Compute the first-order central difference approximations of O(h4) for each of the following functions at the specified location

and for the specified step size:

(a) y = x³ + 4x – 15                  at x = 0,           h = 0.25

(b) y = x² cos x                        at x = 0.4,        h = 0.1

(c) y = tan(x/3)                        at x = 3,           h = 0.5

(d) y = sin(0.5√x)/x                 at x = 1,           h = 0.2

(e) y = e^x + x                           at x = 2,           h = 0.2

Compare your results with the analyticalsolutions.

Transcribed Image Text:

- 0.5 0.5 1.5 -2 - 1.5 0.05399 0.12952 0.24197 039894 0.35207 0.39894 0.24197 0.12952 0.05399 f(x)