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Math Help - Use comparison test to determine whether interval converges.

  1. #1
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    Use comparison test to determine whether interval converges.

    Integral of 2^(-x^2) from 1 to infinity.
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  2. #2
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    for x > 1

    x\cdot 2^{-x^{2}} > 2^{-x^{2}}
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    for x > 1

    x\cdot 2^{-x^{2}} > 2^{-x^{2}}
    How did you derive this?
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  4. #4
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    Well, "derive" is not that great a word for the process. I wanted to invent a structure that was easily integrated. The x^{2} in the exponent suggested another 'x' out front would be good - thinking about the simple substitution u = x^{2}. After that, it was just a bit of thought to determine EXACTLY why the problem suggested the Domain [1,\infty) rather than [0,\infty).

    That's about it. You just have to think it through and figure it out.
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