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1. Suppose 7(t) = (t,t³,t²) at the point (1,1, 1). A) Find an equation of a line tangent to 7(t) = (t,t³,t²) at the point (1, 1, 1). B) Calculate how quickly a particle travelling on ř(t) = (t, t³,t²) at the point (1, 1, 1) is changing position. C) Write an integral equation to determine how far a particle travels along 7(t) = (t, t³,t²) for every t > 0. Do not evaluate the integral. %3D D) Calculate how quickly the curve ř(t) = (t,t³,t²) changes direction at the point (1,1, 1). %3D

1. Suppose 7(t) = (t,t³,t²) at the point (1,1, 1). A) Find an equation of a line tangent to 7(t) = (t,t³,t²) at the point (1, 1, 1). B) Calculate how quickly a particle travelling on ř(t) = (t, t³,t²) at the point (1, 1, 1) is changing position. C) Write an integral equation to determine how far a particle travels along 7(t) = (t, t³,t²) for every t > 0. Do not evaluate the integral. %3D D) Calculate how quickly the curve ř(t) = (t,t³,t²) changes direction at the point (1,1, 1). %3D

Calculus: Early Transcendentals
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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1. Suppose 7(t) = (t, t³,t²) at the point (1,1, 1). A) Find an equation of a line tangent to 7(t) = (t, t³,t²) at the point (1, 1, 1). B) Calculate how quickly a particle travelling on ř(t) = (t, t³,t²) at the point (1, 1, 1) is changing position. C) Write an integral equation to determine how far a particle travels along 7(t) = (t, t³, t²) for every t > 0. Do not evaluate the integral. D) Calculate how quickly the curve 7(t) = (t,t³3, t²) changes direction at the point (1, 1, 1).
Transcribed Image Text:1. Suppose 7(t) = (t, t³,t²) at the point (1,1, 1). A) Find an equation of a line tangent to 7(t) = (t, t³,t²) at the point (1, 1, 1). B) Calculate how quickly a particle travelling on ř(t) = (t, t³,t²) at the point (1, 1, 1) is changing position. C) Write an integral equation to determine how far a particle travels along 7(t) = (t, t³, t²) for every t > 0. Do not evaluate the integral. D) Calculate how quickly the curve 7(t) = (t,t³3, t²) changes direction at the point (1, 1, 1).
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Suppose r→(t)=t,t3,t2 at the point (1,1,1)

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