Question

MATLAB

5. Given the recurrence formula In+1 = g(n), where g(x) = 1.2 + €0.52 repeat the evaluation of the recurrence formula until the criteria n+1-en < 10-6 is satisfied. Start the procedure with n = 0 and .co = 1. Solve the problem with a while- loop. (Hint: You may wish to corroborate your results by conducting this procedure in an Excel Spreadsheet.) (a) Store the value of n which satisfies the given criteria in a scalar variable. Apply the naming convention for your answer. (b) Store the value of n+1 which satisfies the given criteria in a scalar variable, Apply the naming convention for your answer.

Answer 1

Code:

g = @(x) 1/(1.2 + exp(0.5 * x)); ... Defining the given function g(x) in MATLAB

n=0; ... Initializing n to 0

x_n = 1; ... Initializing x0 to 1

x_n1 = g(1); ... Initializing x n+1 to g(x) (Here x n+1 is g(1) )

while(abs(x_n1 - x_n) > 10^-6) ... Using while to loop until the given codition fails ( till x n+1 - x <= 10^-6)
  
n=n+1; ... Updating n as the loop progreses
  
x_n = x_n1; ... Updating x_n as x_n1 (x n+1) the loop progreses
  
x_n1 = g(x_n); ... Updating x_n1 as g(x_n) (g(x n)) the loop progreses
  
end

disp(n) ... Displaying the scalar value of n

disp(x_n1)

Code :

g = @(x) 1/(1.2 + exp(0.5 * x)); -- Defining the given function g(x) in MATLAB n=0; * Initializing n to o x_n = 1; - Initializing xo to i x_nl = g(1); - Initializing x n+1 to g(x) (Here x n+l is g(1) ) Q ile (abs(x_nl - x_n) > 10^-6) --- Using while to loop until the given codition fails ( till x n+1 - x <= 10^-6) n=n+1; - Updating n as the loop progreses x_n = x_nl; - Updating x_n as x_nl (x n+1) the loop progreses x_nl = g(x_n); - Updating x_nl as g(x_n) (g(x n)) the loop progreses Land Shipping-Tool disp(n) - Displaying the scalar value of n disp (x_nl) New Mede D elay X Select the ship mode using the Mode button or click the N

Output:

disp (n) ** Displaying the scalar value of n disp (x_nl) 0.4118