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r(t) = (8tet - 6)i + (sin(3t) − 2)j + (4 ln(t + 1) + 5)k. dr (a) Compute (0) and -(0). Show your process. dt (b) Use your answer from part (a) to find the equation equation for the line tangent to the curve at t = 0. (c) Explain how dr (0) and the tangent line are related geometrically. dt

r(t) = (8tet - 6)i + (sin(3t) − 2)j + (4 ln(t + 1) + 5)k. dr (a) Compute (0) and -(0). Show your process. dt (b) Use your answer from part (a) to find the equation equation for the line tangent to the curve at t = 0. (c) Explain how dr (0) and the tangent line are related geometrically. dt

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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r(t) = (8te¹ — 6)i + (sin(3t) − 2)j + (4 ln(t + 1) + 5)k. dr (a) Compute (0) and (0). Show your process. dt (b) Use your answer from part (a) to find the equation equation for the line tangent to the curve at t = 0. dr (c) Explain how (0) and the tangent line are related geometrically. dt
Transcribed Image Text:r(t) = (8te¹ — 6)i + (sin(3t) − 2)j + (4 ln(t + 1) + 5)k. dr (a) Compute (0) and (0). Show your process. dt (b) Use your answer from part (a) to find the equation equation for the line tangent to the curve at t = 0. dr (c) Explain how (0) and the tangent line are related geometrically. dt
Expert Solution
Step 1

Concept:

Putting the value of t=0 in the vector we will get the value of r→(0) and r→'(0) 

Then putting these value in the equation L→(t)=r→(t)+tr→(t)

We have the equation of line tangent to the curve

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