7(4) = X

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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Find the unit tangent vector f(t) to the parametrized curve (t) = (t, arctan(t), -t) when t = 4. (Your instructors prefer angle bracket notation <> for vectors.)
î(4) =
X
Transcribed Image Text:Find the unit tangent vector f(t) to the parametrized curve (t) = (t, arctan(t), -t) when t = 4. (Your instructors prefer angle bracket notation <> for vectors.) î(4) = X
Expert Solution
Step 1

given parametrized curve is r(t) = t , arc tant , -t then we have to find the unit tangent vector to the curve when  t =4since   r(t) = t , tan-1t , -t

 

now , r'(t)  = ddt t , arc tant , -t r'(t)  = 1 , 11+t2 , -1

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