Suppose that we want to estimate Z = limh→0 f (h) and that we calculate f (1), f (2−1), f (2−2), f (2−3), . . . , f (2−10). Then suppose also that it is known that Z = f (h) + ah2 + bh4 + ch6. Show how to obtain an improved estimate of Z from the 11 numbers already computed. Show how Z can be determined exactly from any 4 of the 11 computed numbers.
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