(a) Show that vector = (y²cosx + z³)+ (2ysinx - 4)+ (3xz² + 2) is a conservative field. (8 分)

1. In the engine shown in Figure 1, a 7-inch connecting rod is fastened to a crank of radius 3 inches. The crankshaft rotates counterclockwise at a constant rate of 200 rpm (revolutions per minute). Find the velocity (i.e., dx/dt) of the piston when θ = π/3. (15 分) Figure 1. The velocity of a piston is related to the angle of the crankshaft.