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In Exercises 1-8, find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 1. r(t) = (2 cos t)i + (2 sin t)j + √5tk, 0≤t≤T

In Exercises 1-8, find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 1. r(t) = (2 cos t)i + (2 sin t)j + √5tk, 0≤t≤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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In Exercises 1-8, find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 1. r(t) = (2 cost)i + (2 sin t)j + √5tk, 0≤ t ≤ T 0≤ t ≤ T = 2. r(t) (6 sin 2t)i + (6 cos 2t)j + 5tk, 3. r(t) = ti + (2/3)t³/2k, 0≤ t ≤8 4. r(t) = (2+t)i (t + 1)j + tk, 0≤t≤3 5. r(t) = 6. r(t) = 7. r(t) = (cos³ t)j + (sin³t)k, 0≤ t ≤ π/2 6t³i - 2t³j - 3t³k, 1 ≤ t ≤2 (t cos t)i + (t sin t)j + (2√2/3)1³/2k, 0≤t≤ T
Transcribed Image Text:In Exercises 1-8, find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. 1. r(t) = (2 cost)i + (2 sin t)j + √5tk, 0≤ t ≤ T 0≤ t ≤ T = 2. r(t) (6 sin 2t)i + (6 cos 2t)j + 5tk, 3. r(t) = ti + (2/3)t³/2k, 0≤ t ≤8 4. r(t) = (2+t)i (t + 1)j + tk, 0≤t≤3 5. r(t) = 6. r(t) = 7. r(t) = (cos³ t)j + (sin³t)k, 0≤ t ≤ π/2 6t³i - 2t³j - 3t³k, 1 ≤ t ≤2 (t cos t)i + (t sin t)j + (2√2/3)1³/2k, 0≤t≤ T
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