(b) Let the domain V be the volume defined by the inequalities x2 + y2 + z²21, Vx2 + y2 +z3H and x > 0, y 20, z > 0. (i)

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B Let The Domain V Be The Volume Defined By The Inequalities X2 Y2 Z 21 Vx2 Y2 Z3h And X 0 Y 20 Z 0 I 1 (73.18 KiB) Viewed 67 times

(b) Let the domain V be the volume defined by the inequalities x2 + y2 + z²21, Vx2 + y2 +z3H and x > 0, y 20, z > 0. (i) Determine the value Ho such that for all H > H., the sphere x2 + y2 + z2 = 1 does not intersect the cone V x2 + y2 + z = H (ii) Setting H = 2, sketch the intersection of the domain V with each of the following planes: z = 0, z = 1, y = 0. (iii) Compute the volume of V in the case H = 2. (c) If H = 2 in the definition of the domain V in part (b), and f(x, y, z) = V x² + y² Vx2 + y2 evaluate SII, sex, y, z)av.