Question

Evaluate the limit of the function as x approaches negative infinity of:
f(x) = (x + \sqrt{x^2 + 2x}

Attempt:
Multiplying by the conjugate:
=
(x + \sqrt{x^2 + 2x} * (x - \sqrt{x^2 + 2x}
----------------
1 ((x - \sqrt{x^2 + 2x})

Simplifying:

= 2x / x - \sqrt{x^2 + 2x}

Multiplying both top and bottom by 1/x
2x (1/x)
-------
x - \sqrt{x^2 + 2x}

Simplifying and I get:

2/0 = DNE..

Is this correct?