Let s(x) = x^2 - cos x. a prove that has exactly one root on the interval (0.5, 0.9]. b) use the bisection method starting with the interval (0.5, 0.9] to approximate the solution to within 0.001 . show a, b & midpt at each step. justify why the number of iterations performed is sufficient. c) determine the number of steps of the bisection method that would be necessary to guarantee an absolute error of less than 10 -". (note that n steps means that the nth midpoint is accepted as the approximation.)