For each of the following two functions f: R R, check whether the function is continuous...

 

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For each of the following two functions f: R R, check whether the function is continuous at (0,0), and justify your answer. (a) f(x,y) { for (x, y) (0,0) for (x, y) =(0,0). (b) f(x, y) = [o (x + y) log(x + y) for (x, y) (0,0) for (x, y)=(0,0). Hint: For (b), polar coordinates are useful! (4 marks) For each of the following two functions f: R R, check whether the function is continuous at (0,0), and justify your answer. (a) f(x,y) { for (x, y) (0,0) for (x, y) =(0,0). (b) f(x, y) = [o (x + y) log(x + y) for (x, y) (0,0) for (x, y)=(0,0). Hint: For (b), polar coordinates are useful! (4 marks)