. Consider the following function. xy f(x, y) = x + y 0 (x, y) =...

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. Consider the following function. xy³ f(x, y) = x² + y² 0 (x, y) = (0,0) (x, y) = (0,0) (a) Compute lim f(x,y) along the path c₁(t) = (0, t). (x,y)→(0,0) (b) Compute lim f(x, y) along the path c₂(t) = (t³, t). (x,y) →(0,0) (c) The choice of the paths c₁ and c₂ is mysterious. Something about the formula for f(x, y) suggested that these paths would yield different limits. Brielfy describe what properties of the formula for f(x, y) suggest the choice of the paths c₁ and c₂. C2. . Consider the following function. xy³ f(x, y) = x² + y² 0 (x, y) = (0,0) (x, y) = (0,0) (a) Compute lim f(x,y) along the path c₁(t) = (0, t). (x,y)→(0,0) (b) Compute lim f(x, y) along the path c₂(t) = (t³, t). (x,y) →(0,0) (c) The choice of the paths c₁ and c₂ is mysterious. Something about the formula for f(x, y) suggested that these paths would yield different limits. Brielfy describe what properties of the formula for f(x, y) suggest the choice of the paths c₁ and c₂. C2.