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Limit of x/[Sqrt(x^2+r^2)*r^2]

  1. Dec 28, 2005 #1
    Can someone tell me how to show that the value of

    x/[Sqrt(x^2+r^2)*r^2]

    approaches 1/r^2 when x approaches infinity? Cant figure out how to show this analytically, but by plotting the function it is obvious.

    Btw, how do I get latex graphics to work?? It doesn't really work when I preview the post.

    Thanks!
     
  2. jcsd
  3. Dec 28, 2005 #2
    to use latex use [tex] [tex] and [/tex][/tex].
    and as for the limit.. as x goes to infinity, [tex] \sqrt{x^2+r^2}[/tex] goes to x, because [tex] r^2 [/tex] is much smaller and can be neglected.
    so you get [tex] \frac{x}{xr^2} [/tex]
    and as you can see the x's are cancelled out giving [tex] \frac{1}{r^2} [/tex]
     
    Last edited: Dec 28, 2005
  4. Dec 28, 2005 #3
    Change the x in the numerator to sqrt(x^2) the multiply top and bottom by sqrt(1/(x^2))
     
  5. Dec 28, 2005 #4
    Thank you for the quick answers! I see it clearly now :-)
     
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