Problem (2): Use Newton's Method to find the only real root of the equation , correct to 9 decimal places, and take an initial guess x0 = 1.5.
It would help if we had the equation.
you have the function and the formula.
So apply it. Show your work if you get stuck.
To use Newton's Method to find the real root of an equation, follow these steps:
Step 1: Start with an initial guess, x0, for the root of the equation.
In this case, the initial guess is x0 = 1.5, as given in the problem.
Step 2: Find the derivative of the function represented by the equation.
Take the derivative of the function with respect to the variable of interest (in this case, x).
Step 3: Use the formula for Newton's Method to iteratively update the guess.
The formula for Newton's Method is:
x(n+1) = x(n) - f(x(n))/f'(x(n))
where x(n) represents the current guess and x(n+1) is the updated guess, f(x(n)) is the value of the function at x(n), and f'(x(n)) is the derivative of the function at x(n).
Step 4: Iterate until the result is accurate to the desired decimal places.
Continue applying the formula in Step 3 until the result converges to the desired accuracy. In this case, the desired accuracy is 9 decimal places.
Now, let's apply these steps to find the root using the given information:
Step 1: x0 = 1.5 (as given)
Step 2: We need the equation or function to find its derivative. Since you haven't provided the equation, please provide the equation so that we can proceed with the next steps.
Once you provide the equation, we can proceed with Steps 2, 3, and 4 to find the real root using Newton's Method.