Let f (x) = ln(x3 x + 1). The third Taylor polynomial at a = 1 is T3(x) = 2(x 1) + (x 1)
Chapter 8, Problem 38(choose chapter or problem)
Let f (x) = ln(x3 x + 1). The third Taylor polynomial at a = 1 is T3(x) = 2(x 1) + (x 1) 2 7 3 (x 1) 3 Find the maximum possible value of |f (1.1) T3(1.1)|, using the graph in Figure 11 to find an acceptable value of K. Verify your result by computing |f (1.1) T3(1.1)| using a calculator. 20 40 41 0.9 1.0 1.1 1.2 y x FIGURE 11 Graph of f (4), where f (x) = ln(x3 x + 1).
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