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Math Help - [SOLVED] limit comparison test

  1. #1
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    [SOLVED] limit comparison test

    i dont know know how to use the limit comparison to show whether or not integral of 1/[x^(1/3) + x^(1/2) + x)] from 1 to inifinitty
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  2. #2
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    When it's hard to bound, apply the limit comparison test, but this is not hard to bound because by putting x=u^6 the integral is \int_{1}^{\infty }{\frac{6u^{5}}{u^{2}+u^{3}+u^{6}}\,du} and for all u\ge1 it's \frac{u^{5}}{u^{2}+u^{3}+u^{6}}\ge \frac{u^{5}}{3u^{6}}=\frac{1}{3u} thus the integral diverges by direct comparison with \int_{1}^{\infty }{\frac{du}{u}}.
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