Using differentials approximate the amount of material

Question

1. If z =8x³ +2 x² y - y evaluate dz where x =1,y=1,dx=.02, and dy=.03

2. Using differentials, approximate the amount of material needed to make a cylindrical drinking glass tumbler with inside diameter 3 cm and inside height 9 cm. Assume the walls and bottom of the tumbler are 0.1 cm thick. (The tumbler has a bottom but no top.)

3. Evaluate ₂∫⁵ [(5 + 3y) / √x] dy

4. Evaluate ₁₆∫²⁵ ₂∫⁵ [(5 + 3y) / √x] dy.

5. If R is the region with boundaries -1 ≤ x ≤ 0 and -x² ≤ y ≤ x² then evaluate ∫ R ∫ (x² - y) dy dx (the R in this equation should be under the double integral symbol).