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3. Consider the parametric curve F(t) = (e' cost, e' sint, √2e), teR. (a) Show that the curve lies on a cone. Sketch the curve and the cone. (b) Find the length of the arc of the curve from the point (1,0, √2) to the point (e²,0, √2²). (c) Reparametrize the curve with respect to arc length measured from the point (1,0, √2) in the direction of increasing t..

3. Consider the parametric curve F(t) = (e' cost, e' sint, √2e), teR. (a) Show that the curve lies on a cone. Sketch the curve and the cone. (b) Find the length of the arc of the curve from the point (1,0, √2) to the point (e²,0, √2²). (c) Reparametrize the curve with respect to arc length measured from the point (1,0, √2) in the direction of increasing 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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3. Consider the parametric curve F(t) = (e cost, e' sint, √2e), t€ R. (a) Show that the curve lies on a cone. Sketch the curve and the cone. (b) Find the length of the arc of the curve from the point (1,0, √2) to the point (e²,0, √2²). (c) Reparametrize the curve with respect to arc length measured from the point (1,0, √2) in the direction of increasing t..
Transcribed Image Text:3. Consider the parametric curve F(t) = (e cost, e' sint, √2e), t€ R. (a) Show that the curve lies on a cone. Sketch the curve and the cone. (b) Find the length of the arc of the curve from the point (1,0, √2) to the point (e²,0, √2²). (c) Reparametrize the curve with respect to arc length measured from the point (1,0, √2) in the direction of increasing t..
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