Question: 1. Decide if the vector field 2xy i + x27 is the gradient of a function f. If so, find f. If not, explain why

1. Decide if the vector field 2xy i + x27 is

1. Decide if the vector field 2xy i + x27 is the gradient of a function f. If so, find f. If not, explain why not. 2. Decide if the vector field (x2 + y?) i + 2ry j is the gradient of a function f. If so, find f. If not, explain why not. 3. Decide if the vector field i + 2 + 4 is the gradient of a function f. If so, find f. If not, explain why not. 4. Decide if the vector field , i - ,2 7 is the gradient of a function f. If so, find f. If not, explain why not. 5. Use Green's Theorem to calculate the circulation of F = yi - r j around the unit circle, oriented counterclockwise. 6. Use Green's Theorem to calculate the circulation of F = ry j around the square 0

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