P. Figure 4.9 EXERCISES In each of the following cases, a region D is defined. T
ID: 3168287 • Letter: P
Question
P. Figure 4.9 EXERCISES In each of the following cases, a region D is defined. Tell whether the region is a domain.I it is a domain, determine whether or not it is simply connected. If it is not a domain, explain why not. 1. The region of definition of a magnetic field due to a steady current flowing along the points (x.y.z) such that x2 + y2 > 0]. axis li.e, the region consisting of all 2. The region of definition of an electric field due to n point charges. 3. The region consisting of all points above the xy plane [i.e., all points (x.y,z) such that z >0]. 4. The region D consisting of all points (x,y,z) for which z 0. 5. The region D consisting of all points (x.y.z) such that x2+ y+ z>4 6. The region D consisting of all points (x.y,z) for which l xyExplanation / Answer
The region between in space between two concentric spheres are domain and the region is simply connected.
Reason:
Think about a region and imagine sticking a curve there, now shrinking it down so when the curve hits the boundary of the interior sphere it can simply slide along that surface to shrink it to a point.It doesn;t have to just sit at an equator.That extra dimension in which to shrink is what it makes it different from the space between two concentric circles in the plane
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