Mark the correct claims. i. The arc length does not depend on the choice of constantly determinant parameterization, if the parameterization is injective. ii. If the starting point of the plane curve is at the origin and its end point is (1,1), then its arc length is finite. iii. The curvature calculated with the help of the continuously determinant parameterization of the plane curve is always finite. iv. The curvature usually depends on the choice of parameterization. v. The curvature of the plane curve can also be defined geometrically without parameterization.
Mark the correct claims. i. The arc length does not depend on the choice of constantly determinant parameterization, if the parameterization is injective. ii. If the starting point of the plane curve is at the origin and its end point is (1,1), then its arc length is finite. iii. The curvature calculated with the help of the continuously determinant parameterization of the plane curve is always finite. iv. The curvature usually depends on the choice of parameterization. v. The curvature of the plane curve can also be defined geometrically without parameterization.
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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Question
Mark the correct claims.
i.
The arc length does not depend on the choice of constantly determinant parameterization, if the parameterization is injective.
ii.
If the starting point of the plane curve is at the origin and its end point is (1,1), then its arc length is finite.
iii.
The curvature calculated with the help of the continuously determinant parameterization of the plane curve is always finite.
iv.
The curvature usually depends on the choice of parameterization.
v.
The curvature of the plane curve can also be defined geometrically without parameterization.
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