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Problem 17 (Fixed-point method). Consider the equation e- - xln r - r = 0 over the interval (1, 3). Convert the equation from the form f(x) = 0 to the form r = g(x) and use the standard fixed-point iteration method of the form In+1 = g(in) with the initial condition to = 1 to find the approximation zz for the root of the equation. Warning: If [5'(278)| > 1, then the scheme (locally) diverges away from the location of the root its (a) 1.0601 (b) 0.2846 (c) 1.1100 (d) iteration sequence locally diverges from root (e) None of these Problem 18 (Fixed-point method). Consider the equation cos = sin x over the interval [0,*/2] that has an exact root (true solution) ITS = 7/4. Convert the equation from the form f(x) = 0 to the form 1 = g(x) and use the standard fixed-point iteration method of the form In+1 = 9(2n) with the initial condition to = 0 to find the approxima- tion 13 for the root of the equation. Make sure to rewrite the equation in a form where |g'(ITS) 1, and the scheme will not converge. Round your answer to four significant digits. Warning: If \g'(ITS)| > 1, then the scheme (locally) diverges away from the location of the root Irs. (a) 0.6988 (b) 0.8211 (c) 0.7706 (d) no g exists with g' (ITS)