Let 1 (x) = x and define a sequence of functions by n+1 (x) =
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Let ƒ1(x) = x and define a sequence of functions by ƒn+1(x) = 1/2 (ƒn(x) + x/ƒn(x)). For example,ƒ2(x) = 1/2 (x + 1). Use a computer algebra system to compute ƒn(x) for n = 3, 4, 5 and plot y = ƒn(x) together with y = √x for x ≥ 0. What do you notice?
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