lim when x approaching to negative infinity

Question

sqrt(x^2+ ln |x|) +x

Evaluate the limit.

Answer 1

x² dominates the expression under the radical, i.e. the expression under the radical approaches y=x as

x approaches -∞ and therefore the whole expression approaches 0 as x approaches -∞...and a graph will confirm this.

What steps?

The expression under the radical approaches y=x as x->-∞.

Then you have x-x in the limit which is clearly 0.