3. Find the partial derivative (0,1) (0,0) əz Ox for the given equation (2,1) (2,0) x²y+ · cos(ry) = 100. 4. Evaluate the line integral of the following gradient vector field over defined by y = r³ for 1 ≤ x ≤ 4. Vf = (4x³y², 2x¹y) 5. Write an equation of a line that is parallel to vector (1,2, 1) and pas point (-3, 7, 20). 6. Set up and evaluate the triple integral of f(2, y, z) = x + y over the reg x = 0, y = 0, z = 0, y = 4, and z=4- x². The region and its 2D slic below.

4- 3 2- 10 20 30 5.

Arrange these steps in the correct order to prove that if you have an 8-gallon jug of water and two empty jugs with capacities of 5 gallons and 3 gallons, respectively, then you can measure 4 gallons by successively pouring some of or all of the water in a jug into another jug in the correct order. Rank the options below. Fill the 3-gallon jug from the 5-gallon jug, leaving (3, 2, 3). Empty the 5-gallon jug's contents into the 3-gallon jug, leaving (6, 0, 2), and then fill the 5-gallon jug from the 8-gallon jug, producing (1, 5, 2). Fill the 5-gallon jug from the 8-gallon jug, leaving the contents (3, 5, 0), where the ordered triple is used to record the amount of water in the 8-gallon jug, the 5-gallon jug, and the 3-gallon jug, respectively. Top off the 3-gallon jug from the 5-gallon jug, and there will be (1, 4, 3), with four gallons in the 5-gallon jug. Pour the contents of the 3-gallon jug back into the 8-gallon jug, leaving (6, 2, 0). ❤ ← ←