Loading [MathJax]/jax/output/HTML-CSS/jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

A.7.6: Section 7.6 Answers

( \newcommand{\kernel}{\mathrm{null}\,}\)

1. y1=x(1x+34x21336x3+);y2=y1lnx+x2(1x+65108x2+)

2. y1=x1(12x+92x2203x3+);y2=y1lnx+1154x+13318x2+

3. y1=1+xx2+13x3+;y2=y1lnxx(312x3118x2+)

4. y1=x1/2(12x+52x22x3+);y2=y1lnx+x3/2(194x+176x2+)

5. y1=x(14x+192x2493x3+);y2=y1lnx+x2(3434x+2089x2+)

6. y1=x1/3(1x+56x212x3+);y2=y1lnx+x2/3(11112x+2536x2+)

7. y1=12x+74x279x3+;y2=y1lnx+x(3154x+239108x2+)

8. y1=x2(12x+52x23x3+);y2=y1lnx+34136x+

9. y1=x1/2(1x+14x2+118x3+);y2=y1lnx+x1/2(321316x+154x2+)

10. y1=x1/4(114x732x2+23384x3+);y2=y1lnx+x3/4(14+564x1572304x2+)

11. y1=x1/3(1x+76x22318x3+);y2=y1lnxx5/3(11213108x)

12. y1=x1/2n=0(1)n(n!)2xn;y2=y1lnx2x1/2n=1(1)n(n!)2(nj=11j)xn

13. y1=x1/6n=0(23)nnj=1(3j+1)n!xn;y2=y1lnxx1/6n=1(23)nnj=1(3j+1)n!(nj=11j(3j+1))xn

14. y1=x2n=0(1)n(n+1)2xn;y2=y1lnx2x2n=1(1)nn(n+1)xn

15. y1=x3n=02n(n+1)xn;y2=y1lnxx3n=12nnxn

16. y1=x1/5n=0(1)nnj=1(5j+1)125n(n!)2xn;y2=y1lnxx1/5n=1(1)nnj=1(5j+1)125n(n!)2(nj=15j+2j(5j+1))xn

17. y1=x1/2n=0(1)nnj=1(2j3)4nn!xn;y2=y1lnx+3x1/2n=1(1)nnj=1(2j3)4nn!(nj=11j(2j3))xn

18. y1=x1/3n=0(1)nnj=1(6j7)281n(n!)2xn;y2=y1lnx+14x1/3n=1(1)nnj=1(6j7)281n(n!)2(nj=11j(6j7))xn

19. y1=x2n=0(1)nnj=1(2j+5)(n!)2xn;y2=y1lnx2x2n=1(1)nnj=1(2j+5)(n!)2(nj=1j+5j(2j+5))xn

20. y1=1xn=0(2)nnj=1(2j1)n!xn;y2=y1lnx+1xn=1(2)nnj=1(2j1)n!(nj=11j(2j1))xn

21. y1=1xn=0(1)nnj=1(2j5)n!xn;y2=y1lnx+5xn=1(1)nnj=1(2j5)n!(nj=11j(2j5))xn

22. y1=x2n=0(1)nnj=1(2j+3)2nn!xn;y2=y1lnx3x2n=1(1)nnj=1(2j+3)2nn!(nj=11j(2j+3))xn

23. y1=x2(1+3x+32212x3+);y2=y1lnx5x1(1+54x14x2+)

24. y1=x3(1+20x+180x2+1120x3+);y2=y1lnxx4(26+324x+69683x2+)

25. y1=x(15x+854x2314536x3+);y2=y1lnx+x2(2394x+4499108x2+)

26. y1=1x+34x2712x3+;y2=y1lnx+x(134x+59x2+)

27. y1=x3(1+16x+36x2+16x3+);y2=y1lnxx2(40+150x+2803x2+)

28. y1=xm=0(1)m2mm!x2m;y2=y1lnxx2m=1(1)m2mm!(j=11j)x2m

29. y1=x2m=0(1)m(m+1)x2m;y2=y1lnxx22m=1(1)mmx2m

30. y1=x1/2m=0(1)m4mm!x2m;y2=y1lnxx1/22m=1(1)m4mm!(mj=11j)x2m

31. y1=xm=0(1)mmj=1(2j1)2mm!x2m;y2=y1lnx+x2m=1(1)mmj=1(2j1)2mm!(mj=11j(2j1))x2m

32. y1=x1/2m=0(1)mmj=1(4j1)8mm!x2m;y2=y1lnx+x1/22m=1(1)mmj=1(4j1)8mm!(mj=11j(4j1))x2m

33. y1=xm=0(1)mmj=1(2j+1)2mm!x2m;y2=y1lnxx2m=1(1)mmj=1(2j+1)2mm!(mj=11j(2j+1))x2m

34. y1=x1/4m=0(1)mmj=1(8j13)(32)mm!x2m;y2=y1lnx+132x1/4m=1(1)mmj=1(8j13)(32)mm!(mj=11j(8j13))x2m

35. y1=x1/3m=0(1)mmj=1(3j1)9mm!x2m;y2=y1lnx+x1/32m=1(1)mmj=1(3j1)9mm!(mj=11j(3j1))x2m

36. y1=x1/2m=0(1)mmj=1(4j3)(4j1)4m(m!)2x2m;y2=y1lnx+x1/2m=1(1)mmj=1(4j3)(4j1)4m(m!)2(mj=18j3j(4j3)(4j1))x2m

37. y1=x5/3m=0(1)m3mm!x2m;y2=y1lnxx5/32m=1(1)m3mm!(mj=11j)x2m

38. y1=1xm=0(1)mmj=1(4j7)2mm!x2m;y2=y1lnx+72xm=1(1)mmj=1(4j7)2mm!(mj=11j(4j7))x2m

39. y1=x1(132x2+158x43516x6+);y2=y1lnx+x(141332x2+101192x4+)

40. y1=x(112x2+18x4148x6+);y2=y1lnx+x3(14332x2+11576x4+)

41. y1=x2(134x2964x425256x6+);y2=y1lnx+1221128x22151536x4+

42. y1=x3(1178x2+85256x48518432x6+);y2=y1lnx+x1(258471512x2+1583110592x4+)

43. y1=x1(134x2+4564x4175256x6+);y2=y1lnxx(1433128x2+3951536x4+)

44. y1=1x;y2=y1lnx6+6x83x2

45. y1=1x;y2=y1lnx+4x

46. y1=(x1)2x;y2=y1lnx+33x+2n=21n(n21)xn

47. y1=x1/2(x+1)2;y2=y1lnxx3/2(3+3x+2n=2(1)nn(n21)xn)

48. y1=x2(1x)3;y2=y1lnx+x3(47x+113x26n=31n(n2)(n21)xn)

49. y1=x4x3+x5;y2=y1lnx+6x33x5

50. y1=x1/3(116x2);y2=y1lnx+x7/3(14112m=116mm(m+1)(m+1)!x2m)

51. y1=(1+x2)2;y2=y1lnx32x232x4+m=3(1)mm(m1)(m2)x2m

52. y1=x1/2(112x2+132x4);y2=y1lnx+x3/2(589128x2+m=214m+1(m1)m(m+1)(m+1)!x2m)

56. y1=m=0(1)m4m(m!)2x2m;y2=y1lnxm=1(1)m4m(m!)2(mj=11j)x2m

58. x1/21+x;x1/2lnx1+x

59. x1/33+x;x1/3lnx3+x

60. x2x2;xlnx2x2

61. x1/31+x2;x1/4lnx1+x2

62. x4+3x;xlnx4+3x

63. x1/21+3x+x2;x1/2lnx1+3x+x2

64. x(1x)2;xlnx(1x)2

65. x1/31+x+x2;x1/3lnx1+x+x2


This page titled A.7.6: Section 7.6 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

Support Center

How can we help?