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Math Help - independent constant in limit

  1. #1
    Junior Member
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    independent constant in limit

    Show \lim_{n \rightarrow \infty} b^{\frac{1}{n}}, for b > 0 is independent of b.
    I am not sure what "independent of b". Is it that the value of the limit does not change when b > 0?


    x = \lim_{n \rightarrow \infty} b^{\frac{1}{n}}

    \ln (x) = \lim_{n \rightarrow \infty} \ln (b^{\frac{1}{n}})

    \ln (x) = \lim_{n \rightarrow \infty} \frac{\ln(b)}{n}  = 0
    ln(b) is a constant over the the variable. as n approaches infinity the fraction goes to zero. ln(b) is undefined for values <= 0 therefore b > 0 for the limit to be true.

    \ln (x) =  0, x = 1
    \lim_{n \rightarrow \infty} b^{\frac{1}{n}} = 1
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  2. #2
    Senior Member Spec's Avatar
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    Your solution looks correct.
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