In Exercise 1 you showed that the limit of the function xy/(x2 + y2) as (x, y) → (0, 0) do...

In Exercise 1 you showed that the limit of the function xy/(x2 + y2) as (x, y) → (0, 0) does not exist. Thus the function

is not continuous at (0, 0). Show, however, that both and exist and are equal to zero. How can this happen? If you have a computer graphing program, examine the graph of f near (0, 0). What are the values of f along the lines x = 0 and y = 0?

Exercise 1

In Exercise, explain why the given limit does not exist.