Find the volume of the following solids by double integration: 10. The solid in the first octant bounded by 2x + 3y + 4z = 12 and the coordinate planes. (Check the answer by using the formula for the volume of a pyramid.) [11 The solid in the first octant bounded by the cylinder x² = 4-² and the planes x = 0, y = 0, z = 0 and 4x + 3y = 12.

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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.