Use the two-path test to prove that the following limit does not exist. lim x+2y (x,y)(0,0)x-2y...

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Use the two-path test to prove that the following limit does not exist. lim x+2y (x,y)(0,0)x-2y X N Z= x+2y x-2y x+2y What value does f(x,y) = x-2y approach as (x,y) 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.) OB. f(x,y) has no limit and does not approach co or co as (x,y) approaches (0,0) along the x-axis. What value does f(x,y) = x+2y 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 to complete your choice. OA. f(x,y) approaches (Simplify your answer.) OB. 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? OA. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value. OB. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values. OC. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. OD. The limit does not exist because as (x,y) approaches (0,0), the denominator approaches 0. Use the two-path test to prove that the following limit does not exist. lim x+2y (x,y)(0,0)x-2y X N Z= x+2y x-2y x+2y What value does f(x,y) = x-2y approach as (x,y) 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.) OB. f(x,y) has no limit and does not approach co or co as (x,y) approaches (0,0) along the x-axis. What value does f(x,y) = x+2y 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 to complete your choice. OA. f(x,y) approaches (Simplify your answer.) OB. 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? OA. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value. OB. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values. OC. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. OD. The limit does not exist because as (x,y) approaches (0,0), the denominator approaches 0.