17-20 (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find the curvature. 17. r(t) = (1, 3 cos t, 3 sin t) 18. r(t) = (t², sin t - t cos t, cost + t sin t), *> 0 19. r(t) =(√2t, e', e¯¹) 20. r(t) = (1, 11², 1²)
17-20 (a) Find the unit tangent and unit normal vectors T(t) and N(t). (b) Use Formula 9 to find the curvature. 17. r(t) = (1, 3 cos t, 3 sin t) 18. r(t) = (t², sin t - t cos t, cost + t sin t), *> 0 19. r(t) =(√2t, e', e¯¹) 20. r(t) = (1, 11², 1²)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
19
Transcribed Image Text:17-20
(b) Use Formula 9 to find the curvature.
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
17. r(t) = (1, 3 cos t, 3 sin t)
18. r(t) = (t², sint -t cos t, cost + t sin t), *> 0
19. r(t) =(√2t, e', e¯¹)
20. r(t) = (t, ½t², t²)
ups bri VIMAXE
21-23 Use Theorem 10 to find the curvature.
21. r(t) = t³ j + t² k
22. r(t) = ti + t² j + e' k
23. r(t) = √√61² i + 2t j + 2t³ k
point (1, 0, 0).
24. Find the curvature of r(t) = (t², In t, t In t) at the
31
27-29 Use Formula 11 to find the curvature.
27. y = x^
SA
25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1).
os t. 7
26. Graph the curve with parametric equations x = cos t,
point (1, 0, 0).
y = sin t, z = sin 5t and find the curvature at the
28. y
8 BAUDA
Transcribed Image Text:17-20
(b) Use Formula 9 to find the curvature.
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
17. r(t) = (1, 3 cos t, 3 sin t)
18. r(t) = (t², sint -t cos t, cost + t sin t), *> 0
19. r(t) =(√2t, e', e¯¹)
20. r(t) = (t, ½t², t²)
ups bri VIMAXE
21-23 Use Theorem 10 to find the curvature.
21. r(t) = t³ j + t² k
22. r(t) = ti + t² j + e' k
23. r(t) = √√61² i + 2t j + 2t³ k
point (1, 0, 0).
24. Find the curvature of r(t) = (t², In t, t In t) at the
31
27-29 Use Formula 11 to find the curvature.
27. y = x^
SA
25. Find the curvature of r(t) = (t, t², t³) at the point (1, 1, 1).
os t. 7
26. Graph the curve with parametric equations x = cos t,
point (1, 0, 0).
y = sin t, z = sin 5t and find the curvature at the
28. y
8 BAUDA
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