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Indeterminate form problems

  1. Mar 24, 2008 #1
    Hi I'm new to this forum, i need a help i don't know how can i use l'hospital in these problems;


    lim(x->1, ((arccos(x))^lnx))

    lim(x->[tex]\pi[/tex]/2+ (cosx ln(x - [tex]\pi[/tex]/2 ) )


    Can anyone help?
     
    Last edited: Mar 24, 2008
  2. jcsd
  3. Mar 24, 2008 #2

    nicksauce

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    The second one is greatly simplified if you make a change of variables u = x - pi/2
     
  4. Mar 24, 2008 #3

    Thanks, but still i don't know how can i proceed ? =(

    lim(u->0+ (cos(u+[tex]\pi[/tex]/2) ln(u ) )
     
  5. Mar 24, 2008 #4

    nicksauce

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    Well cos(u+pi/2) = -sin(u)

    Then you can write your function as
    -ln(u) / csc(u), and then apply l'hopital's rule. See where that gets you.
     
  6. Mar 24, 2008 #5
    Now ,i figured it out thank you :wink:
     
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