11.11: A.11.3- Section 11.3 Answers
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1. C(x)=L23+4L2π2∑∞n=1(−1)nn2cosnπxL
2. C(x)=12+4π2∑∞n=11(2n−1)2cos(2n−1)πx
3. C(x)=−2L23+4L2π2∑∞n=11n2cosnπxL
4. C(x)=1−coskπkπ−2kπ∑∞n=1[1−(−1)ncoskπn2−k2cosnx
5. C(x)=12−2π∑∞n=1(−1)n2n−1cos(2n−1)πxL
6. C(x)=−2L23+4L2π2∑∞n=1(−1)nn2cosnπxL
7. C(x)=13+4π2∑∞n=11n2cosnπx
8. C(x)=eπ−1π+2π∑∞n=1[(−1)neπ−1](n2+1)cosnx
9. C(x)=L26−L2π2∑∞n=11n2cos2nπxL
10. C(x)=−2L23+4L2π2∑∞n=11n2cosnπxL
11. S(x)=4π∑∞n=11(2n−1)sin(2n−1)πxL
12. S(x)=2π∑∞n=11nsinnπx
13. S(x)=2π∑∞n=1[1−(−1)ncoskπ]nn2−k2sinnx
14. S(x)=2π∑∞n=11n[1−cosnπ2]sinnπxL
15. S(x)=4Lπ2∑∞n=1(−1)n+1(2n−1)2sin(2n−1)πxL
16. S(x)=π2sinx−16π∑∞n=1n(4n2−1)2sin2nx
17. S(x)=−2π∑∞n=1n[(−1)neπ−1](n2+1)sinnx
18. CM(x)=−4π∑∞n=1(−1)n2n−1cos(2n−1)πx2L
19. CM(x)=−4L2π∑∞n=1(−1)n2n−1[1−8(2n−1)2π2]cos(2n−1)πx2L
20. CM(x)=−4π∑∞n=1[(−1)n+2(2n−1)π]cos(2n−1)πx2
21. CM(x)=−4π∑∞n=112n−1cos(2n+1)π4cos(2n−1)πx2L
22. CM(x)=4π∑∞n=1(−1)n2n−1(2n−3)(2n+1)cos(2n−1)x2
23. CM(x)=−8π∑∞n=11(2n−3)(2n+1)cos(2n−1)x2
24. CM(x)=−8L2π2∑∞n=11(2n−1)2[1+4(−1)n(2n−1)π]cos(2n−1)πx2L
25. SM(x)=4π∑∞n=11(2n−1)sin(2n−1)πx2L
26. SM(x)=−16L2π2∑∞n=11(2n−1)2[(−1)n+2(2n−1)π]sin(2n−1)πx2L
27. SM(x)=4π∑∞n=112n−1[1−cos(2n−1)π4]sin(2n−1)πx2L
28. SM(x)=4π∑∞n=12n−1(2n−3)(2n+1)sin(2n−1)x2
29. SM(x)=8π∑∞n=1(−1)n(2n−3)(2n+1)sin(2n−1)x2
30. SM(x)=8L2π2∑∞n=11(2n−1)2[(−1)n+4(2n−1)π]sin(2n−1)πx2L
31. C(x)=−7L45−144L4π4∑∞n=1(−1)nn4cosnπxL
32. C(x)=−2L45−48L4π4∑∞n=11+(−1)n2n4cosnπxL
33. C(x)=3L45−48L4π4∑∞n=12+(−1)nn4cosnπxL
34. C(x)=L430−3L4π4∑∞n=11n4cos2nπxL
36. S(x)=8L2π3∑∞n=11(2n−1)3sin(2n−1)πxL
37. S(x)=−4L3π3∑∞n=1(1+(−1)n2)n3sinnπxL
38. S(x)=−12L3π3∑∞n=1(−1)nn3sinnπxL
39. S(x)=96L4π5∑∞n=11(2n−1)5sin(2n−1)πxL
40. S(x)=−720L5π5∑∞n=1(−1)nn5sinnπxL
41. S(x)=−240L5π5∑∞n=11+(−1)n2n5sinnπxL
43. CM(x)=−64L3π3∑∞n=11(2n−1)3[(−1)n+3(2n−1)π]cos(2n−1)πx2L
44. CM(x)=−32L2π3∑∞n=1(−1)n(2n−1)3cos(2n−1)πx2L
45. CM(x)=−96L3π3∑∞n=11(2n−1)3[(−1)n+2(2n−1)π]cos(2n−1)πx2L
46. CM(x)=96L3π3∑∞n=11(2n−1)3[(−1)n3+4(2n−1)π]cos(2n−1)πx2L
47. CM(x)=96L3π3∑∞n=11(2n−1)3[(−1)n5+8(2n−1)π]cos(2n−1)πx2L
48. CM(x)=−384L4π4∑∞n=11(2n−1)4[1+(−1)n4(2n−1)π]cos(2n−1)πx2L
49. CM(x)=−768L4π4∑∞n=11(2n−1)4[1+(−1)n2(2n−1)π]cos(2n−1)πx2L
51. SM(x)=32L2π3∑∞n=11(2n−1)3sin(2n−1)πx2L
52. SM(x)=−96L3π3∑∞n=11(2n−1)3[1+(−1)n4(2n−1)π]sin(2n−1)πx2L
53. SM(x)=96L3π3∑∞n=11(2n−1)3[1+(−1)n2(2n−1)π]sin(2n−1)πx2L
54. SM(x)=192L3π4∑∞n=1(−1)n(2n−1)4sin(2n−1)πx2L
55. SM(x)=1536L4π4∑∞n=11(2n−1)4[(−1)n+3(2n−1)π]sin(2n−1)πx2L
56. SM(x)=384L4π4∑∞n=11(2n−1)4[(−1)n+4(2n−1)π]sin(2n−1)πx2L