Q1 (9 points) Calculate the triple integral SSSE x³ y² z dV where E is the region bounded by z — y = 1, = z+y=1, z= 0, x = 0, and x = 1.

A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.

The area D is the area in the XY-plane bounded by the X-axis, Y-axis, and the 4x + line5y = 0. Determine the maximum and minimum values f (x, y) = 2x2 + 2y2 - 4x - 2y + 3 in the region