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5. Find the length of the curve • r(t) = cos(t)i + sin(t)j +ln(cos(t))k 0≤t≤n/4

5. Find the length of the curve • r(t) = cos(t)i + sin(t)j +ln(cos(t))k 0≤t≤n/4

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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Certainly! Here's a transcription of the content: --- 5. Find the length of the curve - \(\mathbf{r}(t) = \cos(t) \mathbf{i} + \sin(t) \mathbf{j} + \ln(\cos(t)) \mathbf{k}\) \quad \(0 \leq t \leq \pi/4\) 6. Use the Chain Rule to find the indicated partial derivative - \(w = xy + yz + zx, \quad x = r \cos(\theta), \quad y = r \sin(\theta), \quad z = r \theta;\) \(w_{\theta} \text{ when } r = 2, \quad \theta = \pi/2\) 7. Find the directional derivative of the function at the given point in the direction of the vector \(\mathbf{v}\) - \(f(x, y, z) = xe^y + ye^z + ze^x, \quad (0, 0, 0) \quad \mathbf{v} = \langle 5, 1, -2 \rangle\) ---
Transcribed Image Text:Certainly! Here's a transcription of the content: --- 5. Find the length of the curve - \(\mathbf{r}(t) = \cos(t) \mathbf{i} + \sin(t) \mathbf{j} + \ln(\cos(t)) \mathbf{k}\) \quad \(0 \leq t \leq \pi/4\) 6. Use the Chain Rule to find the indicated partial derivative - \(w = xy + yz + zx, \quad x = r \cos(\theta), \quad y = r \sin(\theta), \quad z = r \theta;\) \(w_{\theta} \text{ when } r = 2, \quad \theta = \pi/2\) 7. Find the directional derivative of the function at the given point in the direction of the vector \(\mathbf{v}\) - \(f(x, y, z) = xe^y + ye^z + ze^x, \quad (0, 0, 0) \quad \mathbf{v} = \langle 5, 1, -2 \rangle\) ---
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