Question

the question is from my Numerical methods and analysis course

et /()-sin(), where is measured in radians. (a). Calculate approximations to ) using Theorem 6.1 with h-0.1, h-0.01 and h-0.001, Carry eight or nine decimal places. (b). Compare with the value /(0.8)-cos(08), i.e. calculating the error of approximation. s(0.8) Theorem 6.1 (Centered Formula of Order 0(h)). Assume that fe Cla, bl and that x -h. x, x + h e la, bl. Then The notation S) stands for the set of all functions fsuch that f and its first n derivatives are 2h Furthermore, there exists a number c ; : c(x) € [a, b] such that h) + Etrunc(f. h). 一r+h, "f"(x)= continucus on S. where )(C) = ()(11"). Etranc(J. h) = The term E(f, h) is called the truncation error.

Answer 1

sin 0-9) - sin Lo-7) 0.2 0 69 55 46 (0.8-0.01 +0,01) - 2x0.0 sin (0.) - sin (D.79) 0 02 0.696西95 with h= 0.001 Co+Doo) J o-s - o.oo) (0.8) 2 x 001 sin (0. oi) sin . 799) o 002 0.696 0 (b) f1(0.8) = co s Co's) 0.69 607