Let D be the region x ≥ 0, y ≥ 0, z ≥ 0, x + (y/2) + (z/3) ≤ 1. (a) Is this region a domain? (b) Is this region simply connected? (c) If F = 2xi + yj + zk, find the surface integral of the normal component of F over the boundary of this region, oriented by selecting the outward normal.

Question

Let D be the region x ≥ 0, y ≥ 0, z ≥ 0, x + (y/2) + (z/3) ≤ 1.

(a) Is this region a domain?

(b) Is this region simply connected?

(c) If F = 2xi + yj + zk, find the surface integral of the normal component of F over the boundary of this region, oriented by selecting the outward normal.

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