lim x/x

(x,y)->(0,0)

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?