Solve the following problems: Show the complete table of iteration using MS Excel. Find the greatest positive root of the given function: f(x) = 0.3 + e^(-0.5x) (cos^2x + 3sin^2x). Use Bisection Method. b) Use False Position Method. 2. Find the positive root of the given function: f(x) = x^3 - 2x^2 tanx + 1. Use Newton Raphson Method. b) Use Secant Method. Find any point of intersection using Newton Raphson Method for the system of nonlinear equations: f(x,y) = x^2 + y^2 - 4 g(x,y) = x^3 + y^2 - 6xy.
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Find the greatest positive root of the given function: f(x) = 0.3 + e^(-0.5x) (cos(2x) + 3sin(2x)) a) Bisection Method To use the Bisection Method, we first need to find an interval [a, b] such that f(a) * f(b) < 0. Let's take a = 0 and b = 2 as our initial Show more…
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PROBLEM 1 [Solving Nonlinear Equations] [20 marks] 1. Practice Solve the following nonlinear equation using the secant method with x0=0.5 and x1=0.4: f(x) = 8sin(x)e^-x - 1 Use 3 iterations. Check your result and discuss. 2. Theory - Discuss the difference between bracketing and open methods for root location - Sketch the bisection and the Newton-Raphson method.
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Q.1) Solve one of the positive roots of the following non-linear function and compute the approximate interval (a, b) using Rolle's theorem with a step size of Ax = 1. b) Using these interval values (a, b) as initial guesses, calculate the true root of the function using the Secant Method. Compute only for three iterations. c) Write a C++ program for Rolle's theorem. f(x) = x*sin(x) + 1 = 0
Problem (1): Find a zero point of the equation f(x) = x^2 - 2 by using Newton Raphson methods. If initial guess: x_0 = 6. Problem (2): Use Newton's Method to find the only real root of the equation x^3 - x - 1 = 0, correct to 9 decimal places, and take an initial guess x_0 = 1.5. Problem (3): Find this root by using Bisection method of the equation f(x) = x^2 - 3 with initial interval [1,2]. Problem (4): Find this root by using Bisection method of the equation x - cos(x), with initial interval [0,1]. Problem (5): find the root of the following equation by using fixed point iteration x - sin(x) - 0.5 = 0, and take an initial guess x_0 = 1.5. Problem (6): Find this root by using False position method of the equation f(x) = x^2 - 3 with initial interval [1,2]. Problem (7): by using secant method, find a root of the function f(x) = cos(x) + 2 sin(x) + x^2. Use x_0 = 0 and x_1 = -0.1 as an initial approximation. The error must be less than 0.001.
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