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Consider the vector function r(t) that has unit tangent vector T(t)= 1 √1+5t² (1,1,2t), 0≤t≤2. Suppose that the tangent vector of r(t) has magnitude ✓1+5t². Find the curvature x of the curve r(t) at a general point t. (a) (b) Find the vector function r(t) such that r(0) = 0.

Consider the vector function r(t) that has unit tangent vector T(t)= 1 √1+5t² (1,1,2t), 0≤t≤2. Suppose that the tangent vector of r(t) has magnitude ✓1+5t². Find the curvature x of the curve r(t) at a general point t. (a) (b) Find the vector function r(t) such that r(0) = 0.

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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curvature

Consider the vector function r(t) that has unit tangent vector T(t)= 1 √1+5t² (1,1,2t), 0≤t≤2. Suppose that the tangent vector of r(t) has magnitude ✓1+5t². Find the curvature x of the curve r(t) at a general point t. (a) (b) Find the vector function r(t) such that r(0) = 0.
Transcribed Image Text:Consider the vector function r(t) that has unit tangent vector T(t)= 1 √1+5t² (1,1,2t), 0≤t≤2. Suppose that the tangent vector of r(t) has magnitude ✓1+5t². Find the curvature x of the curve r(t) at a general point t. (a) (b) Find the vector function r(t) such that r(0) = 0.
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