Consider the equation g(x) = - +2 1. Use Intermediate Value Theorem to show that the...

Transcribed Image Text:

Consider the equation g(x) = - +2 1. Use Intermediate Value Theorem to show that the above function has a fixed point at 7. E (2,3) (Hint: Create a root finding problem f(r) = 0, which is equivalent to the fixed point problem z = g(x)). *** 2. Perform 10 iterations. Let o 2, and In+1 = g(x), for n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Keep at least 6 significant digits for each iteration and give 71, 72, 710 only. (Please store the first iterations because you will need them to answer Question # 5.) 3. What is the fixed point r.? (You should continue the iteration in Question #2 until results start to repeat. Please store r. in your calculator because you will need them to answer Question #5.) 4. Verify the fixed-point theorem is satisfied in the interval (2,3]. 5. By calculating the ratio, where k = 0, 1,2,3,4,5,6 and 2, is the result you find in Question #3, deduce that the iteration converges linearly. Keep at least 4 significant digits for all ratios. Consider the equation g(x) = - +2 1. Use Intermediate Value Theorem to show that the above function has a fixed point at 7. E (2,3) (Hint: Create a root finding problem f(r) = 0, which is equivalent to the fixed point problem z = g(x)). *** 2. Perform 10 iterations. Let o 2, and In+1 = g(x), for n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, Keep at least 6 significant digits for each iteration and give 71, 72, 710 only. (Please store the first iterations because you will need them to answer Question # 5.) 3. What is the fixed point r.? (You should continue the iteration in Question #2 until results start to repeat. Please store r. in your calculator because you will need them to answer Question #5.) 4. Verify the fixed-point theorem is satisfied in the interval (2,3]. 5. By calculating the ratio, where k = 0, 1,2,3,4,5,6 and 2, is the result you find in Question #3, deduce that the iteration converges linearly. Keep at least 4 significant digits for all ratios.