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Thread: Need help evaluating limits

  1. #1
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    Need help evaluating limits

    Evaluate the following limits

    Lim as x ->0 (2 to the power of x+3) subtract 8 divided by (2 to the power of x) subtract 1


    lim as x ->0 (x + 8 to the power of 1/3) - 2 divided by x

    Any help?
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  2. #2
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    Factor #1.
    $\displaystyle \frac{{2^{x + 3} - 8}}{{2^x - 1}} = \frac{{2^3 \left( {2^x - 1} \right)}}{{2^x - 1}}

    $
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  3. #3
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    Quote Originally Posted by Hockey_Guy14 View Post
    lim as x ->0 (x + 8 to the power of 1/3) - 2 divided by x
    $\displaystyle \lim_{x \to 0} \frac{{(x + 8)^{1/3} - 2}}
    {x}.$

    Substitute $\displaystyle u^3=x+8,$

    $\displaystyle \lim_{x \to 0} \frac{{(x + 8)^{1/3} - 2}}
    {x} = \lim_{u \to 2} \frac{{u - 2}}
    {{u^3 - 8}} = \lim_{u \to 2} \frac{1}
    {{u^2 + 2u + 4}}.$

    The rest follows.

    Quote Originally Posted by Hockey_Guy14 View Post
    Any help?
    Yes
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