6. (1 point) For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, f = F). If it is not conservative, type N. A. F (x, y) = (14x 7y) i + (7x + 10y) j f (x, y) = B. F (x, y) = 7yi + 8xj f (x, y) = C. F (x, y, z) = 7xi + 8yj + k f (x, y, z) = D. F (x, y) = (7 sin y) i + (14y + 7x cos y) j f (x, y) = E. F (x, y, z) = 7x2 i 7y2 j + 5z2 k f (x, y, z) = Note: Your answers should be either expressions of x, y and z (e.g. \"3xy + 2yz\"), or the letter \"N\" \u0001 1. (1 point) Let f (x, y) = 3y2 3x2 + 3xy . Then a standard equation for the tangent plane to the graph of f at the point (1, 3, 15) is . Answer(s) submitted: (incorrect) 2. (1 point) Consider the ellipsoid 3x2 + 2y2 + z2 = 18. Find all the points where the tangent plane to this ellipsoid is parallel to the plane 2y 6x + 2z = 0. (If there are several points, separate them by commas.) Answer(s) submitted: Answer(s) submitted: (incorrect) 3. (1 point) Consider the ellipsoid 5x2 + y2 + z2 = 10. The implicit form of the tangent plane to this ellipsoid at (1, 2, 1) is . The parametric form of the line through this point that is perpendicular to that tangent plane is L(t) = . (incorrect) 7. (1 point) Let F = (10yz) i + (8xz) j + (1xy) k. Compute the following: A. div F = B. curl F = i+ j+ k C. div curl F = Note: Your answers should be expressions of x, y and/or z; e.g. \"3xy\" or \"z\" or \"5\" Answer(s) submitted: (incorrect) 4. (1 point) \u0001 Find the point on the graph of z = 2x2 + y2 at which vector n = h60, 24, 3i is normal to the tangent plane. Answer(s) submitted: P= Answer(s) submitted: (incorrect) (incorrect) 8. (1 point) Let F be any vector field of the form F = f (x) i + g (y) j + h (z) k and let G be any vector field of the form F = f (y, z) i + g (x, z) j + h (x, y) k. Indicate whether the following statements are true or false by placing \"T\" or \"F\" to the left of the statement. 5. (1 point) Find an equation of the tangent plane to the graph of F(r, s) at the given point: F(r, s) = r4 s0.5 s3 , (2, 1, 15) z= 1. 2. 3. 4. Answer(s) submitted: (incorrect) F F G G is irrotational is incompressible is incompressible is irrotational Answer(s) submitted: 1 (B) (incorrect) 9. (1 point) The three figures below show three vector fields. In each case, determine whether the line integral around the circle (oriented counterclockwise) is positive, negative, or zero. Note: Use \"0\" for zero, \"P\" for positive, and \"N\" for negative. (C) Answer(s) submitted: (incorrect) 10. (1 point) Let C be the curve which is the union of two line segments, the first going from (0, 0) to (1, -3) and the second going from (1, -3) to (2, Z 0). 1dy + 3dx. Compute the line integral (A) C Answer(s) submitted: (incorrect) 2