1. May 13, 2008 #1

   chiakimaron

   

   I have no idea of the following question, please help me
   
   Find limit x→∞〔 (a^x - 1 )/(a - 1) 〕^1/x
   
   for (1) 0<a<1
   (2) a>1

    

   chiakimaron, May 13, 2008
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3. May 13, 2008 #2

   malawi_glenn

   

   Science Advisor

   Homework Helper

   what have you tried? If you are not showing your effort, then you can't get any help

    

   malawi_glenn, May 13, 2008
4. May 13, 2008 #3

   chiakimaron

   

   let y=〔 (a^x - 1 )/(a - 1) 〕^1/x
   
   Iny=1/x In(a^x - 1 )/(a - 1)
   
   then I can't do it

    

   chiakimaron, May 13, 2008
5. May 13, 2008 #4

   malawi_glenn

   

   Science Advisor

   Homework Helper

   start with 0<a<1 then what happens?

    

   Last edited: May 13, 2008

   malawi_glenn, May 13, 2008
6. May 13, 2008 #5

   chiakimaron

   

   i really don't know

    

   chiakimaron, May 13, 2008
7. May 13, 2008 #6

   chiakimaron

   

   limit x→∞〔 (a^x - 1 )/(a - 1) 〕^1/x
   
   = [(-1)/(a-1)]^0 = 1
   
   is it correct?

    

   chiakimaron, May 13, 2008
8. May 13, 2008 #7

   benorin

   

   Homework Helper

   Keep going! Let [tex]x\to\infty[/tex]
   
   [tex]\lim_{x\to\infty}\frac{\ln\left(\frac{a^x-1}{a-1}\right)}{x}=\frac{\lim_{x\to\infty}\ln\left(\frac{a^x-1}{a-1}\right)}{\lim_{x\to\infty}x}[/tex]
   
   and remember ln(-1/(a-1)) is some constant.

    

   benorin, May 13, 2008
9. May 13, 2008 #8

   malawi_glenn

   

   Science Advisor

   Homework Helper

   yes! :-)
   
   And what if a>1 ?

    

   malawi_glenn, May 13, 2008

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