Calculus Briggs.pdf D PDF b My Questions | bartleby Microsoft account | Reward: C.S.HomeworkCodes.docx - Single Variable.pdf Single Variable.pdf W PDF FA X Find on page Options Enter text to search No results Add notes Fit to page Page view A Read aloud of 1442 707 Contents 9.2 Properties of Power Series 683 1 Basic Skills 44. g(x) using f(x) (12)2 1 x2 9-28. Interval and radius of convergence Determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence 1 45. g(x)n (1 - 3x) using f(x) 1 3x (2x) (x 1) 11. Σ2 )* 10. У k! 9. 46. g(x) n 1 x2) using f(x) 1 + x2 (x -1) 12. > k! 13. 2kx 14.k! (x 10)* 47-52. Functions to power series Find power series representations centered at 0 for the following functions using known power series. Give the interval of convergence for the resulting series. 21) k 16. -3) sin 15. 17. 1 1 48. f(x) 1 47. f(x) .2 1 + x x4 К(х — 4)* 20. Σ(-1" Σ-1y 5k 19. У 18. 2k 49. f(x) 3 50. f(x)In Vi - r2 3 x k2x2k 21. > k! x2k1 22. 2k (x-1) 23. 52. f(x) tan (4x2) 51. f(x) In V4 - x2 3k-1 (-2) (x 3) Further Explorations 1)k (k 1 2k (x 25.> 24.> 10 26. 3k+1 53. Explain why or why not Determine whether the following state ments are true and give an explanation or counterexample a. The interval of convergence of the power series 2ck (x - 3) could be (-2, 8) b. The series 2(-2r) converges on the interval - x < z. c. If f(x) £ckx^ on the interval |x|<1, then f(x2) ECkx2 on the interval x|1 d. If f(x) c xk Ck 0, for all k 28. 2-1) 27* 27. (2k1) 29-34. Combining power series Use the geometric series 1 x, for x f(x) 1 1, k 0 0, for all x on an interval (-a, a), then to find the power series representation for the following functions (centered at 0). Give the interval of convergence of the new series 54. Radius of convergence Find the radius of convergence of 3 Σ(1 1 29. f(3x) 30. g(x) 1 3x k 2x3 1 55. Radius of convergence Find the radius of convergence of 32. f(x3) 1 31. h(x) х3 1 4x12 33. p(x) 1 34. f(-4x) 56-59. Summation notation Write the following power series in sum- 14x _ X 8:28 PM Type here to search N W 6 PDF 10/17/2019 DD