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

  • #1
270
1

Homework Statement



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

Homework Equations





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?
 

Answers and Replies

  • #2
jamesrc
Science Advisor
Gold Member
476
1
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.
 
  • #3
270
1
So I did that and I got 1 / [(x+1)/(x^2)]^(1/2)
 
Last edited:
  • #4
743
1
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 [itex] x^2 [/itex]. Also I believe that you mean [itex] \sqrt{\frac{x^2+1}{x^2}} [/itex]
 
Last edited:
  • #5
270
1
yes I get it now I messed up with one of the x's in the denominator not being squared thanks everyone
 

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

  • Last Post
Replies
1
Views
7K
Replies
7
Views
2K
  • Last Post
Replies
5
Views
10K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
5K
Replies
30
Views
8K
Replies
5
Views
2K
Replies
15
Views
2K
Replies
4
Views
2K
Top