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  • 5 years ago

use the limit comparison theorem to determine if the following integral diverges or converges: integral from 2 to infinite: (x^2 dx)/[(x-1)^2 * (x+3)]

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  1. anonymous
    • 5 years ago
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    This is how I'm reading the integral given, the integral of {(x^2)/[(x-1)(x-1)(x+3)]} dx from 2 to a as a grows unbounded (or approaches infinity as many like to say). When x=2, (x^2)/[(x-1)(x-1)(x+3)] is 4/5, and this value is the initial point of the integral. This means this 4/5 is less than or equal to the integral over our given bounds (2+) since the derivative of the polynomial is positive over the same bounds of integration so the integral is constantly getting a little positive addition to it. The integral of 4/5 over the same bound clearly grows unbounded or diverges, and since the integral of 4/5 is smaller at every point within the bounds of integration than the given integral, then the given integral must diverge too.

  2. anonymous
    • 5 years ago
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    mary beth and steve like to shop at a warehouse store .they get a 10% discount on everything they buy.what fractional part of the disscount do they recieve? a.1/20 b.1/10 c.1/510 d.1/520

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