3. (3p.+ 3p. + 2p.) Consider the function g: R2 + R2 given by : 1 - ery , xy) if (x,y) = (0,0) x2 + y2 g(x,y) (0,0) if (

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3 3p 3p 2p Consider The Function G R2 R2 Given By 1 Ery Xy If X Y 0 0 X2 Y2 G X Y 0 0 If 1 (50.59 KiB) Viewed 35 times

3. (3p.+ 3p. + 2p.) Consider the function g: R2 + R2 given by : 1 - ery , xy) if (x,y) = (0,0) x2 + y2 g(x,y) (0,0) if (x, y) = (0,0). (a) Decide if g is continuous at (0,0). g (b) Decide if the partial derivatives of g exist at (0,0); if the answer is affirmative, then compute them. (c) Decide if g is differentiable at (0,0); if the answer is affirmative, then find Dg(0,0).