To calculate a planets space coordinate, we have to solve the function f(x) x 1 0 5 sin x Let the base point be xi 2 on the interval 0, Determine the highest order Taylor series expansion resulting in a maximum error of 0 015 on the specified interval The error is equal to the absolute value of the...

The derivatives can be computed as The first through fourthorder Taylor serie ...

To calculate a planets space coordinate, we have to solve the function f(x) = x 1

Question:

To calculate a planet’s space coordinate, we have to solve the function f(x) = x – 1 – 0.5 sin x Let the base point be α = xi = π/2 on the interval [0, π]. Determine the highest-order Taylor series expansion resulting in a maximum error of 0.015 on the specified interval. The error is equal to the absolute value of the difference between the given function and the specific Taylor series expansion.