Larson Calculus Ch10 Series and Taylor Polynomials

1. Write ithe ifirst ifive iterms iof ithe isequence. an i= i A) B) C) D) E) none iof ithe iabove Ans: B 2. Write ithe ifirst ifive iterms iof ithe isequence. an i= i A) B) C) D) E) Ans: A 3. Find ithe ilimit iof ithe isequence i . A) B) C) D) E) The isequence idiverges. Ans: C 4. Find ithe ilimit iof ithe ifollowing isequence. A) B) C) D) E) The isequence idiverges. Ans: A 5. Find ithe ilimit iof ithe ifollowing isequence. A) B) 1 C) 2 D) E) The isequence idiverges. Ans: E 6. Find ithe ilimit iof ithe ifollowing isequence. A) –1 B) 1 C) D) 2 E) The isequence idiverges. Ans: C 7. Determine ithe iconvergence ior idivergence iof ithe isequence i . iIf ithe isequence iconverges, iuse ia isymbolic ialgebra iutility ito ifind iits ilimit. A) 7 B) 1 C) 2 D) E) The isequence idiverges. Ans: A 8. Write ian iexpression ifor ithe inth iterm iof ithe isequence i2, i8, i26, i80, i.... A) B) C) i D) E) Ans: C 9. Write ian iexpression ifor ithe inth iterm iof ithe isequence. A) B) C) D) E) Ans: C 10. Write ian iexpression ifor ithe inth iterm iof ithe isequence i . A) B) C) D) E) Ans: A 11. What iare ithe inext ithree iterms iin ithe iarithmetic isequence i ? A) B) C) D) E) Ans: A 12. Find ithe inext ithree iterms iof ithe igeometric isequence. A) B) C) D) E) Ans: B 13. Give ian iexample iof ia isequence ithat iconverges ito i . A) B) C) D) E) Ans: D 14. Consider ithe isequence i(An) iwhose inth iterm iis igiven iby iAn i where iP iis ithe iprincipal, iAn iis ithe iamount iof icompound iinterest iafter in imonths, iand ir iis ithe iannual ipercentage irate. iWrite ithe ifirst ifour iterms iof ithe isequence ifor iP i= i 9,500 iand ir i= i0.04. iRound iyour ianswer ito itwo idecimal iplaces. A) 9531.67, i9573.51, i9620.26, i9627.30 B) 9532.67, i9573.51, i9620.26, i9660.34 C) 9531.67, i9563.44, i9595.32, i9627.30 D) 9532.67, i9573.51, i9595.32, i9627.30 E) 9532.67, i9563.44, i9595.32, i9660.34 Ans: C 15. A ideposit iof i 800 iis imade ieach imonth iin ian iaccount ithat iearns i8.4% iinterest, icompounded imonthly. iThe ibalance iin ithe iaccount iafter in imonths iis igiven iby . iFind ithe ibalance iafter i20 iyears iby icomputing ithe i240th iterm iof ithe isequence. iRound iyour ianswer ito itwo idecimal iplaces. A) $696,946.54 B) $1,018,546.54 C) $24,073.84 D) $343,954.07 E) $1,125.60 Ans: A 16. A iball iis idropped ifrom ia iheight iof i10 ifeet, iand ion ieach irebound iit irises ito i iits ipreceding iheight. iWrite ian iexpression ifor ithe iheight iof ithe inth irebound. A) B) C) D) E) Ans: B 17. Write ithe ifirst ifive iterms iof ithe isequence iof ipartial isums. i A) B) C) D) E) Ans: C 18. Find ithe isum iof ithe iconvergent iseries. A) B) C) D) 7 E) 1 Ans: A 19. Find ithe isum iof ithe iconvergent iseries. A) B) C) D) E) Ans: D 20. Determine ithe iconvergence ior idivergence iof ithe ifollowing iseries. iUse ia isymbolic ialgebra iutility ito iverify iyour iresult. A) The iseries iconverges. B) The iseries idiverges. Ans: B 21. Determine ithe iconvergence ior idivergence iof ithe iseries i . iUse ia isymbolic ialgebra iutility ito iverify iyour iresult. A) The iseries iconverges. B) The iseries idiverges. Ans: A 22. Determine ithe iconvergence ior idivergence iof ithe iseries i . iUse ia isymbolic ialgebra iutility ito iverify iyour iresult. A) The iseries iconverges. B) The iseries idiverges. Ans: B 23. The irepeating idecimal i iis iexpressed ias ia igeometric iseries i . iWrite ithe idecimal i ias ithe iratio iof itwo iintegers. A) i B) C) D) E) Ans: C 24. Express ithe ivalue iof ithe igiven irepeating idecimal ias ia ifraction. i[Hint: iWrite ias ian iinfinite iseries.] A) B) C) D) E) Ans: D 25. A icompany iproduces ia inew iproduct ifor iwhich iit iestimates ithe iannual isales ito ibe i7000 iunits. iSuppose ithat iin iany igiven iyear i % iof ithe iunits i(regardless iof iage) iwill ibecome iinoperative. iHow imany iunits iwill ibe iin iuse iafter in iyears? A) i B) C) D) E) Ans: A 26. Bouncing iBall. iA iball idropped ifrom ia iheight iof i38 ifeet ibounces ito i iof iits iformer iheight iwith ieach ibounce. iFind ithe itotal ivertical idistance ithat ithe iball itravels. A) 266 ifeet B) 304 ifeet C) 146 ifeet D) 104 ifeet E) 152 ifeet Ans: A 27. The iannual ispending iby itourists iin ia iresort icity iis i300 imillion idollars. iApproximately i50% iof ithat irevenue iis iagain ispent iin ithe iresort icity, iand iof ithat iamount iapproximately i50% iis iagain ispent iin ithe iresort icity. iIf ithis ipattern icontinues, iwrite ithe igeometric iseries ithat igives ithe itotal iamount iof ispending igenerated iby ithe i300 imillion idollars i(including ithe iinitial ioutlay iof i300 imillion idollars) iand ifind ithe isum iof ithe iseries. A) The igeometric iseries iis i . The isum iof ithe iseries iis i 600.00 imillion. B) The igeometric iseries iis i . The isum iof ithe iseries iis i 15,000 imillion. C) The igeometric iseries iis i . The isum iof ithe iseries iis i 600.00 imillion. D) The igeometric iseries iis i . The isum iof ithe iseries iis i 15,000 imillion. E) The igeometric iseries iis i . The isum iof ithe iseries iis i 150.00 imillion. Ans: C 28. You iaccept ia ijob ithat ipays ia isalary iof i 70,000 ithe ifirst iyear. iDuring ithe inext i39 iyears, iyou iwill ireceive ia i6% iraise ieach iyear. iWhat iwould ibe iyour itotal icompensation iover ithe i40-year iperiod? iRound iyour ianswer ito ithe inearest iinteger. A) 10,833,338 B) 1,166,667 C) 65,800 D) 420,000 E) 4,200 Ans: A 29. A ifactory iis ipolluting ia iriver isuch ithat iat ievery imile idown iriver ifrom ithe ifactory ian ienvironmental iexpert ifinds i15% iless ipollutant ithan iat ithe ipreceding imile. iIf ithe ipollutant’s iconcentration iis i500 ippm i(parts iper imillion) iat ithe ifactory, iwhat iis iits iconcentration i15 imiles idown iriver? A) 75.00 ippm B) 225.00 ippm C) 43.68 ippm D) 588.24 ippm E) 51.38 ippm Ans: C 30. Determine iwhether ithe iseries i iis ia ip-series. A) is inot ia series. B) is ia series. Ans: B 31. Determine ithe iconvergence ior idivergence iof ithe ip-series i . A) The iseries idiverges. B) The iseries iconverges. Ans: A 32. Determine ithe iconvergence ior idivergence iof ithe ifollowing ip-series. A) The iseries iconverges. B) The iseries idiverges. Ans: B 33. Use ithe iRatio iTest ito idetermine ithe iconvergence ior idivergence iof ithe iseries. A) Ratio iTest iis iinconclusive B) diverges C) converges Ans: B 34. Use ithe iRatio iTest ito idetermine ithe iconvergence ior idivergence iof ithe iseries. A) converges B) diverges C) Ratio iTest iis iinconclusive Ans: A 35. Use ithe iRatio iTest ito idetermine ithe iconvergence ior idivergence iof ithe iseries i . A) The iseries iconverges. B) The iseries idiverges. Ans: A 36. Approximate ithe isum iof ithe iconvergent iseries i iusing ithree iterms. iEstimate ithe imaximum ierror iof iyour iapproximation. iRound iyour ianswers ito ifour idecimal iplaces. A) The iapproximate ivalue iis i2.1854. The imaximum ierror iof iyour iapproximation iis i0.0588. B) The iapproximate ivalue iis i1.1620. The imaximum ierror iof iyour iapproximation iis i0.0556. C) The iapproximate ivalue iis i2.1676. The imaximum ierror iof iyour iapproximation iis i0.0721. D) The iapproximate ivalue iis i3.1591. The imaximum ierror iof iyour iapproximation iis i1.0527. E) The iapproximate ivalue iis i1.1644. The imaximum ierror iof iyour iapproximation iis i0.0573. Ans: B 37. Determine ithe iconvergence ior idivergence iof ithe ifollowing iseries. A) converges B) diverges Ans: A 38. Determine ithe iconvergence ior idivergence iof ithe iseries. A) diverges B) converges C) inconclusive Ans: B 39. Determine ithe iconvergence ior idivergence iof ithe iseries. A) inconclusive B) diverges C) converges Ans: C 40. Test ithe iseries i ifor iconvergence ior idivergence iusing iany iappropriate itest. A) diverges B) converges Ans: B 41. Test ithe iseries i ifor iconvergence ior idivergence iusing iany iappropriate itest. A) diverges B) converges Ans: A 42. Write ithe ifirst ifive iterms iof ithe ipower iseries i . A) B) C) D) E) Ans: C 43. Find ithe iradius iof iconvergence iof ithe iseries i . A) 14 B) 16 C) 1 D) 8 E) 7 Ans: E 44. Find ithe iradius iof iconvergence iof ithe ipower iseries. A) 0 B) 10 C) 20 D) 100 E) Ans: E 45. Find ithe iradius iof iconvergence iof ithe iseries i . A) 14 B) 5 C) 1 D) 9 E) 8 Ans: C 46. Find ithe iradius iof iconvergence iof ithe ipower iseries. A) B) 1 C) D) -1 E) 0 Ans: C 47. Find ithe iradius iof iconvergence iof ithe iseries i . A) 1 B) 4 C) 6 D) 8 E) 5 Ans: A 48. Apply iTaylor’s iTheorem ito ifind ithe ipower iseries icentered iat i ifor ithe ifunction i . A) B) C) D) E) Ans: C 49. Apply iTaylor’s iTheorem ito ifind ithe ipower iseries icentered iat i ifor ithe ifunction i . A) B) C) D) E) Ans: C 50. Find ithe iradius iof iconvergence icentered iat i ifor ithe ifollowing ifunction. A) 3 B) 2 C) 0 D) 1 E) Ans: D 51. Find ithe iradius iof iconvergence iof i iwhere i . A) 1 B) C) D) 8 E) 16 Ans: D 52. Find ithe ipower iseries ifor ithe ifunction i iusing ithe ipower iseries ifor i . A) B) C) D) E) Ans: B 53. Find ithe ipower iseries ifor ithe ifunction i iusing ithe ipower iseries ifor i . A) B) C) D) E) Ans: D 54. Integrate ithe iseries ifor i ito ifind ithe ipower iseries ifor ithe ifunction i . A) B) C) D) E) Ans: E 55. Differentiate ithe iseries ifor i ito ifind ithe ipower iseries ifor ithe ifunction i . A) B) C) D) E) Ans: C 56. Find ithe ithird iTaylor ipolynomial iat i ifor ithe igiven ifunction. i i i A) B) C) D) E) Ans: E 57. Find ithe ithird idegree iTaylor ipolynomial icentered iat ic i= i4 ifor ithe ifunction. A) B) C) D) E) Ans: A 58. A iTaylor ipolynomial iapproximation iof i iis igiven ibelow. iUse ia igraphing iutility ito igraph iboth ifunctions. A) B) C)