Find all second-order partial derivatives. Determine which of the following functions are solutions to Laplace's Equation. (a) f(x,y) = x² – y? (b) f(x, y) = x² + y? (c) f(x,y) = ln[(x² + y²)²] (d) f(x, y) = e-" cos(y) – e-Y cos(x) (e) f(x,y) = e-" sin(2y) (f) f(x, y) = In[cos(x – 2y)] -

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...
Question
Find all second-order partial derivatives. Determine which of the following functions are solutions
to Laplace's Equation.
(a) f(x,y) = x² – y?
(b) f(x, y) = x² + y?
(c)
f(x, y) = ln[(x² + y²)²]
(d) f(x, y) = e¬ª cos(y) – e¬Y cos(x)
(e) f(x, y) = e= sin(2y)
(f) f(x,y) = ln[cos(x – 2y)]
Transcribed Image Text:Find all second-order partial derivatives. Determine which of the following functions are solutions to Laplace's Equation. (a) f(x,y) = x² – y? (b) f(x, y) = x² + y? (c) f(x, y) = ln[(x² + y²)²] (d) f(x, y) = e¬ª cos(y) – e¬Y cos(x) (e) f(x, y) = e= sin(2y) (f) f(x,y) = ln[cos(x – 2y)]
Which functions in Question 2 are solutions of the Laplace's Equation
Fex + Fyy = 0.
(a),(c) and (d)
(a),(c) and (e)
(c), (d) and (f)
(a),(d) and (f)
Transcribed Image Text:Which functions in Question 2 are solutions of the Laplace's Equation Fex + Fyy = 0. (a),(c) and (d) (a),(c) and (e) (c), (d) and (f) (a),(d) and (f)
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