Question

Evaluate the limit of x-1 / square root of x - 2x as x approaches to 1.

NOTE: 2X does not belong to the square root.

Answer 1

so, write it clearly:

limit as x->1 of (x-1)/(√x - 2x)

I see no problem here, since √x - 2x -> -1, which is not zero.

(x-1)/(√x-2x) -> 0

Apparently I have it wrong, but cannot see an easy way to massage it into something which -> 0/0

Anyway, try l'Hospital's Rule if you get a 0/0 limit.