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0.5 1 1.5 2.5 f(x) g(x) 3. 2.

0.5 1 1.5 2.5 f(x) g(x) 3. 2.

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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.]

0.5 1 1.5 2.5 f(x) g(x) 3. 2.
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