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Math Help - Solving this limit

  1. #1
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    Solving this limit

    Find n such that
    \lim_{x\rightarrow\infty}            \frac {((nx+1)^x)}{(nx+1)^x}= 9


    i know the question ends up as e^(-2/n) but can someone show me a different way of solving it other than the fact that
    e^a = \lim_{x\rightarrow\infty} (1+ (a/x))^x ?

    i attempted to solve it with ln, moving the x's down but it would be great if i could get some assistance

    Edit: sorry i couldn't get the language for this math down, any help on the actual problem? XD sorry
    Last edited by icedragontt; May 26th 2009 at 08:09 PM.
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  2. #2
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    If your question is find n such that \lim_{x \to \infty}(nx+1)^x=9 no such n (with n a real number) exists

    Now if we let n be a polynomial, well we already know that \lim_{x \to \infty}{(\frac{y}{x}+1)^x}=e^y so what y will make e^y=9 this is a simple equation and you can probably see that y must be 2ln3 or ln9

    So we need nx to be \frac{ln9}{x} so n must be \frac{ln9}{x^2}
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  3. #3
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    Soo Sorry, i wrote the question out wrong, could i get some assistance on the actual problem now? Again, i didn't know the language for making the site draw sigma, sorry.
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