1. Let f,g: R R be defined by f(x, y) = + y and...

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1. Let f,g: R² → R be defined by f(x, y) = √² + y² and g(x, y) = |xy| for (x, y) = R². Determine which of the following statements is true. Justify your answer. (a) Both f and g are differentiable at (0,0). (b) f is differentiable at (0,0), but g is not differentiable at (0,0). (c) is differentiable at (0,0), but f is not differentiable at (0,0). (d) Neither f nor g is differentiable at (0,0). [2 marks for correct alternative (T/F); 3 marks for correct justification] 1. Let f,g: R² → R be defined by f(x, y) = √² + y² and g(x, y) = |xy| for (x, y) = R². Determine which of the following statements is true. Justify your answer. (a) Both f and g are differentiable at (0,0). (b) f is differentiable at (0,0), but g is not differentiable at (0,0). (c) is differentiable at (0,0), but f is not differentiable at (0,0). (d) Neither f nor g is differentiable at (0,0). [2 marks for correct alternative (T/F); 3 marks for correct justification]

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