Please # 39, 43, 47, 49, 59, 65, 67

39-48 Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function. 39. f(x) = arctan (x?) 40. f(x) = sin (7x/4) 41. f(x) = x cos 2x 42. f (x) = e3x - e2x 43. f(x) = x cos(2x2) 44. f(x) = x2 In(1 + x3)45. f(x) = 46. f(x) = 63-66 Use series to approximate the definite integral to within V4+ x2 V2 + x the indicated accuracy. 47. f(x) = sin x Hint: Use sin2x = (1 - cos 2x).] 63. x' arctan x dx (four decimal places) x - sin x if x * 0 64. sin(x*) dx (four decimal places) 48. f(x) = if x = 0 65. VI + x dx (lerror) (-1)" n x 4 n! 80. E(-1) "-1 2 4 "=0 n 58. (a) Expand 1/V/1 + x as a power series. (b) Use part (a) to estimate 1/41.1 correct to three decimal x2n+1 x2n+1 81. (-1)" places. 22"+1 ( 2n + 1 ) 82. 2(-1)" - 2 2 + 1 ( 2n + 1 ) ! 59-62 Evaluate the indefinite integral as an infinite series. 83-90 Find the sum of the series. 59. ( Vitx dx 60. x2 sin(x?) dx 83. (-1)" 84. (-1)" TT 20 n! 7 0 62"(2n)! 61. [ cos x -dx 62. arctan(x?) dx 85. E (-1)"-1 3" 86. 3" n 5" 7 0 5" n