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F(t) = (sint — tcost)ī + (cost + tsint)j + 2t²k, answer each of the following: Show that the curve lies on the paraboloid 2(x² + y²) = z +2 Find the arclength of the curve from t = 0 to increasing values of t Find the curvature of the curve as a function of t. Find the components of the acceleration in the direction of the unit tangent vector and the principal normal vector. (i) (ii) (iv)

F(t) = (sint — tcost)ī + (cost + tsint)j + 2t²k, answer each of the following: Show that the curve lies on the paraboloid 2(x² + y²) = z +2 Find the arclength of the curve from t = 0 to increasing values of t Find the curvature of the curve as a function of t. Find the components of the acceleration in the direction of the unit tangent vector and the principal normal vector. (i) (ii) (iv)

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...
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Answer questions (iii) and (iv)

r(t) (i) (ii) (iii) (iv) (sint — tcost)ī + (cost + tsint)] + 2t²k, answer each of the following: Show that the curve lies on the paraboloid 2(x² + y²) =z +2 Find the arclength of the curve from t = 0 to increasing values of t Find the curvature of the curve as a function of t. = Find the components of the acceleration in the direction of the unit tangent vector and the principal normal vector.
Transcribed Image Text:r(t) (i) (ii) (iii) (iv) (sint — tcost)ī + (cost + tsint)] + 2t²k, answer each of the following: Show that the curve lies on the paraboloid 2(x² + y²) =z +2 Find the arclength of the curve from t = 0 to increasing values of t Find the curvature of the curve as a function of t. = Find the components of the acceleration in the direction of the unit tangent vector and the principal normal vector.
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