i Which of the following regions are simply-connected? a) the half-plane lying above the x-axis b) the plane minus the line segment joining (0,0) and (0,1) c) the plane minus the positive x-axis

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter12: Conic Sections
Section12.5: Rotation Of Axes
Problem 1E: Suppose the x- and y-axes are routed through an acute angle to produce the new X- and Y-axes. A...
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i Which of the following regions are simply-connected?
a) the half-plane lying above the a-axis
b) the plane minus the line segment joining (0,0) and (0,1)
c) the plane minus the positive x-axis
d) the plane minus the entire r-axis
e) in polar coordinates, the region where r> 0, 0 < 0 < 0o
f) the region between two concentric circles
g) the region in the plane between the two branches of the hyperbola ry = 1
Transcribed Image Text:i Which of the following regions are simply-connected? a) the half-plane lying above the a-axis b) the plane minus the line segment joining (0,0) and (0,1) c) the plane minus the positive x-axis d) the plane minus the entire r-axis e) in polar coordinates, the region where r> 0, 0 < 0 < 0o f) the region between two concentric circles g) the region in the plane between the two branches of the hyperbola ry = 1
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