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Experiment 13: Roots Finding of Nonlinear Equations (Newton Raphson and Bisection methods) 1. Using Newton Raphson method Find the smallest positive zero of: f(x) = x* - 6.4x + 6.45x² + 20.538x – 31.752 Near to x 2

Experiment 13: Roots Finding of Nonlinear Equations (Newton Raphson and Bisection methods) 1. Using Newton Raphson method Find the smallest positive zero of: f(x) = x* - 6.4x + 6.45x² + 20.538x – 31.752 Near to x 2

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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Experiment 13: Roots Finding of Nonlinear Equations (Newton Raphson and Bisection methods) 1. Using Newton Raphson method Find the smallest positive zero of: f(x) = x* – 6.4x³ + 6.45x2 + 20.538x – 31.752 Near to x = 2 2. Use MATLAB to sketch the graph y f(x) for each of the following functions, and verify from the graph that f(a) and f(b), where a and b defined below, have opposite signs. Then, use Newton's method to estimate the root of f(x) = 0 that lies between a and b. a. f,(x) = x'+x- 3 a = 1 b = 2 b. f,(x) = /2x +1-x+ 4 a = 2 b = 4 Hint: Start with x, (a+b)/2 3. Find the zero of fix)=x-tan(x) in the interval (4,20) by the method of bisection Using Matlab codes. Using both Newton Raphson and Bisection methods 4. A root of f(x) = x - 10x? + 5 = 0 lies close to x-0.7. Compute this root with the Newton- Raphson method. 29
Transcribed Image Text:Experiment 13: Roots Finding of Nonlinear Equations (Newton Raphson and Bisection methods) 1. Using Newton Raphson method Find the smallest positive zero of: f(x) = x* – 6.4x³ + 6.45x2 + 20.538x – 31.752 Near to x = 2 2. Use MATLAB to sketch the graph y f(x) for each of the following functions, and verify from the graph that f(a) and f(b), where a and b defined below, have opposite signs. Then, use Newton's method to estimate the root of f(x) = 0 that lies between a and b. a. f,(x) = x'+x- 3 a = 1 b = 2 b. f,(x) = /2x +1-x+ 4 a = 2 b = 4 Hint: Start with x, (a+b)/2 3. Find the zero of fix)=x-tan(x) in the interval (4,20) by the method of bisection Using Matlab codes. Using both Newton Raphson and Bisection methods 4. A root of f(x) = x - 10x? + 5 = 0 lies close to x-0.7. Compute this root with the Newton- Raphson method. 29
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