Question

How do you find the limit of `sqrt(x^2 + x + 1) / x` as x approaches infinity?

Answer 1

Reqd. Limit`=1`.

Explanation:

Reqd. Limit`=lim_(xrarroo) sqrt(x^2+x+1)/x`

`=lim_(xrarroo) sqrt{x^2(1+1/x+1/x^2)}/x`

`=lim_(xrarroo) {cancelxsqrt(1+1/x+1/x^2)}/cancelx`

`=lim_(xrarroo) sqrt(1+1/x+1/x^2)`

`=sqrt(1+0+0)`

`=1`.