Let $\displaystyle F(x,y)=\frac {x-y^4}{x^3-y^4}$
Determine whether $\displaystyle lim(x,y)\rightarrow(1,1) F(x,y)$ exists.
Any insight is appreciated, thanks.
ok, my first method remains valid, but the lines i chose were silly choices.
again, approach the limit along $\displaystyle y = x$, you will find that the limit is 3
but approach the limit along $\displaystyle x = 2 - y^2$, you will find that the limit is 3/5
(i'm so used to approaching the origin, i said to approach along $\displaystyle x = 0$ without even realizing that we could never get close to the point $\displaystyle (1,1)$ by doing that)