Exercise. 1. A constant force F=3i+5j+10k moves an object along a straight line from the point...

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Exercise. 1. A constant force F=3i+5j+10k moves an object along a straight line from the point (1,0,2) to (5, 3, 8). Find the work done of the distance is measured in meters and the force in newtons. (3 marks) 2 2. Show that the level curves of the cone z = r + y and paraboloid z = r + y are circles, and make a sketch that illustrates the difference between the contour plot of the two functions. 3. Find the vectors T, N and B of the following vector function. r(t) e' sin ti + e' costj + 3k. (3 marks) (3+3+4 marks) 4. Find the local linear approximation L to the specified function f at the designated point P. Also, compare the error in approximating f by L at the specified point Q with the distance between P and Q. f(x, y)=x+ey P = (3,0), Q = (3.04,0.05). (5+2 marks) 5. Use Lagrange Multiplier to find all relative extrema of subject to the constraint f(x, y) = xy 4x + y = 8. (7 marks) Exercise. 1. A constant force F=3i+5j+10k moves an object along a straight line from the point (1,0,2) to (5, 3, 8). Find the work done of the distance is measured in meters and the force in newtons. (3 marks) 2 2. Show that the level curves of the cone z = r + y and paraboloid z = r + y are circles, and make a sketch that illustrates the difference between the contour plot of the two functions. 3. Find the vectors T, N and B of the following vector function. r(t) e' sin ti + e' costj + 3k. (3 marks) (3+3+4 marks) 4. Find the local linear approximation L to the specified function f at the designated point P. Also, compare the error in approximating f by L at the specified point Q with the distance between P and Q. f(x, y)=x+ey P = (3,0), Q = (3.04,0.05). (5+2 marks) 5. Use Lagrange Multiplier to find all relative extrema of subject to the constraint f(x, y) = xy 4x + y = 8. (7 marks)