The equation x-x-2=0 may be solved by using iterative process if you write it as xn+1...

  

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The equation x²-x-2=0 may be solved by using iterative process if you write it as xn+1 = x -2. When you reach a point where xn+1 = Xn, you have solved the equation. However, this process may not work because it is very sensitive to the initial value. In this assignment, you will explore this sensitivity on initial value of the nonlinear system. Do the following: 1. Try the initial value x₁ 0. See if it leads to a solution. 2. Try the initial value x₁ = 1. See if it leads to a solution. 0.5. See if it leads to a solution. Try the initial value x₁ 0.2. See if it leads to a solution. 3. Try the initial value x₁ = (Optional) If you find an initial value that does not lead to a solution, try as many steps as possible and see how the values jump on the x-axis. Note: you need to come at least x10 to assume if it leads to a solution or not. 4. 5. The equation x²-x-2=0 may be solved by using iterative process if you write it as xn+1 = x -2. When you reach a point where xn+1 = Xn, you have solved the equation. However, this process may not work because it is very sensitive to the initial value. In this assignment, you will explore this sensitivity on initial value of the nonlinear system. Do the following: 1. Try the initial value x₁ 0. See if it leads to a solution. 2. Try the initial value x₁ = 1. See if it leads to a solution. 0.5. See if it leads to a solution. Try the initial value x₁ 0.2. See if it leads to a solution. 3. Try the initial value x₁ = (Optional) If you find an initial value that does not lead to a solution, try as many steps as possible and see how the values jump on the x-axis. Note: you need to come at least x10 to assume if it leads to a solution or not. 4. 5.

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SOLUTION 1 x1 0 Lets start with the initial value x1 0 Plugging this value into the iterative formula xn 1 xn2 2 we get x1 1 02 2 x1 1 2 Since x1 1 is ... View the full answer