Mathematics, 18.08.2020 17:01 queenkimm26

It would be nice if average values (AV) of integrable functions obeyed the following rules on an interval [a, b]. Do these rules ever hold? Give reasons for your answers. a) AV(f + g) = AV(f) + AV(g)
b) AV(kf) = k*AV(f) for any number k
c) AV(f) ≤ AV(g) if f(x) ≤ g(x) on [a, b]

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It would be nice if average values (AV) of integrable functions obeyed the following rules on an interval [a, b]. Do these rules ever hold? Give reasons for your answers. a) AV(f + g) = AV(f) + AV(g) b) AV(kf) = k*AV(f) for any number k c) AV(f) ≤ AV(g) if f(x) ≤ g(x) on [a, b]

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It would be nice if average values (AV) of integrable functions obeyed the following rules on an interval [a, b]. Do these rules ever hold? Give reasons for your answers. a) AV(f + g) = AV(f) + AV(g)
b) AV(kf) = k*AV(f) for any number k
c) AV(f) ≤ AV(g) if f(x) ≤ g(x) on [a, b]