(2) iteration. Problem 5.2: For part (a), plot the function using Matlab from x = 0 to 1, and guess the root. For part (b), write a Matlab function to do the Bisection Method. Print the code and the answer for an error tolerance εa = 0.01%. 5.2 Determine the real root of f(x) = 5x³- 5x² + 6x - 2: (a) Graphically. (b) Using bisection to locate the root. Employ initial guesses of x = 0 and x₁ = 1 and iterate until the estimated error ε falls below a level of ε, = 10%.

3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0

Problem 2 (25 points) (CCO 3)/MatlabGrader Develop a Matlab function that finds a root of a function g(x) starting from the given initial estimates x (-1) and x (0) with a tolerance in function of at least OK using the secant method. Name the function mySecant using as input the anonymous function g, the initial estimates x00 and x0, the maximum number of iterations to perform N, and the required tolerance in function epsok. As output, the function shall return four scalar variables: the numerical solution x, its tolerance in function tolFunc, its estimated relative error ere, and the number of iterations performed n. If the requested tolerance in function cannot be reached within N iterations, the function shall execute Matlab's error("...") function with an appropriate error message. Other than this potential error message, do not print out any results to screen or do any plotting within the function. You must minimize the number of function calls g(x) required per iteration, by…

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