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Homework Help: Evaluate lim of f.

  1. Feb 17, 2012 #1
    1. The problem statement, all variables and given/known data[/b]

    Evaluate lim x goes to ∞ positive
    ((x-1)*(bx-1)/(b-1))(1/x)

    2. Relevant equations

    3. The attempt at a solution[/b]
    I try to take log but it does not seem to work
     
    Last edited: Feb 17, 2012
  2. jcsd
  3. Feb 17, 2012 #2
    Is this the problem?

    [tex]
    \lim_{x\to\infty}\frac{(b^{x}-1)}{x(b-1)}^{\frac{1}{x}}
    [/tex]
     
  4. Feb 18, 2012 #3
    Yes. I tried taking log but to no avail
     
  5. Feb 18, 2012 #4
  6. Feb 18, 2012 #5
    still cannot solve it. Need help guys! Appreciated.
     
  7. Feb 18, 2012 #6
    To clarify, is it this?
    [tex]
    \lim_{x\to\infty}\left(\frac{b^{x}-1}{x(b-1)}\right)^{\frac{1}{x}}
    [/tex]
    Or is it this?
    [tex]
    \lim_{x\to\infty}\frac{(b^{x}-1)^{\frac{1}{x}}}{x(b-1)}
    [/tex]

    For the latter, note that for all x > 1, b > 1,
    $$0 \leq (b^{x}-1)^{\frac{1}{x}} \leq b$$
    For the former, I am not immediately sure.
     
    Last edited: Feb 18, 2012
  8. Feb 18, 2012 #7

    Dick

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    Homework Helper

    Judging by you initial parentheses I think you actually mean. [tex]\lim_{x\to\infty} \big( \frac{b^{x}-1}{x(b-1)} \big) ^{\frac{1}{x}}[/tex].

    And can you show why taking the log isn't working. Or something?
     
  9. Feb 19, 2012 #8
    I simplified it down to calculate
    limx->infinity (b^x-1)/x
    ......can help me to proceed?
     
  10. Feb 19, 2012 #9

    Dick

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    Science Advisor
    Homework Helper

    I don't see how you got that. You need to show us.
     
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