Is limit of function -1/0 ok? A quick question, i'm determining the limit of this function:
$$\lim_{x→1}\frac{x^2 - 2x}{x^2 -2x +1}$$
When I divide numerator and denominator by $x^2$ and fill in $1$, I get $-1/0$. This is an illegal form right? Or does it indicate it is going to $∞$ or $-∞$? 

$$\frac{x^2-2x}{x^2-2x+1}=\frac{x(x-2)}{(x-1)^2}\xrightarrow[x\to1]{}-\infty$$
since $\;x(x-2)\to-1\;$ and $\;(x-1)^2\to 0^+\;$ (meaning: approximates to zero from the positive side), so your limit is negative infinity.
Some may define this as "the limit doesn't exist", but I think it is more accurate to say "the limit doesn't exist finitely" and/or "the limit exists in the wide sense of the word", " the function diverges to $\;-\infty\;$",  or something similar.
