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Consider the curve r(t) = (t, t²) for -1 ≤t≤ 1. Thus curve paramaterizes the parabola y = x² between x = -1 and x = 1. At which point(s) along this curve is the radius of curvature the greatest? Explain your answers. (You shouldn't have to make ANY calculations.)

Consider the curve r(t) = (t, t²) for -1 ≤t≤ 1. Thus curve paramaterizes the parabola y = x² between x = -1 and x = 1. At which point(s) along this curve is the radius of curvature the greatest? Explain your answers. (You shouldn't have to make ANY calculations.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the curve r(t) = (t, t²) for -1 ≤ t ≤1. Thus curve paramaterizes the parabola y = x² between x = -1 and x = 1. At which point (s) along this curve is the radius of curvature the greatest? Explain your answers. (You shouldn't have to make ANY calculations.)
Transcribed Image Text:Consider the curve r(t) = (t, t²) for -1 ≤ t ≤1. Thus curve paramaterizes the parabola y = x² between x = -1 and x = 1. At which point (s) along this curve is the radius of curvature the greatest? Explain your answers. (You shouldn't have to make ANY calculations.)
Expert Solution
Step 1

The given curve is a parabola of the form y=x2 between x=-1 and x=1.

 

Take a point of a curve and a small arc centered around the point of the curve and the arc can be approximated as an arc of a circle of some specific radius, the center of the circle corresponding to the arc is called the center of curvature and the radius of the circle is called the radius of curvature.

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