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Indeterminate Products Giving Me Two Different Limits

  1. Dec 9, 2008 #1
    1. The problem statement, all variables and given/known data

    lim x-->0 of [tex]x lnx[/tex]

    2. Relevant equations



    3. The attempt at a solution

    1) [tex]\frac{lnx}{1/x}[/tex] = [tex]\frac{1/x}{-1/x^{2}}[/tex] = (-x) = 0

    2) [tex]\frac{x}{1/lnx}[/tex] = [tex]\frac{1}{1/1/x}[/tex] = [tex]\frac{1}{x}[/tex] = [tex]\infty[/tex]
     
    Last edited: Dec 9, 2008
  2. jcsd
  3. Dec 9, 2008 #2

    gabbagabbahey

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    hmmm...are you sure [tex]\frac{d}{dx} \frac{1}{\ln (x)}=\frac{1}{\frac{1}{x}}[/tex]?:wink:
     
  4. Dec 9, 2008 #3
    yea I realized it after a minute of looking at it again. this is exactly the sort of stupid mistake that lowers my marks in tests.

    and oops. I didn't see you answer or I wouldn't have edited the entry back.

    edit edit: there, I put it back up... but for some reason I think I made a double of the thread... agh. it's 4 AM. I'm tired :rofl:

    edit edit edit: and, of course: thanks.

    (I go sleep now)
     
    Last edited: Dec 9, 2008
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