Use the Frenet-Serret formulas to prove each of the following. (Primes denote derivatives with respect to t.)

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(a) r" s"T + K(s')N (b) r' X r" = K(s')B (c) r" = [s" - K(s')]T + [3ks's" + K'(s')2 ]N + KT (S') B (r' X r")

Data from Frenet-Serret formulas

1. dT/ds = KN 2. dN/ds = KT + TB - 3. dB/ds - TN =

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Calculus

ISBN: 9780495011606

6th Edition

Authors: James Stewart

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Question Posted: Oct 23, 2023 04:12 AM

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Use the Frenet-Serret formulas to prove each of the following. (Primes denote derivatives with respect to t.)

Question:

(a) r" s"T + K(s')²N (b) r' X r" = K(s')³B (c) r" = [s" - K²(s')³]T + [3ks's" + K'(s')2 ]N + KT (S')³ B (r' X r") r" |r' xr" |² (d) T=

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Calculus

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