Question

This sont Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation, f(x) = 2 sin x + 3x + 3, Xo = 1.5 Complete the table. (Do not round until the final answer. Then found to six decimal places as needed) k k XX 1 6 2 7 3 8 4 9 5 10

Answer 1

given: function f(x) = 2sin(x) + 3x + 3 ,Xo=1.5

1. Compute the derivative of the function, f'(x).
2. Use the iterative formula: Xₖ₊₁ = Xₖ - f(Xₖ) / f'(Xₖ)
3. Repeat the process 10 times.

First, let's find the derivative of f(x):
f'(x) = 2cos(x) + 3

Now, use the iterative formula to compute the iterations:

X₁ = X₀ - f(X₀) / f'(X₀)
X₂ = X₁ - f(X₁) / f'(X₁)
...
X₁₀ = X₉ - f(X₉) / f'(X₉)

Remember to not round any values until the final answer, and then round to six decimal places. Since I cannot actually compute the iterations, I encourage you to use a calculator or program to find the values for each Xₖ using the provided formula.