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Math Help - Mystifying limit

  1. #1
    Junior Member
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    Mystifying limit

    Hey, I was wondering if someone might give me a hand with taking a limit; I'm attaching a pdf version of the limit and my solution attempt. Essentially, what I've done is multiply by the conjugate and then simplified as far as possible - at which point someone involved has obviously made a mistake, since the key claims that the correct answer is -2. At the same time, I can't help but notice that if you were to change the sign before the last x^3 term, you'd get +2, tempting me to suggest that I'm not the one at fault here. But yea, anyone wanna give me a hand figuring out where I'm going wrong here? Thanks in advance!
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  2. #2
    MHF Contributor
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    Re: Mystifying limit

    Let x<0. Then x^6>0, \sqrt{x^6}>0, but x^3<0. Hence, \sqrt{x^6} = -x^3.
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  3. #3
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    Re: Mystifying limit

    That... makes a ridiculous amount of sense. Thanks a lot!
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