Recall that we proved that (a) = na-1 for all positive integers n (the so-called power...

 

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Recall that we proved that (a) = na-1 for all positive integers n (the so-called "power rule"). (a) Derive the power rule in the case where n > 0 is rational, i.e. n = p/q, where p and q are integers and g 0. (Hint: if y=z/, then y = x³.) (b) Derive the power rule in the case where n> 0 is irrational. (c) Derive the power rule in the case where n < 0. (d) Derive the power rule in the case where n = 0. Recall that we proved that (a) = na-1 for all positive integers n (the so-called "power rule"). (a) Derive the power rule in the case where n > 0 is rational, i.e. n = p/q, where p and q are integers and g 0. (Hint: if y=z/, then y = x³.) (b) Derive the power rule in the case where n> 0 is irrational. (c) Derive the power rule in the case where n < 0. (d) Derive the power rule in the case where n = 0.

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