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Evaluate-27 ^4/3/8 a) - 81/16 b) 81/16 c) 16/81

Which approach to the theory-and-research cycle does the following sequence reflect: (1) specific observations suggest generalizations, (2) generalizations produce a tentative theory, (3) the theory is tested through the formation of hypotheses, and (4) hypotheses may provide suggestions for additional observations?

What is the average rate of change for this function for the interval from x=2 to x=4 ?