1. Given that z = 3x2 + 9xy - y2, compare the actual change in z Δz and the estimated change in z dz as (x,y) changes from (3, 9) to (2.95, 9.05), Express the absolute value of the difference as a percentage of the absolute value of the actual change.
|- Δz + dz| = ________ percent of |Δz|
2. A manufacturer is making Beans cans 7 cm high with a radius of 3 cm. Use differentials to estimate the amount of material used for the can if the top and bottom are 1/5 mm thick and the side is 1/10 mm thick.
Change mm to cm before proceeding. Also, be sure to count the top and bottom in your estimate.