# Lim sqrt(x)/sqrt(10x+1) ?

lim sqrt(x)/sqrt(10x+1) ??

Limit as x tends to infinity of sqrt(x)/sqrt(10x+1) = sqrt(1/10), but how?

I'm trying to understand this, so, it's the sqrt[x/(10x+1)], but how do i simplify that to make it a limit i can set to infinity. I know the problem isn't my calculus skills, but my algebra skills!

Mark44
Mentor

Factor x out of both terms in the denominator.
$$\frac{x}{10x + 1}~=~\frac{x}{x(10 + 1/x)}$$

Now, what's the limit of the latter expression as x gets large?

If we set x to infinity we get infinity/infinity(10) which is just equal to infinity/infinity?? The limit as x gets very large is 1 though.

Why did you take off the radical sign, btw, is that part of simplification?

nevermind, i got it. thanks a lot.

Mark44
Mentor

If we set x to infinity we get infinity/infinity(10) which is just equal to infinity/infinity?? The limit as x gets very large is 1 though.

Why did you take off the radical sign, btw, is that part of simplification?

infinity/infinity or infinity - infinity is NEVER the answer.

I was working inside the radical...