Question

LIM X ----> 1 ^ -

|X - 1|/ X - 1

Answer 1

when x<1 ,
|x-1| = -(x-1) = -x+1

Answer 2

hint : as x->1-
|x-1|=-(x-1)

Answer 3

thats because, if \[x \rightarrow 1^-\]
means, x is very very near to 1, but less than 1.
so, \[x<1 \implies x-1 <0 \implies |x-1|=-(x-1)\]