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Suppose f ( x ) , 0 x 1 , is a continuou s function. (1) Use calculus to find such that 0 1 (

Suppose f(x),0x1 , is a continuou s function.

(1) Use calculus to find such that 01(f(x))2dx is minimum.

(2) Let x1,...,xn be a sequence of numbers. Find to minimize x1+...+xn

(3) Find to minimize 01f(x)dx

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