Given the vector-valued function for curve C as r(t) = (3t², 8e¹, 2t), answer the following. (a) Provide an arc length reparametrization of the curve measured from the point (0,8,0) moving in the direction of increasing t. (b) Determine the curvature of the function r(t) at a general point (i.e. leave in terms of t). (c) Determine the curvature at the point (0,8,0). (d) Determine the normal vector at the point (0,8,0).

Given the vector-valued function for curve C as r(t) = (3t², 8e¹, 2t), answer the following. (a) Provide an arc length reparametrization of the curve measured from the point (0,8,0) moving in the direction of increasing t. (b) Determine the curvature of the function r(t) at a general point (i.e. leave in terms of t). (c) Determine the curvature at the point (0,8,0). (d) Determine the normal vector at the point (0,8,0).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 18T

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