(b) Let f: R2 → R be a rational function. Show that fay(a, b) = fyæ (a, b) for all (a, b) E D(f).
(b) Let f: R2 → R be a rational function. Show that fay(a, b) = fyæ (a, b) for all (a, b) E D(f).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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Needed b part to be solved
![Q3. In Unit 4, we learned about Clairaut's Theorem, which states that if f is C2 in a neighbour-
hood of (a, b), then fry (a, b) = fyæ(a, b). In this exercise, you will prove Clairaut's Theorem
in the special case of a rational function.
(a) Let P(x, y) = Eo<ij<n@ija*y³ be a polynomial in x and y.' Show that
Pay (a, b) = Pya (a, b)
for all (a, b) E R².
(b) Let f: R2 →R be a rational function. Show that
fry(a, b) = fyæ (a, b)
for all (a, b) E D(f).
P(x, y)
Q(x, y)
[Hint: Write f(x, y)
where P and Q are polynomials.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F243cbcac-2ab1-4f56-bbf2-467d69e9f625%2F00354978-7cf0-4ed9-be23-f642c497fa19%2F62xa48t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q3. In Unit 4, we learned about Clairaut's Theorem, which states that if f is C2 in a neighbour-
hood of (a, b), then fry (a, b) = fyæ(a, b). In this exercise, you will prove Clairaut's Theorem
in the special case of a rational function.
(a) Let P(x, y) = Eo<ij<n@ija*y³ be a polynomial in x and y.' Show that
Pay (a, b) = Pya (a, b)
for all (a, b) E R².
(b) Let f: R2 →R be a rational function. Show that
fry(a, b) = fyæ (a, b)
for all (a, b) E D(f).
P(x, y)
Q(x, y)
[Hint: Write f(x, y)
where P and Q are polynomials.]
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