that the reparametrizatIon by arc-length traverses the curve with unit speed. That is, snow ||7 (8)|| all 8. (b) Consider the curve 7 (t) = (- sin t, cos t, 1). Reparametrize this curve by arc-length starting from the point (-1,0, 1).
that the reparametrizatIon by arc-length traverses the curve with unit speed. That is, snow ||7 (8)|| all 8. (b) Consider the curve 7 (t) = (- sin t, cos t, 1). Reparametrize this curve by arc-length starting from the point (-1,0, 1).
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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How do you solve b)?
![(a) Let 7 : [a, b| → R" be a curve with 7 (t) 7 0 for all t E [a, b|]. Let s = s(t) be the arc-length function. Show
that the reparametrization by arc-length traverses the curve with unit speed. That is, show |T (s)||
= 1 for all s.
(b) Consider the curve 7 (t) = (- sin t, cos t, 1). Reparametrize this curve by arc-length starting from the point
(-1,0, 1).
(c) Use your answer from part (b) to find the point on the curve ř(t) = (- sint, cos t, 1) that is T/4 units away
from (–1,0, 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F246c87a5-9ee3-4eeb-82a9-9957c9a962ba%2Fae20446a-62ea-427a-81ed-3cecfd8d048f%2Fjmlihr_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Let 7 : [a, b| → R" be a curve with 7 (t) 7 0 for all t E [a, b|]. Let s = s(t) be the arc-length function. Show
that the reparametrization by arc-length traverses the curve with unit speed. That is, show |T (s)||
= 1 for all s.
(b) Consider the curve 7 (t) = (- sin t, cos t, 1). Reparametrize this curve by arc-length starting from the point
(-1,0, 1).
(c) Use your answer from part (b) to find the point on the curve ř(t) = (- sint, cos t, 1) that is T/4 units away
from (–1,0, 1).
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