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Math Help - Relative Rates of Growth

  1. #1
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    Relative Rates of Growth

    Order the function from slowest-growing to fastest growing as x--> infinity. Show your work.

    x^(6), e^(x), 6^(x), (ln(6))^(x)


    I don't know how I would go about comparing 4 functions together.. also i'm having trouble evaluating

    e^x to 6^x.. i keep getting an indeterminate form..
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  2. #2
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    Quote Originally Posted by AIYAH View Post

    e^x to 6^x.. i keep getting an indeterminate form..
    Can't you say as

    6 > e then as  x\to\infty, 6^x > e^x
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  3. #3
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    Quote Originally Posted by pickslides View Post
    Can't you say as

    6 > e then as  x\to\infty, 6^x > e^x

    Oh yes that is true.. now the next part of the question... hmm.
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  4. #4
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    The next part? I'm not sure exactly what you mean?


     6 > e > \ln(6) then as x\to\infty, 6^x > e^x > \ln(6)^x
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  5. #5
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    ohhh.. i can do that to the other problems too.
    i get it now ^.^
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