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

  • Thread starter Repetit
  • Start date
  • #1
128
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!
 

Answers and Replies

  • #2
315
6
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:
  • #3
1,074
1
Change the x in the numerator to sqrt(x^2) the multiply top and bottom by sqrt(1/(x^2))
 
  • #4
128
1
Thank you for the quick answers! I see it clearly now :-)
 

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