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

  • #1
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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!
 

Answers and Replies

  • #2
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Factor x out of both terms in the denominator.
[tex]\frac{x}{10x + 1}~=~\frac{x}{x(10 + 1/x)}[/tex]

Now, what's the limit of the latter expression as x gets large?
 
  • #3
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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?
 
  • #4
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nevermind, i got it. thanks a lot.
 
  • #5
35,303
7,178


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...
 

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