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2. Determine the positive real root of In(x²) = 0.7 (a) graphically, (b) using three iterations of the bisection method, with initial guesses of x = 0.5 and XR = 2, and (c) using three iterations of the false-position method, with the same initial guesses as in (b).

2. Determine the positive real root of In(x²) = 0.7 (a) graphically, (b) using three iterations of the bisection method, with initial guesses of x = 0.5 and XR = 2, and (c) using three iterations of the false-position method, with the same initial guesses as in (b).

Advanced Engineering Mathematics
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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2. Determine the positive real root of In(x²) = 0.7 (a) graphically, (b) using three iterations of the bisection method, with initial guesses of x₁ = 0.5 and XR = 2, and (c) using three iterations of the false-position method, with the same initial guesses as in (b). 3. Employ fixed-point iteration to locate the root of f(x) = sin √√x - x Use an initial guess of Xo = 0.5 and iterate until a ≤ 0.01%. Verify that the process is linearly convergent. 4. Use (a) fixed-point iteration and (b) the Newton-Raphson method to determine a root of f(x) = -0.9x² + 1.7x + 2.5 using xo = 5. Perform the computation relative error is 0.01. 5. Determine the highest real root of f(x) = x³ - 6x² + 11x - 6.1: (a) Graphically. (b) Using the Newton-Raphson method (three iterations, xo = 3.5). (c) Using the secant method (three iterations, xa = 2.5 and xb 3.5). =
Transcribed Image Text:2. Determine the positive real root of In(x²) = 0.7 (a) graphically, (b) using three iterations of the bisection method, with initial guesses of x₁ = 0.5 and XR = 2, and (c) using three iterations of the false-position method, with the same initial guesses as in (b). 3. Employ fixed-point iteration to locate the root of f(x) = sin √√x - x Use an initial guess of Xo = 0.5 and iterate until a ≤ 0.01%. Verify that the process is linearly convergent. 4. Use (a) fixed-point iteration and (b) the Newton-Raphson method to determine a root of f(x) = -0.9x² + 1.7x + 2.5 using xo = 5. Perform the computation relative error is 0.01. 5. Determine the highest real root of f(x) = x³ - 6x² + 11x - 6.1: (a) Graphically. (b) Using the Newton-Raphson method (three iterations, xo = 3.5). (c) Using the secant method (three iterations, xa = 2.5 and xb 3.5). =
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