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Thread: Calc 2 Question

  1. #1
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    Calc 2 Question

    Suppose we have a postiive, differentiable function f such that |f'(x)| <= f(x) for any x.

    Prove that the integral from 1\to \infty of f converges iff the sum from 1 \to n of f(n) converges
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  2. #2
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    Sorry I should have added that a hint was to use legrange to show that for every n, and every x in [n,n+1], f(n)/10 <= f(x) <= 10f(n)

    Or perhaps an easier way to solve it?
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