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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