P5: nts) Assume that f is a function such that fæy and fy exist and are continuous. Assume additionally that f(tx, ty) = t™ f(x, y). for all numbers x, y, and t. Show that x202f ?x2 8² f əxəy 20² f дуг Hint: Differentiate twice with respect to t. Then take t = 1. + 2xy- +y²5 - m(m − 1)f(x, y)
P5: nts) Assume that f is a function such that fæy and fy exist and are continuous. Assume additionally that f(tx, ty) = t™ f(x, y). for all numbers x, y, and t. Show that x202f ?x2 8² f əxəy 20² f дуг Hint: Differentiate twice with respect to t. Then take t = 1. + 2xy- +y²5 - m(m − 1)f(x, y)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.2: Partial Derivatives
Problem 48E
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![P5:
nts) Assume that f is a function such that fay and fyr exist and are continuous.
Assume additionally that
tm f(x, y).
f(tx, ty)
for all numbers x, y, and t. Show that
20² f
?x2
a² f
+ 2xy- +
əxəy
28² f
320
= m(m — 1) ƒ (x, y)
дуг
Hint: Differentiate twice with respect to t. Then take t = 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a5ac2db-d584-49da-a0ed-efa785bd6c28%2F4dd6b0d2-a7f9-45fb-aada-72308823a19b%2Fh4yc71_processed.png&w=3840&q=75)
Transcribed Image Text:P5:
nts) Assume that f is a function such that fay and fyr exist and are continuous.
Assume additionally that
tm f(x, y).
f(tx, ty)
for all numbers x, y, and t. Show that
20² f
?x2
a² f
+ 2xy- +
əxəy
28² f
320
= m(m — 1) ƒ (x, y)
дуг
Hint: Differentiate twice with respect to t. Then take t = 1.
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