Finite Difference Approximation and Error Analysis of the First Derivative for a Trigonometric Function

Given the function
y(x)
=sin(4 sin(2x))
π
and the mesh x1 = xo ik, where xo
π
determine the central finite difference for the first derivative of y with step size k =
14
at mesh point i = 4.
At the same point, also calculate the exact first derivative y'(xi).
Calculate the absolute value of the error of the finite difference approximation at the point x¿.
Work to at least 6 decimal places throughout and enter your answers to 2 decimal places.
(a) Enter the finite difference approximation
(b) Enter the exact derivative
(c) Enter the absolute error
(d) If we were to divide the step size by 10, the error will be approximately multiplied by a factor of
Select