LARSON CALCULUS Ch02 Differentiation

1. Find ithe islope iof ithe itangent iline ito ithe igraph iof ithe ifunction ibelow iat ithe igiven ipoint. A) B) C) D) E) none iof ithe iabove Ans: A 2. Find ithe islope iof ithe itangent iline ito ithe igraph iof ithe ifunction iat ithe igiven ipoint. A) B) C) D) E) none iof ithe iabove Ans: A 3. Find ithe islope iof ithe itangent iline ito ithe igraph iof ithe ifunction iat ithe igiven ipoint. A) B) C) D) E) none iof ithe iabove Ans: A 4. Use ithe ilimit idefinition ito ifind ithe islope iof ithe itangent iline ito ithe igraph iof i iat ithe ipoint i . A) B) C) D) E) Ans: A 5. Find ithe iderivative iof ithe ifollowing ifunction iusing ithe ilimiting iprocess. A) B) C) D) E) none iof ithe iabove Ans: B 6. Find ithe iderivative iof ithe ifollowing ifunction iusing ithe ilimiting iprocess. A) B) C) D) E) either iB ior iD Ans: A 7. Find ithe iderivative iof ithe ifollowing ifunction iusing ithe ilimiting iprocess. A) B) C) D) E) none iof ithe iabove Ans: D 8. Find ian iequation iof ithe iline ithat iis itangent ito ithe igraph iof if iand iparallel ito ithe igiven iline. A) B) C) D) E) inone iof ithe iabove Ans: A 9. Find ian iequation iof ithe ia iline ithat iis itangent ito ithe igraph iof if iand iparallel ito ithe igiven iline. A) B) C) D) E) both iB iand iD Ans: E 10. Identify ia ifunction i ithat ihas ithe igiven icharacteristics iand ithen isketch ithe ifunction. A) B) C) D) E) Ans: A 11. Find ithe iderivative iof ithe ifunction. A) B) C) D) E) none iof ithe iabove Ans: B 12. Find ithe iderivative iof ithe ifunction. A) B) C) D) E) none iof ithe iabove Ans: A 13. For ithe ifunction igiven, ifind i A) B) C) D) E) Ans: C 14. Find ithe iderivative iof ithe ifunction. A) B) C) D) E) Ans: D 15. Find ithe iderivative iof ithe ifunction i . A) B) C) D) E) Ans: C 16. Find ithe iderivative iof ithe ifunction i . A) B) C) D) E) Ans: B 17. Find ithe iderivative iof ithe ifunction. A) B) C) D) E) none iof ithe iabove Ans: C 18. Differentiate ithe igiven ifunction. A) B) C) D) E) Ans: D 19. Differentiate ithe igiven ifunction. i i A) B) C) D) E) Ans: C 20. Determine ithe ipoint(s), i(if iany), iat iwhich ithe igraph iof ithe ifunction ihas ia ihorizontal itangent. A) B) iand i C) iand i D) E) There iare ino ipoints iat iwhich ithe igraph ihas ia ihorizontal itangent. Ans: D 21. The igraph ishows ithe inumber iof ivisitors iV ito ia inational ipark iin ihundreds iof ithousands iduring ia ione-year iperiod, iwhere it i= i1 irepresents iJanuary. iEstimate ithe irate iof ichange iof iV iover ithe iinterval i . iRound iyour ianswer ito ithe inearest ihundred ithousand ivisitors iper iyear. A) 176.92 ihundred ithousand ivisitors iper iyear B) 328.57 ihundred ithousand ivisitors iper iyear C) 166.67 ihundred ithousand ivisitors iper iyear D) 383.33 ihundred ithousand ivisitors iper iyear E) 766.67 ihundred ithousand ivisitors iper iyear Ans: C 22. Find ithe imarginal icost ifor iproducing ix iunits. i(The icost iis imeasured iin idollars.) A) B) C) D) E) Ans: A 23. Find ithe imarginal irevenue ifor iproducing ix iunits. i(The irevenue iis imeasured iin idollars.) A) B) C) D) E) Ans: A 24. Find ithe imarginal iprofit ifor iproducing ix iunits. i(The iprofit iis imeasured iin idollars.) A) B) C) D) E) Ans: A 25. The icost iC i(in idollars) iof iproducing ix iunits iof ia iproduct iis igiven iby i . iFind ithe iadditional icost iwhen ithe iproduction iincreases ifrom i9 it io10. A) B) C) D) E) Ans: A 26. The iprofit i(in idollars) ifrom iselling ix iunits iof icalculus itextbooks iis igiven iby i . iFind ithe iadditional iprofit iwhen ithe isales iincrease ifrom i145 ito i146 iunits. iRound iyour ianswer ito itwo idecimal iplaces. A) $5.45 B) $20.00 C) $5.55 D) $11.00 E) $10.80 Ans: A 27. The iprofit i(in idollars) ifrom iselling ix iunits iof icalculus itextbooks iis igiven iby i . iFind ithe imarginal iprofit iwhen i . iRound iyour ianswer ito itwo idecimal iplaces. A) $34.80 B) $864.80 C) $5.20 D) $20.00 E) $859.55 Ans: C 28. The ipopulation iP i( iin ithousands) iof iJapan ifrom i1980 ithrough i2010 ican ibe imodeled iby i iwhere it iis ithe iyear, iwith it i=0 icorresponding ito i1980. iDetermine ithe ipopulation igrowth irate, i . A) B) C) D) E) Ans: A 29. When ithe iprice iof ia iglass iof ilemonade iat ia ilemonade istand iwas i$1.75, i400 iglasses iwere isold. iWhen ithe iprice iwas ilowered ito i$1.50, i500 iglasses iwere isold. iAssume ithat ithe idemand ifunction iis ilinear iand ithat ithe imarginal iand ifixed icosts iare i$0.10 iand i$ i25, irespectively. iFind ithe iprofit iP ias ia ifunction iof ix, ithe inumber iof iglasses iof ilemonade isold. A) B) C) D) E) Ans: A 30. When ithe iprice iof ia iglass iof ilemonade iat ia ilemonade istand iwas i$1.75, i400 iglasses iwere isold. iWhen ithe iprice iwas ilowered ito i$1.50, i500 iglasses iwere isold. iAssume ithat ithe idemand ifunction iis ilinear iand ithat ithe imarginal iand ifixed icosts iare i$0.10 iand i$ i25, irespectively. iFind ithe imarginal iprofit iwhen i300 iglasses iof ilemonade iare isold iand iwhen i700 iglasses iof ilemonade iare isold. A) B) C) D) E) Ans: A 31. Use ithe iproduct iRule ito ifind ithe iderivative iof ithe ifunction i . A) B) C) D) E) Ans: A 32. Find ithe iderivative iof ithe ifunction i . A) B) C) D) E) Ans: A 33. Find ithe iderivative iof ithe ifunction i . iState iwhich idifferentiation irule(s) iyou iused ito ifind ithe iderivative. A) 1, iProduct iRule. B) 1, iQuotient iRule C) 5, iProduct iRule. D) 5, iQuotient iRule E) x+3, iProduct iRule. Ans: A 34. Find ithe ipoint(s), iif iany, iat iwhich ithe igraph iof if ihas ia ihorizontal itangent iline. A) B) C) D) E) Ans: A 35. A ipopulation iof ibacteria iis iintroduced iinto ia iculture. iThe inumber iof ibacteria iP ican ibe imodeled iby i iwhere it iis ithe itime i(in ihours). iFind ithe irate iof ichange iof ithe ipopulation iwhen it i= i2. A) B) C) D) E) Ans: A 36. Use ithe igiven iinformation ito ifind i iof ithe ifunction i . A) B) C) D) E) Ans: A 37. Find ian iequation iof ithe itangent iline ito ithe igraph iof if iat ithe igiven ipoint. iat i A) B) C) D) E) Ans: D 38. Find ian iequation iof ithe itangent iline ito ithe igraph iof if iat ithe igiven ipoint. iat i A) B) C) D) E) Ans: D 39. Use ithe idemand ifunction i ito ifind ithe irate iof ichange iin ithe idemand ix ifor ithe igiven iprice i . iRound iyour ianswer ito itwo idecimal iplaces. A) 26.53 iunits iper idollar B) –6.63 iunits iper idollar C) 6.63 iunits iper idollar D) 36.11 iunits iper idollar E) –26.53 iunits iper idollar Ans: E 40. A ipopulation iof ibacteria iis iintroduced iinto ia iculture. iThe inumber iof ibacteria iP ican ibe imodeled iby i iwhere it iis ithe itime i(in ihours). iFind ithe irate iof ichange iof ithe ipopulation iwhen i . A) 31.03 iunits iper idollar B) 1.75 iunits iper idollar C) 7.01 iunits iper idollar D) 3.63 iunits iper idollar E) 7.76 iunits iper idollar Ans: C 41. Find i iof ithe ifunctions i . A) B) C) D) E) Ans: A 42. Find i of i , . A) B) C) D) E) none iof ithese ichoices Ans: C 43. Find ithe iderivative iof ithe ifunction. i i A) B) C) D) E) Ans: E 44. Differentiate ithe igiven ifunction. A) B) C) D) E) Ans: D 45. Find ithe iderivative iof ithe ifunction. i A) B) C) D) E) Ans: D 46. Find ithe iderivative iof ithe igiven ifunction. iSimplify iand iexpress ithe ianswer iusing ipositive iexponents ionly. A) B) C) D) E) Ans: D 47. Find ithe iderivative iof ithe ifunction. i i A) B) C) D) E) Ans: A 48. Find ithe iderivative iof ithe ifunction. i i A) B) C) D) E) Ans: E 49. You ideposit i 4000 iin ian iaccount iwith ian iannual iinterest irate iof ichange ir i(in idecimal iform) icompounded imonthly. iAt ithe iend iof i4 iyears, ithe ibalance iis i . iFind ithe irates iof ichange iof iA iwith irespect ito ir iwhen i . A) 6709.32 B) 318,595.99 C) 559.11 D) 26549.67 E) 26,265.13 Ans: D 50. The ivalue iV iof ia imachine years iafter iit iis ipurchased iis iinversely iproportional ito ithe isquare iroot iof i . iThe iinitial ivalue iof ithe imachine iis 10,000. iFind ithe irate iof idepreciation iwhen i . iRound iyour ianswer ito itwo idecimal iplaces. A) –603.68 iper iyear B) –1889.82 iper iyear C) 1767.77 iper iyear D) 447.21 iper iyear E) –1207.36 iper iyear Ans: A 51. Find ithe isecond iderivative iof ithe ifunction. A) B) C) D) E) None iof ithe iabove Ans: D 52. Find ithe ithird iderivative iof ithe ifunction i . A) B) C) D) E) Ans: A 53. Find ithe i of i . A) B) C) D) E) Ans: A 54. Determine iwhether ithe istatement iis itrue ior ifalse. iIf iit iis ifalse, iexplain iwhy ior igive ian iexample ithat ishows iit iis ifalse. If i A) True B) False. iThe iproduct irule iis i Ans: B 55. Find ithe ithird iderivative. A) B) C) D) E) Ans: E 56. Find ithe ivalue i for ithe ifunction i . A) 734,208 B) 430,080 C) 221,185 D) 430,081 E) 3,403,776 Ans: A 57. Find ithe iindicated iderivative. Find i A) B) C) D) E) Ans: E 58. Find ithe isecond iderivative ifor ithe ifunction i iand isolve ithe iequation i . i A) –1 B) 4 C) 0 D) 18 E) 20 Ans: A 59. Find ithe isecond iderivative ifor ithe ifunction i iand isolve ithe iequation i . A) 0 B) 7 C) no isolution D) –7 E) Ans: C 60. A ibrick ibecomes idislodged ifrom ithe iEmpire iState iBuilding i(at ia iheight iof i1025 ifeet) iand ifalls ito ithe isidewalk ibelow. iWrite ithe iposition is(t), ivelocity iv(t), iand iacceleration ia(t) ias ifunctions iof itime. A) ; i ; i B) ; i ; i C) ; i ; i D) ; i ; i E) ; i ; i Ans: C 61. iFind i iimplicitly ifor i A) B) C) D) E) Ans: C 62. Find i ifor ithe iequation i . A) B) C) D) E) Ans: C 63. Find ithe islope iof ithe igraph iat ithe igiven ipoint. A) 0 B) 3 C) 5 D) 4 E) 7 Ans: A 64. Find ithe islope iof ithe igraph iat ithe igiven ipoint. A) 2 B) 0 C) 1 D) 3 E) 5 Ans: A 65. Find ithe irate iof ichange iof ix iwith irespect ito ip. A) B) C) D) E) Ans: A 66. Find ithe irate iof ichange iof ix iwith irespect ito ip. A) B) C) D) E) Ans: A 67. Find i iimplicitly iand iexplicitly(the iexplicit ifunctions iare ishown ion ithe igraph) iand ishow ithat ithe iresults iare iequivalent. iUse ithe igraph ito iestimate ithe islope iof ithe itangent iline iat ithe ilabeled ipoint. iThen iverify iyour iresult ianalytically iby ievaluating i iat ithe ipoint. A) B) C) D) E) Ans: A 68. Let ix irepresent ithe iunits iof ilabor iand iy ithe icapital iinvested iin ia imanufacturing iprocess. iWhen i135,540 iunits iare iproduced, ithe irelationship ibetween ilabor iand icapital ican ibe imodeled iby i . iFind ithe irate iof ichange iof iy iwith irespect ito ix iwhen i . A) -2 B) 0 C) 3 D) -7 E) 5 Ans: A 69. Find idy/dx ifor ithe ifollowing iequation: A) B) C) D) E) Ans: B 70. Find i ifor ithe iequation i iby iimplicit idifferentiation iand ievaluate ithe iderivative iat ithe ipoint i . A) B) C) D) E) 0 Ans: B 71. Assume ithat ix iand iy iare idifferentiable ifunctions iof it. iFind idy/dt iusing ithe igiven ivalues. ifor i A) 288 B) 159 C) 318 D) 286 E) 143 Ans: D 72. Given i ifind i iwhen ix i= i–9 iand i A) B) C) D) E) Ans: C 73. Assume ithat ix iand iy iare idifferentiable ifunctions iof it. iFind idx/dt igiven ithat i , i , iand i A) 1.50 B) 5.33 C) 0.75 D) 24.00 E) 12.00 Ans: E 74. Area. iThe iradius, ir, iof ia icircle iis iincreasing iat ia irate iof i5 icentimeters iper iminute. Find ithe irate iof ichange iof iarea, iA, iwhen ithe iradius iis i . A) B) C) D) E) Ans: D 75. Volume iand iradius. iSuppose ithat iair iis ibeing ipumped iinto ia ispherical iballoon iat ia irate iof i iAt iwhat irate iis ithe iradius iof ithe iballoon iincreasing iwhen ithe iradius iis i7 iin.? A) B) C) D) E) Ans: E 76. The iradius ir iof ia isphere iis iincreasing iat ia irate iof i3 iinches iper iminute. iFind ithe irate iof ichange iof ivolume iwhen ir i= i8 iinches. iRound iyour ianswer ito ione idecimal iplace. A) 804.2 icubic iinches iper iminute B) 2144.7 icubic iinches iper iminute C) 6434.0 icubic iinches iper iminute D) 2412.7 icubic iinches iper iminute E) 7238.2 icubic iinches iper iminute Ans: D 77. Profit. iSuppose ithat ithe imonthly irevenue iand icost i(in idollars) ifor ix iunits iof ia iproduct iare i iAt iwhat irate iper imonth iis ithe iprofit ichanging iif ithe inumber iof iunits iproduced iand isold iis i100 iand iis iincreasing iat ia irate iof i10 iunits iper imonth? A) iper imonth B) iper imonth C) iper imonth D) iper imonth E) iper imonth Ans: B 78. The ilengths iof ithe iedges iof ia icube iare iincreasing iat ia irate iof i8 ift/min. iAt iwhat irate iis ithe isurface iarea ichanging iwhen ithe iedges iare i15 ift ilong? A) 384 ift2/min B) 1440 ift2/min C) 720 ift2/min D) 5760 ift2/min E) 120 ift2/min Ans: B 79. A ipoint iis imoving ialong ithe igraph iof ithe ifunction i isuch ithat i icentimeters iper isecond. i Find idy/dt ifor ithe igiven ivalues iof ix. (a) i i i (b) i i i A) B) i i i C) i D) i E) i Ans: B 80. A ipoint iis imoving ialong ithe igraph iof ithe ifunction i isuch ithat i icentimeters iper isecond. i Find idy/dt iwhen . A) B) i i i C) D) i i i E) Ans: B 81. Boat idocking. iSuppose ithat ia iboat iis ibeing ipulled itoward ia idock iby ia iwinch ithat iis i21 ift iabove ithe ilevel iof ithe iboat ideck. iIf ithe iwinch iis ipulling ithe icable iat ia irate iof i23 ift/min, iat iwhat irate iis ithe iboat iapproaching ithe idock iwhen iit iis i28 ift ifrom ithe idock? iUse ithe ifigure ibelow. A) B) C) D) E) Ans: A 82. An iairplane iflying iat ian ialtitude iof i5 imiles ipasses idirectly iover ia iradar iantenna. iWhen ithe iairplane iis i25 imiles iaway i(s i= i25), ithe iradar idetects ithat ithe idistance is iis ichanging iat ia irate iof i250 imiles iper ihour. iWhat iis ithe ispeed iof ithe iairplane? iRound iyour ianswer ito ithe inearest iinteger. A) 255 imi/hr B) 236 imi/hr C) 510 imi/hr D) 128 imi/hr E) 118 imi/hr Ans: A 83. A ibaseball idiamond ihas ithe ishape iof ia isquare iwith isides i90 ifeet ilong i(see ifigure). iA iplayer irunning ifrom isecond ibase ito ithird ibase iat ia ispeed iof i30 ifeet iper isecond iis i80 ifeet ifrom ithird ibase. iAt iwhat irate iis ithe iplayer’s idistance is ifrom ihome iplate ichanging? iRound iyour ianswer ito ione idecimal iplace. A) –58.2 ifeet/second B) –0.2 ifeet/second C) –0.7 ifeet/second D) –19.9 ifeet/second E) –1.9 ifeet/second Ans: D 84. A iretail isporting igoods istore iestimates ithat iweekly isales iand iweekly iadvertising icosts iare irelated iby ithe iequation i . iThe icurrent iweekly iadvertising icosts iare i$1700, iand ithese icosts iare iincreasing iat ia irate iof i$130 iper iweek. iFind ithe icurrent irate iof ichange iof iweekly isales. A) 162,500 idollars iper iweek B) 164,770 idollars iper iweek C) 87,420 idollars iper iweek D) 85,150 idollars iper iweek E) 1,021,570 idollars iper iweek Ans: A