Need Solution for 6.15 using PYTHON PROGRAMMING?
where x is in radians. Use four iterations of the secant method with guesses of*,-1 - initial guesses of (a) Xi-1 x; 2.5, and (c) x 1-1.5 and x = 225 to locate the root. (d) Use secant method ( 0.05) to determine a root of x)-XS-1605/ + the graphical method to explain your results. 6.8 Determine the real root of x3.5 80, with the modified secant of x 0.5825 and 0.01%. Explain your results. method to within ,-0.1% using an initial guess ofXy-3.5 and =0.01 6.9 Determine the highest real root of x)--6x2+11 61 formulated as (a) Graphically (b) Using the Newton-Raphson method (three iterations, Xi = 3.5) (c) Using the secant method (three iterations,x2.5 and 6.14 Use (a) the Newton-Raphson method and (b) the modified 88.75x - 192.0375x 116.35x + 31.6875 using an initial guess 6.15 The "divide and average" method, an old-time method for ' = 1.0 and x, = 3.0; (b) 4-1-1.5 and approximating the square root of any positive number a, can be = 3.5). Prove that this is equivalent to the Newton-Raphson algorithm 6.16 (a) Apply the Newton-Raphson method to the function f(x) = tanh(x2-9) to evaluate its known real root at x-3. Use an initial guess of = 3.2 and take a minimum of four iterations. (b) Did the method exhibit convergence onto its real root? Sketch the plot with the results for each iteration shown 6.17 The polynomial f(x) = 0.0074x. 0.284x3 + 3.355r' 12.183x + 5 has a real root between 15 and 20. Apply the Newton Raphson method to this function using an initial guess ofxo Explain your results. 6.18 Use the secant method on the circle function (x 1)2 + (y-2)2 = 16 to find a positive real root. Set your initial guess to x,-3 and xi-1-0.5. Approach the solution from the first and (d) Using the modified secant method (three terations, x, 35. 0.01) 6.10 Determine the lowest positive root off(x) = 7sin (x)e-x-1: (a) Graphically (b) Using the Newton-Raphson method (three iterations, x 0.3) (c) Using the secant method (five iterations, x,-0.5 and = 0.4). (d) Using the modified secant method (three terations, X,-03, 16.15 = 0.01) 6.11 Use the Newton-Raphson method to find the root of f(x) = e-0.5"(4-x)-2 Employ initial guesses of (a) 2, (b) 6, and (c) 8. Explain your results. fourth quadrants. When solving for fx) in the fourth quadrant, be 6.12 Given sure to take the negative value of the square root. Why does your solution diverge? 6.19 You are designing a spherical tank (Fig. P6.19) to hold water for a small village in a developing country. The volume of liquid it can hold can be computed as f(x) =-2' _ 1.5x4 + 10x + 2 Use a root location technique to determine the maximum of this function. Perform iterations until the approximate relative error
