i am a little confused about multivariate limits. i know that for a single variable, this limit is trivial and is simply 1, but for this limit i suspect it to be 1 but i am not sure. based on the definition of the limit, it says that for all epsilon there exists a delta such that when the distance between (x,y) and (0,0) is less than delta, then the distance between f(x) and the limit L is less than epsilon. but this function x/x is not defined along the line x=0. this means that in some delta neighborhood of (0,0) the function will not be defined there.
some definitions of limits i read say that x must be in the domain of the function, but other definitions don't seem to say it explicitly.
for example (from wikipedia):
Let ƒ be a function defined on an [COLOR=rgb(0, 0, 0)]open interval[/COLOR] containing c (except possibly at c) and let L be a real number. then for each real ε > 0 there exists a real δ > 0 such that for all x with 0 < |x − c| < δ, we have |ƒ(x) − L| < ε
this definition does not seem to mention that fact that x must be in the domain of the function. is this definition incorrect then?