Limit Problem: Solving Lim as x goes to infinity of sqrt(x^2 + 1) / x

[icosane]

Homework Statement

Lim as x goes to infinity of sqrt(x^2 + 1) / x

The Attempt at a Solution

know you are supposed to divide by the highest power of x, but how does that work when you have an x^2 within a sqrt?

 

[danago]

Try writing x²+1 as x²(1+1/x²).

See if that helps.

 

[HallsofIvy]

And remember that $(1/x)\sqrt{x^2+ 1}= \sqrt{(1/x^2)(x^2+ 1}$

 

[rclakmal]

put your x into the square root by making it X^2...then it will be easy because you will get something like
limit x--->infinity sqrt(1+1/X^2)
and when x goes to infinity 1/X^2 goes to zero
so your final limit will go to 1
hope you got it!

 

[HallsofIvy]

You've got three responses saying the same thing in different ways!