Need help with this question. Please explain each step and neatly type up. Thank you :) Question 2. Let U CR³ be open, f: UR a smooth function, and letS = {x €U : f(x)=0}. Suppose that for all p € S, Vƒ(p) ‡ 0. Show thatV f||vf||is a unit normal on S. Conclude that any level surface is orientable.N =

To show that N = nabla f / || nabla f || is a unit normal on S, we need to verify two things: N is…

Answered: Question 2. Let U CR³ be open, f: U R a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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Question 2. Let U CR³ be open, f: U R a smooth function, and let S = {x €U : f(x)=0}. Suppose that for all p € S, Vƒ(p) ‡ 0. Show that N = Vf ||vf|| is a unit normal on S. Conclude that any level surface is orientable.