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Homework Help: Nice limit

  1. Oct 30, 2005 #1
    Hi all,

    could you help me how to solve this limit?

    [tex]
    \lim_{x \rightarrow \infty} \left( 1 + 10^{-x}\right)^\left(10^x\right)
    [/tex]

    Common adjustments for log involving the limit log (1)/0 don't work and no other idea comes to my mind...

    Thank you for any help.
     
  2. jcsd
  3. Oct 30, 2005 #2

    VietDao29

    User Avatar
    Homework Helper

    Hmm,...
    Look at the problem again, it looks incredibly like:
    [tex]\lim_{x \rightarrow \infty} \left( 1 + \frac{1}{x} \right) ^ x = e[/tex]
    Can you go from here?
    Viet Dao,
     
  4. Oct 30, 2005 #3
    Yep, you're right, can't believe I didn't see it :) Thanks.
     
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