Yes.
Consider x to 2, with x>2 (from the right). Then x-2>0.
So it will be positive infinity.
Consider x to 2, with x<2 (from the left). Then x-2<0.
So it will be negative infinity.
Thus
This means the limit doesn't exist, because the limit is not the same from the right and from the left.
It's essential that left hand and right and right hand limits are always considered.
It's not good enough to say x - 2 --> 0 etc.
You need to consider and , whether the limiting value of x - 2 etc. is or and consequently whether the left and right handed limits are +oo or -oo ....