2. Homotopy Continuation (10 pts) Code. Applying Newton’s Method to find the root of the equation, f(x) = 2x − 4 + sin(2πx) = 0, diverges if the initial guess, x0 = 0, is used. Solve this problem by homotopy continuation using the step δt = 0.05. Plot the number of iterations needed and the estimated root as a function of t. Use residual tolerance of εy = 10−8 and Nmax = 100 as the maximum number of iterations.