Does there exist an oriented simple closed curvey in the plane of length 2π such that fx dy-y dx > 2π? Indicate whether or not such a curve exists, along with the best reasoning/explanation from the choices below. Select one: a. Yes, there exists such a curve. In fact, there exists a convex curve with these properties. b. Yes, there exists such a curve, but any such curve is not convex. Oc. No, no such curve exists, by the Jordan curve theorem. O d. No, no such curve exists, by Hopf's Umlaufsatz. Oe. No, no such curve exists, by Fenchel's theorem. Of. No, no such curve exists, by the isoperimetric inequality. O g. No, no such curve exists, by Green's theorem. Oh. No, no such curve exists, by Gauss' Theorema Egregium. O. No, no such curve exists, by the Gauss-Bonnet theorem.
Does there exist an oriented simple closed curvey in the plane of length 2π such that fx dy-y dx > 2π? Indicate whether or not such a curve exists, along with the best reasoning/explanation from the choices below. Select one: a. Yes, there exists such a curve. In fact, there exists a convex curve with these properties. b. Yes, there exists such a curve, but any such curve is not convex. Oc. No, no such curve exists, by the Jordan curve theorem. O d. No, no such curve exists, by Hopf's Umlaufsatz. Oe. No, no such curve exists, by Fenchel's theorem. Of. No, no such curve exists, by the isoperimetric inequality. O g. No, no such curve exists, by Green's theorem. Oh. No, no such curve exists, by Gauss' Theorema Egregium. O. No, no such curve exists, by the Gauss-Bonnet theorem.
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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Does there exist an oriented simple closed curvey in the plane of length 2π such that fx dy - y dx > 2π?
Indicate whether or not such a curve exists, along with the best reasoning/explanation from the choices below.
Select one:
Yes, there exists such la curve. In fact, there exists a convex curve with these properties.
b. Yes, there exists such a curve, but any such curve is not convex.
C. No, no such curve exists, by the Jordan curve theorem.
50 0
a.
d. No, no such curve exists, by Hopf's Umlaufsatz.
No, no such curve exists, by Fenchel's theorem.
No, no such curve exists, by the isoperimetric inequality.
No, no such curve exists, by Green's theorem.
No, no such curve exists, by Gauss' Theorema Egregium.
No, no such curve exists, by the Gauss-Bonnet theorem.
e.
f.
g.
h.
OL
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