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Use ihe Frenet-Serret formulas to prove each of the following. (Primes denote derivatives with respect to t. Start as in the proof of Theorem 10.)
(a) r″ = s″T + κ(sr)2N
(b) rr × rn = κ(sr)3B
(c) rm = [sm − κ2(sr)3]T + [3κs′s″ + κ′(s′)2]N + κτ(s′)3B
(d)
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Chapter 10 Solutions
Essential Calculus
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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