Question

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

Answer 1

The limit does not exist (it diverges to infinity)

Explanation:

We want `lim_(x rarr oo) sqrt(x^2+2x) + x`

Both `x^2` and `x` (and therefore `2x`) increase without bound as `x` increases, hence `sqrt(x^2+2x)` also increases without bound and the limit diverges.