Let for ƒ(t) = 1/t t ≠ 0.
a. Find the average rate of change of ƒ with respect to t over the intervals (i) from t = 2 to t = 3, and (ii) from to t = 2 to t = T.
b. Make a table of values of the average rate of change of ƒ with respect to t over the interval [2, T], for some values of T approaching 2, say T = 2.1, 2.01, 2.001, 2.0001, 2.00001, and 2.000001.
c. What does your table indicate is the rate of change of ƒ with respect to t at t = 2?
d. Calculate the limit as T approaches 2 of the average rate of change of ƒ with respect to t over the interval from 2 to T. You will have to do some algebra before you can substitute T = 2.
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