sin(4πt)e-6x Problem. 7: Find the differential of the function z = dz = ? dx + ? dt Problem. 8: If z = x² + 4y² and (x, y) changes from (2, 1) to (1.8, 1.05), calculate the differential dz. dz = ? Problem. 9: The length and width of a rectangle are measured as 31 cm and 34 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle. cm² Problem. 10: Use differentials to estimate the amount of metal in a closed cylindrical can that is 60 cm high and 20 cm in diameter if the metal in the top and the bottom is 0.5 cm thick and the metal in the sides is 0.05 cm thick. dV = ? cm³