Let f Cro-h, xo+h] (for h>0). Show that (20) f(xo+h)-2f(x0) + f (x0 - h) h2...

  

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Let f Cro-h, xo+h] (for h>0). Show that "(20) f(xo+h)-2f(x0) + f (x0 - h) h2 +Kh+Kh, write out the explicit expressions for K and K2 (where K2 depends on f(6) (E) for some in (ro-h, xo+h)). (b) (5 points) Apply the Richardson's extrapolation on (a) to derive an approximation formula of order O(h) for f" (20). (c) (5 points) Let f(x) = e/3+x with x0 = 0, h = 0.2. Use the formula from (a) and (b) to approximate "(0). Let f Cro-h, xo+h] (for h>0). Show that "(20) f(xo+h)-2f(x0) + f (x0 - h) h2 +Kh+Kh, write out the explicit expressions for K and K2 (where K2 depends on f(6) (E) for some in (ro-h, xo+h)). (b) (5 points) Apply the Richardson's extrapolation on (a) to derive an approximation formula of order O(h) for f" (20). (c) (5 points) Let f(x) = e/3+x with x0 = 0, h = 0.2. Use the formula from (a) and (b) to approximate "(0).