Defining a Triangle: Investigating $\lim_{x\rightarrow 1} \frac{y}{1-x}$

[daudaudaudau]

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.

 

[HallsofIvy]

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.

 

[daudaudaudau]

Hmm, yeah, maybe it does not make much sense. Fortunately, I was able to fix my problem in another way, which gave a result with no singularities. So I don't have to solve this problem :) Phew.