calculate limit of f(x,y) as (x,y) tends to 0 and f(x,y) is defined as 1 when x,y is not equal to 0 and is 0 when x,y is equal to 0

Question

calculate limit of f(x,y) as (x,y) tends to 0 and f(x,y) is defined as 1 when x,y is not equal to 0 and is 0 when x,y is equal to 0

Answer 1

Since f(x,y) = 1 everywhere except the origin, this limit is 1. This is because, along every path, as we approach the origin, the value remains exactly 1 along the whole path.