Use the two-path test to prove that the following limit does not exist. X + 2y What value does f(x,y) = x - 2y approach as (X,y) approaches (0,0) along the x + 2y lim x-axis? Select the correct choice below and, if necessary, fill in the answer box (x.y)-+(0.0) X - 2y to complete your choice. O A. f(x y) approaches Z X+ Ly (Simplify your answer.) z=- x - 2v O B. f(x,y) has no limit and does not approach co or - co as (X,y) approaches (0,0) along the x-axis. x+ 2y What value does f(x,y) = x - 2y approach as (X,y) approaches (0,0) along the y-axis? Select the correct choice below and, if necessary, fill in the answer box y to complete your choice. O A. f(x,y) approaches (Simplify your answer.) O B. f(x,y) has no limit and does not approach co or - co as (x,y) approaches (0,0) along the y-axis. Why does the given limit not exist? O A. As (X,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value O B. The limit does not exist because as (x,y) approaches (0,0), the denominator approaches 0 O C. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value. O D. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values.