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Homework Help: Valid method of evaluating limit?

  1. Jun 24, 2008 #1


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    1. The problem statement, all variables and given/known data
    I don't know if the following is valid, so I'll appreciate if someone could tell me if it's ok. I want to find
    [tex] \lim_{x\rightarrow \infty} \frac{x}{\sqrt{a^2+x^2}} [/tex]

    2. Relevant equations

    3. The attempt at a solution
    Using L'Hopital rule doesn't appear to help, because repeatedly differentiating both the top and bottom gives the same limit. So I did a substitution:

    [tex]x=a \tan \theta[/tex]
    And the problem now becomes [tex]\lim_{\theta \rightarrow \frac{\pi}{2}} \sin \theta [/tex] which easily evaluates to 1. Is this correct?
  2. jcsd
  3. Jun 24, 2008 #2
    Physical method would be: a^2 is small compared to infinity, so we can ignore it. Sqrt(x^2)=x, so limit is 1 :P
    But yes, I guess your method is just fine.
  4. Jun 24, 2008 #3


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    It's valid, but why would you want to do it that way? Just divide numerator and denominator by x and use algebra. Which is what Zizy is saying.
  5. Jun 24, 2008 #4


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    OK thanks. I got confused for a moment over something.
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