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Let r(t) = (-4t¹ - 4, 4e-2t, sin(-3t)) = Find the unit tangent vector T(t) at the point t T (0) = 0. Round to 4 decimal places.

Let r(t) = (-4t¹ - 4, 4e-2t, sin(-3t)) = Find the unit tangent vector T(t) at the point t T (0) = 0. Round to 4 decimal places.

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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Please give steps to the final soloution so I can understand thanks!

Let \(\vec{r}(t) = \langle -4t^4 - 4, 4e^{-2t}, \sin(-3t) \rangle\). Find the unit tangent vector \(\vec{T}(t)\) at the point \(t = 0\). Round to 4 decimal places. \[\vec{T}(0) = \underline{\phantom{insert answer here}}\]
Transcribed Image Text:Let \(\vec{r}(t) = \langle -4t^4 - 4, 4e^{-2t}, \sin(-3t) \rangle\). Find the unit tangent vector \(\vec{T}(t)\) at the point \(t = 0\). Round to 4 decimal places. \[\vec{T}(0) = \underline{\phantom{insert answer here}}\]
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Step 1

Given;

r(t)=<-4t4-4, 4e-2t, sin(-3t)>.

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