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18. r(t) = (tan-¹ t, 2e², 8tet), t=0 19. r(t)= cos ti+ 3t j+ 2 sin 2t k, t=01 Answer 20. r(t) = sin ti+ cos² tj+tan² tk, t = */4 21. If r(t) = (t, t², t³), find r' (t), T (1), r" (t), and r' (t) x r" (t).

18. r(t) = (tan-¹ t, 2e², 8tet), t=0 19. r(t)= cos ti+ 3t j+ 2 sin 2t k, t=01 Answer 20. r(t) = sin ti+ cos² tj+tan² tk, t = */4 21. If r(t) = (t, t², t³), find r' (t), T (1), r" (t), and r' (t) x r" (t).

Advanced Engineering Mathematics
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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18, 20, & 21 only 17, 18, 19 and 20 Find the unit tangent vector T (t) at the point with the given value of the parameter t. 17. r(t)-(-2,1+3+1)=2 Answer + 18. r(t) = (tan-¹ t, 2e², 8te²), t=0 19. r(t)= cos ti+ 3t j+ 2 sin 2t k, t=0 Answer+ 20. r(t) = sin ti+ cos² tj+tan² tk, t= /4 21. Ifr (t) = (t, t², t³), find r' (t), T (1), r" (t), and r' (t) x r" (t).
Transcribed Image Text:18, 20, & 21 only 17, 18, 19 and 20 Find the unit tangent vector T (t) at the point with the given value of the parameter t. 17. r(t)-(-2,1+3+1)=2 Answer + 18. r(t) = (tan-¹ t, 2e², 8te²), t=0 19. r(t)= cos ti+ 3t j+ 2 sin 2t k, t=0 Answer+ 20. r(t) = sin ti+ cos² tj+tan² tk, t= /4 21. Ifr (t) = (t, t², t³), find r' (t), T (1), r" (t), and r' (t) x r" (t).
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