Find the gradient vector field Vf of f. - y)² Vf(x, y) = f(x, y) = (x 3 Sketch the gradient vector field.
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- 2. Plot the gradient vector field of f together with its contour map. (a) f(x,y)=4- 4-4-4 (b) f(x, y)=√x² + y²3. Let f(x, y) = sin x + sin y. (NOTE: You may use software for any part of this problem.) (a) Plot a contour map of f. (b) Find the gradient Vf. (c) Plot the gradient vector field Vf. (d) Explain how the contour map and the gradient vector field are related. (e) Plot the flow lines of Vf. (f) Explain how the flow lines and the vector field are related. (g) Explain how the flow lines of Vf and the contour map are related.Find the gradient vector field of f(x, y) = xe3xy.