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Math Help - limit at infinity

  1. #1
    DBA
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    limit at infinity

    Find the limit

    lim x-> infinity [1/x] / [1/3 x ^(-2/3)]


    First, I do not understand how I get to the simplyfied term:

    lim x-> infinity 3 / x^1/3


    Second, I do not understand why the answer is zero.


    Thanks
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  2. #2
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    Quote Originally Posted by DBA View Post
    Find the limit

    lim x-> infinity [1/x] / [1/3 x ^(-2/3)]


    First, I do not understand how I get to the simplyfied term:

    lim x-> infinity 3 / x^1/3


    Second, I do not understand why the answer is zero.


    Thanks
    \frac{\frac{1}{x}}{\frac{1}{3}x^{-\frac{2}{3}}}

    \frac{\frac{1}{x}}{\frac{1}{3x^{\frac{2}{3}}}}

    remember how to divide fractions?

    \frac{1}{x} \cdot \frac{3x^{\frac{2}{3}}}{1} = \frac{3}{x^{\frac{1}{3}}}


    now ... what happens to the value \frac{3}{x^{\frac{1}{3}}} as x gets very large?
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  3. #3
    DBA
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    Yes remember
    3x^3/3-2/3 = 3x^1/3 Thanks, I got that now.

    lim x->infinity 3/x^1/3 = 0

    the nominator stays 3 and the denominator gets larger and larger. So, the entire term gets smaller and smaller. Thus closer and closer to zero.

    Thanks!
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