Use the two-path test to prove that the following limit does not exist. y² - 2x² y² + x² lim (x,y)→→(0,0) y + What value

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Use The Two Path Test To Prove That The Following Limit Does Not Exist Y 2x Y X Lim X Y 0 0 Y What Value 1 (112.29 KiB) Viewed 12 times

Use the two-path test to prove that the following limit does not exist. y² - 2x² y² + x² lim (x,y)→→(0,0) y + What value does f(x,y) = y²-2x² y² + x² 4 What value does f(x,y) = O A. f(x,y) approaches (Simplify your answer.) B. f(x,y) has no limit and does not approach ∞ or - ∞ as (x,y) approaches (0,0) along the x-axis. y² - 2x² 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. 4 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. O A. f(x,y) approaches (Simplify your answer.) B. f(x,y) has no limit and does not approach ∞o or-coas (x,y) approaches (0,0) along the y-axis. Why does the given limit not exist? A. As (x,y) approaches (0,0) along different paths, f(x,y) approaches two different values. B. As (x,y) approaches (0,0) along different paths, f(x,y) does not always approach a finite value. OC. As (x,y) approaches (0,0), the denominator approaches 0. D. As (x,y) approaches (0,0) along different paths, f(x,y) always approaches the same value.