Express the given elementary region in R* in terms of individual inequalities on p,0, and p. Express the given elementary region in R° in terms of a set using set notation. If p an o do not depend upon 0 then there is rotational symmetry around the z-axis. The trace of the boundary of region E wll therefore be the same in any half-plane 0 = 0, (where p2 0, 0 <0< #) extending from the z-axis at a fixed angle 6,. from the positive r-axis (like a door hinged to the z-axis). Sketch the trace of the boundary of E in this half-plane and then shade E. Imagine what results by revolving this shaded region through the range of relevant 0 angles.
Express the given elementary region in R* in terms of individual inequalities on p,0, and p. Express the given elementary region in R° in terms of a set using set notation. If p an o do not depend upon 0 then there is rotational symmetry around the z-axis. The trace of the boundary of region E wll therefore be the same in any half-plane 0 = 0, (where p2 0, 0 <0< #) extending from the z-axis at a fixed angle 6,. from the positive r-axis (like a door hinged to the z-axis). Sketch the trace of the boundary of E in this half-plane and then shade E. Imagine what results by revolving this shaded region through the range of relevant 0 angles.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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E is the region contained between and on the sphere of radius 2 and the sphere of radius 5 centered at the origin.
Transcribed Image Text:Express the given elementary region in R* in terms of individual inequalities on p, 0, and p.
Express the given elementary region in R in terms of a set using set notation.
If p an o do not depend upon 6 then there is rotational symmetry around the z-axis. The trace of the boundary of region E will
therefore be the same in any half-plane 0 = 0. (where p2 0, 0 <¢ < 7) extending from the z-axis at a fixed angle 6, from the
positive r-axis (like a door hinged to the z-axis). Sketch the trace of the boundary of E in this half-plane and then shade E. Imagine
what results by revolving this shaded region through the range of relevant 0 angles.
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