Suppose F: R2 Ris a function of class C1. Call S = F-({0}). Define A CSto be the set of all critical points, p, of F which also satisfy F(p) = 0. Define BC S to be the set of all points p in S such that for any open neighbourhood UCR? of p, Sn U cannot be described as the graph of a C1 function. Which of the following correctly describes the relationship between A and B by the implicit function theorem? O ACB O AÇB O BCA O BÇA O A = B O None of the above.

Suppose F: R2 Ris a function of class C1. Call S = F-({0}). Define A CSto be the set of all critical points, p, of F which also satisfy F(p) = 0. Define BC S to be the set of all points p in S such that for any open neighbourhood UCR? of p, Sn U cannot be described as the graph of a C1 function. Which of the following correctly describes the relationship between A and B by the implicit function theorem? O ACB O AÇB O BCA O BÇA O A = B O None of the above.

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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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Suppose F: R? →Rİ a function of class C1. Call S = F-({0}).
Define A C S to be the set of all critical points, p, of F which also satisfy
F(p) = 0.
%3D
Define BC S to be the set of all points p in S such that for any open
neighbourhood UCR of p, SnU cannot be described as the graph of a
C1 function.
Which of the following correctly describes the relationship between A and B
by the implicit function theorem?
O ACB
O AÇB
© BCA
O BÇ A
O A= B
O None of the above.

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