We can extend our definition of average value of a continuous function to an infinite interval by defining the average value of f on the interval a, infin to be (a) Find the average value of y tan1x on the interval a, infin (b) If f(x) 0 and int infin f(x) dx is divergent, show that the average value of f on the interval a, infin is limx rarr infin f(x), if this limit exists (c) If int infin f(x) dx is convergent, what is the average value of f on the interval a, infin (d) Find the average value of on the interval a, infin lim f a Ja (x) dx x

Question: We can extend our definition of average value of a continuous function to an infinite interval by defining the average value of f on the

We can extend our definition of average value of a continuous function to an infinite interval by defining the average value of f on the interval [a, ∞] to be

(a) Find the average value of y = tan€“1x on the interval [a, ∞].
(b) If f(x) > 0 and ∫∞ f(x) dx is divergent, show that the average value of f on the interval [a, ∞] is limx →∞ f(x), if this limit exists.
(c) If ∫∞ f(x) dx is convergent, what is the average value of f on the interval [a, ∞]?
(d) Find the average value of on the interval [a, ∞].

lim f- a Ja (x) dx -x

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