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5 Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), −5 ≤ t ≤5 b) r(t) = √2ti + e¹j+e¯t + etk, 0≤ t ≤1 c) Let C be the curve of the intersection of the parabolic cylinder x² = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6,18,36)

5 Find the length of the curves: a) r(t) = (t, 3 cos t, 3 sin t ), −5 ≤ t ≤5 b) r(t) = √2ti + e¹j+e¯t + etk, 0≤ t ≤1 c) Let C be the curve of the intersection of the parabolic cylinder x² = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6,18,36)

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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show full & complete procedure HANDWRITTEN only. Please answer parts a), b) & c). Note they are subparts of the same question

5 Find the length of the curves: a) r(t) = (t, 3 cost, 3 sin t), -5 ≤t≤5 b) r(t) = √2ti + etj + e + e-tk, 0≤ t ≤1 = c) Let C be the curve of the intersection of the parabolic cylinder x² the exact length of C from the origin to the point (6,18,36) 2y and the surface 3z = xy. Find
Transcribed Image Text:5 Find the length of the curves: a) r(t) = (t, 3 cost, 3 sin t), -5 ≤t≤5 b) r(t) = √2ti + etj + e + e-tk, 0≤ t ≤1 = c) Let C be the curve of the intersection of the parabolic cylinder x² the exact length of C from the origin to the point (6,18,36) 2y and the surface 3z = xy. Find
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