Question 0. Let's put the issue to Mathematica:
1 (4 points). Find the work done when the force F(x,y) = x^2 i - y j acts on an object moving along the curve x[t] = t, y[t] = t^2, from (0,0) to (3,9).
2 (4 points). a) Compute the gradient vector field of the function f(x,y,z) = x ln(y) - z ln(x).
3 (4 points). A solid S consists of the part of a ball of radius 4 that lies within a cone with its vertex at the origin and consisting of points within angle phi ³ ¹/6 from the z-axis, as seen from the origin.
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4. (4 points) Planet Spaceball is a sphere of radius 2 10^8 cm., with no atmosphere. The gravitational force on a 1 gram object at its surface is 400 dynes (c.g.s units of force). A golf ball on this planet, weighing 1 gram, is hit at an angle of ¹/3 with respect to the surface at speed 10^5 cm/sec. What height does it attain?