Question

How do you find the limit `(sqrt(y+1)+sqrt(y-1))/y` as `y->oo`?

Answer 1

The limit is `0`

Explanation:

For `y > 1`, we have

`(sqrt(y+1)+sqrt(y-1))/y = (sqrty(sqrt(1+1/y)+sqrt(1-1/y)))/y`

`= (sqrt(1+1/y)+sqrt(1-1/y))/sqrty`

As `yrarroo` the numerator goes to `2` and the denominator increases without bound.

So the limit is `0`.