In Problems 69–78, find bounds on the real zeros of each polynomial function. x* – 3x 69. - 4 70. f(x) = x - 5x2 - 36 72. f(x) = x – x³ + x – 1 74. f(x) = 3x- 3x-5x2 + 27x - 36 76. f(x) = 4x + x* + x³ + x² – 2x – 2 78. f(x) 71. f(x) = x* + x – x - 1 73. f(x) = 3x + 3x- x- 12x 12 75. f(x) = 4x - x + 2x- 2x² + x - 1 77. f(x) = -x + 3x- 4x2 - 2x + 9 %3D = -4x + 5x³ + 9x² + 3x – 12 In Problems 79–84, use the Intermediate Value Theorem to show that each polynomial function has a real zero in the given interval 79. f(x) = 8x* - 2x² + 5x – 1; [0,1] 80. f(x) = x* + &x – x² + 2; [ –1,0] 81. f(x) = 2x + 6x? – &x + 2; [ -5, -4] 82. f(x) = 3x - 10x + 9; [-3, -2] 83. f(x) = x - x + 7x- 7x- 18x + 18; [1.4, 1.5] 84. f(x) = x - 3x - 2x + 6x² + x + 2; [ 1.7, 1.8]
In Problems 69–78, find bounds on the real zeros of each polynomial function. x* – 3x 69. - 4 70. f(x) = x - 5x2 - 36 72. f(x) = x – x³ + x – 1 74. f(x) = 3x- 3x-5x2 + 27x - 36 76. f(x) = 4x + x* + x³ + x² – 2x – 2 78. f(x) 71. f(x) = x* + x – x - 1 73. f(x) = 3x + 3x- x- 12x 12 75. f(x) = 4x - x + 2x- 2x² + x - 1 77. f(x) = -x + 3x- 4x2 - 2x + 9 %3D = -4x + 5x³ + 9x² + 3x – 12 In Problems 79–84, use the Intermediate Value Theorem to show that each polynomial function has a real zero in the given interval 79. f(x) = 8x* - 2x² + 5x – 1; [0,1] 80. f(x) = x* + &x – x² + 2; [ –1,0] 81. f(x) = 2x + 6x? – &x + 2; [ -5, -4] 82. f(x) = 3x - 10x + 9; [-3, -2] 83. f(x) = x - x + 7x- 7x- 18x + 18; [1.4, 1.5] 84. f(x) = x - 3x - 2x + 6x² + x + 2; [ 1.7, 1.8]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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