Limit Problem

1. May 14, 2009

icosane

1. The problem statement, all variables and given/known data

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

3. 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?

2. May 14, 2009

danago

Try writing x2+1 as x2(1+1/x2).

See if that helps.

3. May 15, 2009

HallsofIvy

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

4. May 16, 2009

rclakmal

put your x in to 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!!!!!!!!!!!!

5. May 16, 2009

HallsofIvy

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