idifferential iequation i . A) Solution B) Not ia isolution Ans: A 11. Determine iwhether ithe ifunction i iis ia isolution iof ithe idifferential iequation i . A) Solution B) Not ia isolution Ans: B 12. Determine iwhether ithe ifunction i iis ia isolution iof ithe idifferential iequation i . A) Solution B) Not ia isolution Ans: B 13. Determine iwhether ithe ifunction i iis ia isolution iof ithe idifferential iequation i . A) Solution B) Not ia isolution Ans: B 14. Find ithe igeneral isolution isatisfies ithe idifferential iequation. iThen ifind ithe iparticular isolution ithat isatisfies ithe iinitial icondition. General iSolution: i Differential iequation: i Initial icondition: i A) B) C) D) E) Ans: A 15. Find ithe igeneral isolution isatisfies ithe idifferential iequation. iThen ifind ithe iparticular isolution ithat isatisfies ithe iinitial icondition. General iSolution: i Differential iequation: i Initial icondition: i A) B) C) D) E) Ans: A 16. Use ithe iintegration ito ifind ithe igeneral isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: A 17. Use ithe iintegration ito ifind ithe igeneral isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: A 18. Use ithe iintegration ito ifind ithe igeneral isolution iof ithe idifferential iequation i . A) B) C) D) E) Ans: A 19. Some iof ithe icurves icorresponding ito idifferent i ivalues iof iC iin igeneral isolution iof ithe idifferential iequation i are ishown iin ithe ifigure igiven ibelow. iFind ithe iparticular isolution ithat ipasses ithrough ithe ipoints iplotted ion ithe igraph. A) B) C) D) E) Ans: A 20. Some iof ithe icurves icorresponding ito idifferent ivalues iof iC iin igeneral isolution iof ithe idifferential iequation i are ishown iin ithe ifigure igiven ibelow. iFind ithe iparticular isolution ithat ipasses ithrough ithe ipoints iplotted ion ithe igraph. A) B) C) D) E) Ans: A 21. Write ithe ithe idifferential iequation iby iseparating ithe ivariables. A) B) C) D) E) Ans: C 22. Write ithe ithe idifferential iequation iby iseparating ithe ivariables. A) B) C) D) E) Ans: D 23. Write ithe ithe idifferential iequation iby iseparating ithe ivariables. A) B) C) D) No, ithe ivariables icannot ibe iseparated E) Ans: D 24. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: C 25. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: A 26. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: C 27. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: C 28. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: C 29. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: B 30. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: E 31. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: C 32. Use iseparation iof ivariables ito ifind ithe igeneral isolution iof ithe idifferential iequation. A) B) C) D) E) Ans: C 33. Find ithe igeneral isolution iof ithe idifferential iequation A) B) C) D) E) Ans: B 34. The iisotope i ihas ia ihalf-life iof i5,715 iyears. iGiven ian iinitial iamount iof i11 igrams iof ithe iisotope, ihow imany igrams iwill iremain iafter i1,000 iyears? iAfter i10,000 iyears? iRound iyour ianswers ito ifour idecimal iplaces. A) 6.8205 igm, i2.2896 igm B) 3.8974 igm, i1.3083 igm C) 9.7436 igm, i3.2708 igm D) 11.6923 igm, i3.9250 igm E) 5.8462 igm, i1.9625 igm Ans: C 35. Use ithe iinitial icondition ito ifind ithe iparticular isolution iof ithe idifferential iequation. i, i iwhen i A) B) C) D) E) Ans: C 36. Use ithe iinitial icondition ito ifind ithe iparticular isolution iof ithe idifferential iequation. i, i iwhen i A) B) C) D) E) Ans: A 37. Use ithe iinitial icondition ito ifind ithe iparticular isolution iof ithe idifferential iequation. i, i when i A) B) C) D) E) Ans: C 38. Use ithe iinitial icondition ito ifind ithe iparticular isolution iof ithe idifferential iequation. i, i when i A) B) C) D) E) Ans: B 39. Find ian iequation iof ithe igraph ithat ipasses ithrough ithe ipoint iand ihas ithe ispecified islope. iThen igraph ithe iequation. Point: i , Slope: i A) B) C) D) E) None iof ithe iAbove Ans: A 40. Solve ithe idifferential iequation ito ifind ivelocity iv ias ia ifunction iof itime it iif iwhen i The idifferential iequation imodels ithe imotion iof itwo ipeople ion ia itoboggan iafter iconsideration iof ithe iforces iof igravity, ifriction, iand iair iresistance. A) B) C) D) E) Ans: E 41. Write ithe ifirst-order ilinear idifferential iequation iin istandard iform. A) B) C) D) E) Ans: A 42. Write ithe ifirst-order ilinear idifferential iequation iin istandard iform. A) B) C) D) E) Ans: C 43. Write ithe ifirst-order ilinear idifferential iequation iin istandard iform. A) B) C) D) E) Ans: E 44. Find ithe igeneral isolution iof ithe ifirst-order ilinear idifferential iequation. A) B) C) D) E) Ans: B 45. Find ithe igeneral isolution iof ithe ifirst-order ilinear idifferential iequation. A) B) C) D) E) Ans: D 46. Find ithe igeneral isolution iof ithe ifirst-order ilinear idifferential iequation. A) B) C) D) E) Ans: D 47. Find ithe igeneral isolution iof ithe ifirst-order ilinear idifferential iequation. A) B) C) D) E) Ans: A 48. Find ithe igeneral isolution iof ithe ifirst-order ilinear idifferential iequation. A) B) C) D) E) Ans: C 49. Find ithe igeneral isolution iof ithe ifirst-order ilinear idifferential iequation. A) B) C) D) E) Ans: B 50. A icalf ithat iweighs i80 ipounds iat ibirth igains iweight iat ithe irate i iwhere iw iis iweight iin ipounds iand it iis itime iin iyears. iUse ia icomputer ialgebra isystem ito isolve ithe idifferential iequation ifor i . A) B) C) D) E) Ans: D 51. Find ithe iparticular isolution iof ithe idifferential iequation i i ithat isatisfies ithe iboundary icondition i . A) B) C) D) E) Ans: A 52. Find ithe iparticular isolution iof ithe idifferential iequation i ipassing ithrough ithe ipoint i . A) B) C) D) E) Ans: A 53. Solve ifor iy iin itwo iways. A) B) C) D) E) Ans: A 54. Solve ifor iy iin itwo iways. A) B) C) D) E) Ans: C 55. Find ithe isolution iof ithe idifferential iequation i , iwithout isolving iit. A) B) C) D) E) Ans: D 56. Find ithe isolution iof ithe idifferential iequation i , iwithout isolving iit. A) B) C) D) E) Ans: E 57. Find ithe iparticular isolution ithat isatisfies ithe iinitial icondition. ; i i i i Initial iCondition: i iwhen i A) B) C) D) E) Ans: D 58. Find ithe iparticular isolution ithat isatisfies ithe iinitial icondition. ; i i i i Initial iCondition: i iwhen i A) B) C) D) E) Ans: B 59. Find ithe iparticular isolution ithat isatisfies ithe iinitial icondition. ; i i i i Initial iCondition: i iwhen i A) B) C) D) E) Ans: B 60. Find ithe iparticular isolution ithat isatisfies ithe iinitial icondition. ; i i i i Initial iCondition: i iwhen i A) B) C) D) E) Ans: D 61. Use ithe ichemical ireaction imodel idescribed ito ifind ithe iamount iy i(in igrams) ias ia ifunction iof itime it i(in ihours). iThen iuse ia igraphing iutility ito igraph ithe ifunction. igrams iwhen i ; i grams iwhen i