Question

How do you find the limit of `sqrt(x^2+4x+1)-1` as `x->oo`?

Answer 1

See below.

Explanation:

As `x` increases without bound, so does `x^2+4x+1`.
So `sqrt(x^2+4x+1)` increases without nound as `x` increases without bound.

Subtracting `1` doesn't change this, so

`lim_(xrarroo)(sqrt(x^2+4x+1)-1) = oo`