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Why are we allowed to do this? v. limits

  1. Nov 26, 2007 #1
    lim(e^(lnx)) as x---> inf. = e^(lim(lnx) as x--->inf.)

    the book just says "by continuity of e^x"

    why are we allowed to do this?
     
  2. jcsd
  3. Nov 26, 2007 #2

    Ben Niehoff

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    You can prove it using the definition of a limit. The continuity of e^x turns out to be important in the proof.
     
  4. Nov 26, 2007 #3
    this isn't an actual homework problem; I ran into this while reading the book... it doesn't elaborate any further
     
  5. Nov 26, 2007 #4

    Hurkyl

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    Refer back to your limit laws; you learned limits of sums, limits of products, et cetera. One of them was limits of compositions.
     
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