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13 Nov 2019
5. Find the length of each the following parametric curves: (a) C(t) = (2t + 3, e' + e-t), 0 t 2. (b) C(t) = (2-3 sin2(t), cos(2t)), 0-K (c) C(t) = (et cost, et sin t), 0 t T. ì¦.
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Lelia Lubowitz
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7 Feb 2019
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Related questions
5. (4 points) Compare the curves represented by the parametric equations. How do they differ? (a) x t, y = t-2 (b) x = cos t, y = sec2 t (c) z = e, y = e-2t
Additional Problem: Evaluate the following line integral, where C is the parametric curve r (t) (sint, cost, sin 2t) , 0 ã t ã 2T. (sin(z)) dz ( cos(y)) dy +z*dz Hint: The curve C lies on the cylinder 2y21 and the surfacez 2xy (why?).
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Additional Problem: Evaluate the following line integral, where C is the parametric curve r (t) (sint, cost, sin 2t) , 0 ã t ã 2T. (sin(z)) dz ( cos(y)) dy +z*dz Hint: The curve C lies on the cylinder 2y21 and the surfacez 2xy (why?).
mauvefox717
11 Find the point on the curve r(t) (12sin t)l (12cos tj 5t k at a distance of 13n units along the curve from the point (0, -12, 0) in the direction opposite to the direction of increasing arc length. 12 Compute T, N, and K at the point 1 of the twisted cubic with position 2' 3 vector r t i j at k. TT 13 Find T, N, Br K, and T for the space curve r() (cos3t)i (sin3 t j, o t 14 Given r t) et cos t)i (et sin t)j 2e k, write a in the form a aTT aNN atta 0 without finding Tand N. 15 Given r(t) (e t cos t)l (et sin tj 2k. Find r, T, N, and B at t 0. Then find the equations for the osculating, normal, and rectifying planes at t 0.
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