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4. This exercise illustrates limitations to the usefulness of graphs. Consider the function f : R - R. - 1/x2 f(x) = 0 X =

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4. This exercise illustrates limitations to the usefulness of graphs. Consider the function f : R - R. - 1/x2 f(x) = 0 X = 0. (a) Why is it reasonable to define f(0) = 0? (b) Using technology, construct a table of values, for the inputs {0, 0.1, 0.2, 0.3, 0.4). (c) Using your answer to (b), attempt to construct a rough graph of f(x) over the interval [0, 0.4]. (d) What property of the function makes it so difficult to construct a meaningful graph? (e) Use technology (graphing calculator or computer algebra system) to graph f. Discuss your results

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