- #1

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Say we want to evaluate the lim( x^2-y^2)/(x+y) as (x,y)->(0,0).

we can factor as follows (x-y)(x+y)/(x+y)

the x+y cancel and we are left with x-y

lim (x-y)=0 as (x,y)->(0,0) since x-y is clearly continuous a continuous function along any path.

Does this work?

What about the path y=-x? Is that entire line a removable discontinuity?