1. Consider the function 2xy (x, y) + (0,0) f(x,y)%3D (x,y) 3D(0,0) (a) Use a computer...

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1. Consider the function 2xy (x, y) + (0,0) f(x,y)%3D (x,y) 3D(0,0) (a) Use a computer to draw a contour diagram for f. Which of the following is the contour diagram? • figure 1 • figure 2 • figure 3 • figure 4 3. -0.8 0.8 -0.5 -1.5 2 1.5 0.42 05 06, -0.2- -3 -2 -1 2 0.4 --0.5- -04 0.6 -1 0.7 -2 1.5 -1.5 0.6 -0.6 1. 2. -2 37 -0.8 30 -115 21 -15 1.5 -0.2 -0.4 0.4 -0.6 0.5 -3 -2 0.4 2. 0.6 1.5 0.2 02 205 3. -15 215.9 x 279.4 AR 4. 1. (b) Is f differentiable at all points (x,y) (0,0)? [?/yes/no] (c) Calculate the partial derivatives of f for (x,y) (0,0): fx fy Do the partial derivatives f and f, exist and are they continuous at all points (x,y) (0,0)? • ? they don't exist at at least one point • they exist but aren't continuous at at least one point • they exist and are continuous at all points 1. Consider the function 2xy (x, y) + (0,0) f(x,y)%3D (x,y) 3D(0,0) (a) Use a computer to draw a contour diagram for f. Which of the following is the contour diagram? • figure 1 • figure 2 • figure 3 • figure 4 3. -0.8 0.8 -0.5 -1.5 2 1.5 0.42 05 06, -0.2- -3 -2 -1 2 0.4 --0.5- -04 0.6 -1 0.7 -2 1.5 -1.5 0.6 -0.6 1. 2. -2 37 -0.8 30 -115 21 -15 1.5 -0.2 -0.4 0.4 -0.6 0.5 -3 -2 0.4 2. 0.6 1.5 0.2 02 205 3. -15 215.9 x 279.4 AR 4. 1. (b) Is f differentiable at all points (x,y) (0,0)? [?/yes/no] (c) Calculate the partial derivatives of f for (x,y) (0,0): fx fy Do the partial derivatives f and f, exist and are they continuous at all points (x,y) (0,0)? • ? they don't exist at at least one point • they exist but aren't continuous at at least one point • they exist and are continuous at all points

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