Let f: R² R2, f = (f1, f2), be defined by f(0,0) = (0,0), and y³ 23 x² + y²¹ f₂(x, y). x² + y² (a) Show that f is continuous at (0,0). (b) Show that f is not differentiable at (0.0). (c) Show that f is differentiable at the point (1,0) by using the limit-definition directly. (You must explicitly give the linear operator f'(1, 0) and show that it is the (Fréchet) derivative of f at that point.) f₁(x, y) = for (x, y) (0,0). #

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