# Finding the limit of x/sqrt(x^2 + 1) as x--> +infty

## Homework Statement

I need to find the limit of (x/sqrt(x^2 + 1)) as x goes to infinite for an infinite sequences problem.

## The Attempt at a Solution

I thought I would do L'H rule but I continually get infinite/infinite type does this mean it does not exist?

jamesrc
Gold Member
Try simplifying the expression by dividing both the numerator and denominator by x (so overall you've just multiplied by x/x=1 and haven't changed the expression). You'll be left with something you can find the limit of without having to use L'Hopital's rule.

So I did that and I got 1 / [(x+1)/(x^2)]^(1/2)

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Right, now simplify everything in the square root sign and you'll find that the equation reduces to something you can easily take the limit of as x-> infinity

Edit: By simplify I mean expand the fraction as two fractions over $x^2$. Also I believe that you mean $\sqrt{\frac{x^2+1}{x^2}}$

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yes I get it now I messed up with one of the x's in the denominator not being squared thanks everyone