Question 1. Consider the function f : R R defines a follows: f(x, y) = (x+y)/(x

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1. Consider the function f : R² → R defines a follows: f(x, y) = (x¹+y³)/(x² + y²) if (x, y) = (0,0) and f(0,0) = 0. State whether the following statements are true or false and justify your answer. (a) The function f is continuous at the origin (0,0). (b) Both the partial derivatives of f exist. [2 marks for correct alternative (T/F); 3 marks for correct justification] 1. Consider the function f : R² → R defines a follows: f(x, y) = (x¹+y³)/(x² + y²) if (x, y) = (0,0) and f(0,0) = 0. State whether the following statements are true or false and justify your answer. (a) The function f is continuous at the origin (0,0). (b) Both the partial derivatives of f exist. [2 marks for correct alternative (T/F); 3 marks for correct justification]

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