Pls. avoid any fancy MATLAB built in functions, provide plots if necessary.

Detailed solution pls.

Thank you!

3. Regula Falsi Method Answer the following questions relating to the regula (a) Derive the equation for finding point trf in terms of a, and b starting from the (b) Code in MATLAB. Find the root of f(r) In -sin on the interval 0.07, 8) (e) How does the Regula Falsi method improve upon the secant method and upon falsi method equation for a straight line to within Ey-5 x 10. Give your final error and number of iterations. the bisection method? Compare the three methods. 4. Code in MATLAB: Consider a mass balance equation for pollutant in a well-mixed lake as follows dt a. Given the parameter values V = 10 m3, Q = 10 m/yr, ll. = 106 g/yr, and k 0.25 gos/(m1.5 yr), use the fixed-point iteration method to solve for the steady-state (de/dt 0) concentration. Employ an initial guess of 4 g/m3 and iterate until the error (lg(c) - el) is lower than 1 x 10- and give the number of iterations b. Provide a table of the estimated during the first 5 iterations. c. Compute the order of convergence (a) and the asymptotic error constant (A). 3. Regula Falsi Method Answer the following questions relating to the regula (a) Derive the equation for finding point trf in terms of a, and b starting from the (b) Code in MATLAB. Find the root of f(r) In -sin on the interval 0.07, 8) (e) How does the Regula Falsi method improve upon the secant method and upon falsi method equation for a straight line to within Ey-5 x 10. Give your final error and number of iterations. the bisection method? Compare the three methods. 4. Code in MATLAB: Consider a mass balance equation for pollutant in a well-mixed lake as follows dt a. Given the parameter values V = 10 m3, Q = 10 m/yr, ll. = 106 g/yr, and k 0.25 gos/(m1.5 yr), use the fixed-point iteration method to solve for the steady-state (de/dt 0) concentration. Employ an initial guess of 4 g/m3 and iterate until the error (lg(c) - el) is lower than 1 x 10- and give the number of iterations b. Provide a table of the estimated during the first 5 iterations. c. Compute the order of convergence (a) and the asymptotic error constant (A)