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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Help with homework question #8
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![Verify that the following function satisfies Laplace's equation,
\[
\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0.
\]
\[
u(x, y) = 7y \left( 3x^2 - y^2 \right)
\]
The function \( u(x, y) = 7y \left( 3x^2 - y^2 \right) \) satisfies the Laplace equation because
\[
\frac{\partial^2 u}{\partial x^2} = \boxed{\ }
\]
and
\[
\frac{\partial^2 u}{\partial y^2} = \boxed{\ }
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a42e238-4116-4e80-81a7-f4d567b4bd0e%2Fba2603e0-3faa-419f-8213-dff1389ee319%2F13cav1a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Verify that the following function satisfies Laplace's equation,
\[
\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0.
\]
\[
u(x, y) = 7y \left( 3x^2 - y^2 \right)
\]
The function \( u(x, y) = 7y \left( 3x^2 - y^2 \right) \) satisfies the Laplace equation because
\[
\frac{\partial^2 u}{\partial x^2} = \boxed{\ }
\]
and
\[
\frac{\partial^2 u}{\partial y^2} = \boxed{\ }
\]
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