1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Valid method of evaluating limit?

  1. Jun 24, 2008 #1

    Defennder

    User Avatar
    Homework Helper

    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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    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

    Defennder

    User Avatar
    Homework Helper

    OK thanks. I got confused for a moment over something.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Valid method of evaluating limit?
  1. Evaluating a limit (Replies: 46)

  2. Evaluate Limit (Replies: 9)

  3. Evaluating limits (Replies: 5)

  4. Evaluate limit (Replies: 3)

Loading...