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

[Repetit]

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!

 

[fargoth]

to use latex use [tex] $$and$$[/tex].
and as for the limit.. as x goes to infinity, $$\sqrt{x^2+r^2}$$ goes to x, because $$r^2$$ is much smaller and can be neglected.
so you get $$\frac{x}{xr^2}$$
and as you can see the x's are canceled out giving $$\frac{1}{r^2}$$

 

[d_leet]

Change the x in the numerator to sqrt(x^2) the multiply top and bottom by sqrt(1/(x^2))

 

[Repetit]

Thank you for the quick answers! I see it clearly now :-)