Question: A positive decreasing function f defined in (0,1] and a variable c>=0 such that the integral from 0 to 1 of (x^c)*f(x) converges Prove that

A positive decreasing function f defined in (0,1] and a variable c>=0 such that the integral from 0 to 1 of (x^c)*f(x) converges Prove that the limit when x approaches 0 from the right of (x^ (c+1))* f(x) converges to 0

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