Question

Use Newton's method to find the number   arcsin(1/3) rounded to 14 digits after the decimal point by solving numerically the equation sin(x)=1/3 on the interval [0,pi/6].

1) Determine f(a) and f(b).

2) Find analytically f', f'' and check if f '' is continuous on the chosen interval [a,b].

3) Determine the sign of f' and f '' on [a,b] using their plots.

4) Determine using the plot the upper bound C and the lower bound c for |f'(x)|.

5) Calculate the function g(x).

6) Determine an upper bound N for |f ''(x)| on [0.4,1] using its plot on [0.39,1].

7) Determine the initial point x_0.

8) Run the iterations of the Newton's method until the error condition is satisfied and roundoff the answer.

Just part 8 please. Please show all steps and calculations. Thank you

Answer 1