2. (3 pts) Evaluate the following limit: 4 lim (x,y) (1,1) 2x-xy-y x - y (Hint:...

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2. (3 pts) Evaluate the following limit: 4 lim (x,y) →(1,1) 2x²-xy-y² x² - y² (Hint: factor both the numerator and the denominator completely) 3. (4 pts) Show that the limit below does not exist. Note that the function is not continuous at (0, 0), so we cannot simply evaluate the limit by plugging in (0, 0). Instead, approach (0,0) from two different paths. First try approaching along the x-axis (when y = 0), and then try approaching along the line y = x. What can you conclude about this limit? x²y² lim (x,y)-(0,0) x4 + 3y4 2. (3 pts) Evaluate the following limit: 4 lim (x,y) →(1,1) 2x²-xy-y² x² - y² (Hint: factor both the numerator and the denominator completely) 3. (4 pts) Show that the limit below does not exist. Note that the function is not continuous at (0, 0), so we cannot simply evaluate the limit by plugging in (0, 0). Instead, approach (0,0) from two different paths. First try approaching along the x-axis (when y = 0), and then try approaching along the line y = x. What can you conclude about this limit? x²y² lim (x,y)-(0,0) x4 + 3y4