For certain x-values, the function f(x)=1/(1 + x) can be well-approximated by the
Chapter 11, Problem 11.2.33(choose chapter or problem)
For certain x-values, the function f(x)=1/(1 + x) can be well-approximated by the polynomial p(x)=1 x + x2 x3 + x4 x5 . (a) Show that p(0.5) f(0.5) = 2/3. To how many decimal places do p(0.5) and f(0.5) agree? (b) Calculate p(1). How well does p(1) approximate f(1)? (c) Graph p(x) and f(x) together on the same set of axes for 1 x 1. Based on your graph, for what range of values of x does p(x) appear to give a good estimate for f(x)?
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