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Find a function from the limit

  1. Jul 20, 2010 #1
    Posted: Tue, 20 Jul 2010 14:49:50 Post subject: find a function from the limit

    [late]\lim_{x \rightarrow \infty} \frac{log f_1(x)}{ log x } = c_1[/late]


    [late]\lim_{x \rightarrow \infty} \frac{log f_2(x)}{ log x } = c_2[/late]

    if [late]c_2>c_1[/late] then

    [late]\lim_{x \rightarrow \infty} \frac{ log f_1(x) + f_2(x) ] }{ log x } = c_2 [/late]

    can anyone tell me how to prove this rigorously?

    Last edited: Jul 20, 2010
  2. jcsd
  3. Jul 20, 2010 #2


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    Science Advisor

    The general idea involves using the fact that fi(x) ~xci. Therefore f1(x)/f2(x) -> 0 as x ->∞. As a result the numerator in your last expression ends up behaving like logf2(x).

    Good luck.
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