Question

the limit of ((square root of (x)^2-(x)-1)+x-1) as x approaches 0

Answer 1

did you try to directly put x=0 in the function ?

Answer 2

is this the limit you are asking ?
\(\large \lim \limits_{x \rightarrow 0} \sqrt{x^2-x+1}+x-1\)

Answer 3

The limit:
sqrt(0^2 - 0 + 1) + 0 - 1 = 1-1 = 0