1. ## Two Variable Limit

Let $F(x,y)=\frac {x-y^4}{x^3-y^4}$

Determine whether $lim(x,y)\rightarrow(1,1) F(x,y)$ exists.

Any insight is appreciated, thanks.

2. ok, my first method remains valid, but the lines i chose were silly choices.

again, approach the limit along $y = x$, you will find that the limit is 3

but approach the limit along $x = 2 - y^2$, you will find that the limit is 3/5

(i'm so used to approaching the origin, i said to approach along $x = 0$ without even realizing that we could never get close to the point $(1,1)$ by doing that)

3. This stuff is new to me so I'm trying my best to absorb it all, the help is really appreciated, thanks a lot.

4. Originally Posted by Len
This stuff is new to me so I'm trying my best to absorb it all, the help is really appreciated, thanks a lot.
well, keep practicing. this is one of those topics it takes a while to get, at least it did for me. i've forgotten a lot of the tricks that work with these though. this limit wasn't that bad

5. I'm rusty at this stuff, but wouldn't some combination of partial derivatives and L'Hospital's rule work?

6. Originally Posted by Prove It
I'm rusty at this stuff, but wouldn't some combination of partial derivatives and L'Hospital's rule work?
perhaps, i have never actually used L'Hopital's rule in a multivariable case, so i can't say