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- The value of f (x - 3y2 + z) ds over the line segment C joining the point (0, 0, 0) to the point (1, 1, 1) isUse LaGrange multipliers to find the points on the surface 2² = x² + y² which are closest to (4, 2, 0).Compute foxy dx + (x³/2 + y³/2) dy where C is the square with vertices (0,0), (0,1), (1,1) and (1,0) oriented clockwise
- Let F(x,y) =(16xy+6x°sin(7y), 8x2+7xcos(7y)). (a) Is F conservative? O Yes, F is conservative O No, F is not conservative (b) Let C be the portion of the parabola y=x²-16 from (4,0) to (-4,0). Which of the following statements are true? (Select all that apply.) O By the Fundamental Theorem of Line Integrals, F.dr = f(-4, 0) - f(4, 0), where f(x,y) is a potential function for F. O By independence of path, F.dr, where C' is the line segment from (-4, 0) to (4, 0). F.dr = OBy Green's Theorem, dA, where D is the region bounded by C. F.dr = O None of the above.c. Let P(x, y) = y² + sin¬1 x² and Q (x, y) = 2xy + 4x. Suppose that C is the parallelogram with vertices (0,0), (4,0), (1,3) and (5,3). Evaluate f rax Pdx + Qdy over CIf F = (2x + y)i+ (3y - 4x)j evaluate ɖ̟e F.dr around a triangle ABC in the xy-plane with A(0. 0). B(2, 0), C(2, 1). (a) in the counterclockwise direction (b) what is the value in the opposite direction?
- Let F(x, y) (6x2 + 4y) i + (4x + 3) j. Calculate a F. dr, where C is the portion of the parabola y = 4x – 2x2 that starts at (0, 0)and ends at (1, 2).Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point (0, 3, 2).At what points (x,y,z) in space are the functions continuous? a. h(x,y,z)= In (2z³ - 3x-3y³ - 5) 1 b. h(x,y,z) = ₂³-√√x+y³ a. At which points is h(x,y,z) = In (2z³ - 3x − 3y³ - 5) continuous? Choose the correct answer below. A. All points satisfying 2z³ - 3x5 G. All points b. At which points is h(x,y,z) = z³. E. OG. All points - 1 x+1 O A. All points satisfying x + y³ > 0 C. All points satisfying z³ >√x+y³ All points satisfying x + y³ 20 OF. All points except (0,0,0) H. No points continuous? Choose the correct answer below. B. All points satisfying x + y³ ≥0 and 2³ √√x + y² # D. All points satisfying x#y #z F. All points satisfying z³ #√x+ OH. No points
