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Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

Let r(t) = (-3t5 - 1, 2e³, 4 sin(4t)) Find the unit tangent vector T(t) at the point t = 0 T(0) -

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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**Problem Statement for Calculus Course:** *Given a Vector Function, Find the Unit Tangent Vector* Let \(\vec{r}(t) = \left\langle -3t^5 - 1, 2e^{3t}, 4\sin(4t) \right\rangle\) Find the unit tangent vector \(\vec{T}(t)\) at the point \(t = 0\). \[ \vec{T}(0) = \left< \quad, \quad, \quad \right> \] **Instructions:** - To find the unit tangent vector \(\vec{T}(t)\), you first need the derivative of \(\vec{r}(t)\), which is \(\vec{r}'(t)\). - Then, evaluate \(\vec{r}'(t)\) at \(t = 0\). - Finally, find the magnitude of \(\vec{r}'(0)\) and use it to normalize the vector to get \(\vec{T}(0)\).
Transcribed Image Text:**Problem Statement for Calculus Course:** *Given a Vector Function, Find the Unit Tangent Vector* Let \(\vec{r}(t) = \left\langle -3t^5 - 1, 2e^{3t}, 4\sin(4t) \right\rangle\) Find the unit tangent vector \(\vec{T}(t)\) at the point \(t = 0\). \[ \vec{T}(0) = \left< \quad, \quad, \quad \right> \] **Instructions:** - To find the unit tangent vector \(\vec{T}(t)\), you first need the derivative of \(\vec{r}(t)\), which is \(\vec{r}'(t)\). - Then, evaluate \(\vec{r}'(t)\) at \(t = 0\). - Finally, find the magnitude of \(\vec{r}'(0)\) and use it to normalize the vector to get \(\vec{T}(0)\).
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