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Math Help - Limit involving a constant to the x

  1. #1
    Member nautica17's Avatar
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    Limit involving a constant to the x

    I need some help with this:

    lim x->0 of ( (3^2x) - 1 ) / ( (3^x) - 1)

    The answer should be 2, but I keep getting 0.

    I multiply the top and bottom by ( (3^x) + 1) and get this:

    ((3^3x) + (3^2x) - (3^x) -1) / ((3^2x) + (3^x) - (3^x) - 1)

    And so that gives me 0/0.

    Any help please? My brain is about to explode.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by nautica17 View Post
    I need some help with this:

    lim x->0 of ( (3^2x) - 1 ) / ( (3^x) - 1)

    The answer should be 2, but I keep getting 0.

    I multiply the top and bottom by ( (3^x) + 1) and get this:

    ((3^3x) + (3^2x) - (3^x) -1) / ((3^2x) + (3^x) - (3^x) - 1)

    And so that gives me 0/0.

    Any help please? My brain is about to explode.
    Just think about it like this 3^{2x}-1=\left(3^x\right)^2-1=\left(3^x-1\right)\left(3^x+1\right)
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  3. #3
    Member nautica17's Avatar
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    Quote Originally Posted by Drexel28 View Post
    Just think about it like this 3^{2x}-1=\left(3^x\right)^2-1=\left(3^x-1\right)\left(3^x+1\right)
    Sweet! Thank-you!
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