What value does f(xy) approach as (xy) approaches (0,0) along the X-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA f(x,y) approaches (Simplify your answer) 0B. f(x,y) has no limit and does not approach c or co as (x,y) approaches (0,0) along the X-axis.
What value does f(x,y) approach as (x,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
0A f(x,y) approaches (Simplify your answer) 0B. f(x,y) has no limit and does not approach c or c as (x,y) approaches (0,0) along the y-axis.
Why does the given limit not exist?
As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values. The limit does not exist because as (x,y) approaches (0,0), the denominator approaches 0. As (xy) approaches (0,0) along different paths, f(xy) always approaches the same value. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value.