# Triangle limit

If I define a triangle like this

$$0\le y\le 1$$ and $$0\le x\le 1-y$$,

then what is

$$\lim_{x\rightarrow 1} \frac{y}{1-x}$$ ?

As far as I can see, there are many possibilities, depending on how you "approach" $$x=1$$.

What you are writing doesn't make sense. Since you are taking the limit only as x goes to 1, y is some fixed number between 0 and 1. If $x\le 1-y$ and y is not 1 then x cannot "approach" 1. If y= 1, then, of course, the limit does not exist.