1) Determine the lagrange polynomial of second degree that can be used to approximate F(1.5) based on the following data. F(x) 1 0.7651977 1.3 0.620086 1.6 0.4559022 1.9 0.2818186 2.2 0.1103623 If F(1.5)=0.51128277 compute the actual error involved.
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- Consider the functions f(x) = x and g(x) = sin x on the interval (0, ). (a) Complete the table and make a conjecture about which is the greater function on the interval (0, ). (b) Use a graphing utility to graph the functions and use the graphs to make a conjecture about which is the greater function on the interval (0, ). (c) Prove that f(x) > g(x) on the interval (0, ). [Hint: Show that h′(x) > 0, where h = f − g.]Suppose function fhas the graph as shown belowP2