exercises exercise see if the secant method fails does the secant method behave better than newton' method in the problem described in exercise try the initial guesses : and : : and : and : and : filenamesecant_failure exercise understand why the bisection method cannot fail solve the same problem as in exercise using the bisection methodbut let the initial interval be oe report how the interval containing the solution evolves during the iterations filenamebisection_nonfailure exercise combine the bisection method with newton' method an attractive idea is to combine the reliability of the bisection method with the speed of newton' method such combination is implemented by running the bisection method until we have narrow intervaland then switch to newton' method for speed write function that implements this idea start with an interval oeaband switch to newton' method when the current interval in the bisection method is fraction of the initial interval ( when the interval has length /potential divergence of newton' method is still an issueso if the approximate root jumps out of the narrowed interval (where the solution is known to lie)one can switch back to the bisection method the value of must be given as an argument to the functionbut it may have default value of try the new method on tanh xd with an initial interval oe filenamebisection_newton py exercise write test function for newton' method the purpose of this function is to verify the implementation of newton' method in the newton function in the file nonlinear_solvers py construct an algebraic equation and perform two iterations of newton' method by hand or with the aid of sympy find the corresponding size of jf / and use this as value for eps when calling newton the function should then also perform two iterations and return the same approximation to the root as you calculated manually implement this idea for unit test as test function test_newton(filenametest_newton py exercise solve nonlinear equation for vibrating beam an important engineering problem that arises in lot of applications is the vibrations of clamped beam where the other end is free this problem can be analyzed analyticallybut the calculations boil down to solving the following nonlinear algebraic equationcosh cos