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Homework Help: Limits- using L'hopital's rule

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Lim tan (x^1/2)/ [x (x+1/2)^1/2 ]
    x-> 0

    3. The attempt at a solution

    I have attempted to differentiate both the denominator and numerator seperately but this just seems to complicate the whole equations and I still get a limit of 0.

    I had an idea to square everything, in which case I get a limit of 1. However, I do not think [tan (x^1/2)]^2 = tanx

    Please help? My friend and I have been trying to work this out. It isn't homework, merely revision and further understanding.
     
  2. jcsd
  3. Apr 4, 2010 #2
    You must have made an error while differentiating, the limit is not 0.

    [tan (x^1/2)]^2 is not the same as tanx. Try [itex] x = \pi [/itex]
     
  4. Apr 4, 2010 #3
    My mistake, the equation is

    tan (x^1/2)/ [x (1+1/x)^1/2 ] sorry

    I'll try your hint, and have another go at differentiating it. Thanks.
     
  5. Apr 4, 2010 #4

    Mark44

    Staff: Mentor

    Minor point - that's not an equation. They're easy to spot because there's one of these- = - in an equation.
     
  6. Apr 5, 2010 #5
    @Mark44: okies, noted.

    I've tried differentiating it again and I get:

    [tex]\frac{\frac{sec^{2}\sqrt{x}}{2\sqrt{x}}}{\sqrt{\frac{1}{x}+1}-\frac{1}{2\sqrt{\frac{1}{x}+x}}}[/tex]

    But it still doesn't give me a limit.

    I'm not too sure how to use your hint. As if i let [tex]\pi=x[/tex] Doesnt it just mean [tex]\pi[/tex] tends towards 0 instead of x ?

    Confused...
     
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