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du Evaluate at (x,y,z)=(4,3,0) for the function u(p,q,r) = e Pacos(r); p = = = ²1/₁, q=x² Iny, r=z. ду X A. 108 B. 4 +3 OC. 0 D. 324

du Evaluate at (x,y,z)=(4,3,0) for the function u(p,q,r) = e Pacos(r); p = = = ²1/₁, q=x² Iny, r=z. ду X A. 108 B. 4 +3 OC. 0 D. 324

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:** Evaluate \(\frac{\partial u}{\partial y}\) at \((x, y, z) = (4, 3, 0)\) for the function \(u(p, q, r) = e^{pq} \cos(r)\); where \(p = \frac{1}{x}\), \(q = x^2 \ln y\), and \(r = z\). **Options:** - A. 108 (Correct answer) - B. \(\frac{4}{3}\) - C. 0 - D. 324 **Explanation:** To solve this problem, you must first compute the partial derivative of the function \(u\) with respect to \(y\), while substituting the expressions of \(p\), \(q\), and \(r\) in terms of \(x\), \(y\), and \(z\). Finally, evaluate this derivative at the point \((x, y, z) = (4, 3, 0)\).
Transcribed Image Text:**Problem:** Evaluate \(\frac{\partial u}{\partial y}\) at \((x, y, z) = (4, 3, 0)\) for the function \(u(p, q, r) = e^{pq} \cos(r)\); where \(p = \frac{1}{x}\), \(q = x^2 \ln y\), and \(r = z\). **Options:** - A. 108 (Correct answer) - B. \(\frac{4}{3}\) - C. 0 - D. 324 **Explanation:** To solve this problem, you must first compute the partial derivative of the function \(u\) with respect to \(y\), while substituting the expressions of \(p\), \(q\), and \(r\) in terms of \(x\), \(y\), and \(z\). Finally, evaluate this derivative at the point \((x, y, z) = (4, 3, 0)\).
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