Exercise 8.6.5: Suppose f: R² → R is a C² function. For all (x, y) = R², compute ƒ(x+t,y)+ƒ(x−t,y)+ƒ(x,y+t) + f(x,y—t) — 4ƒ(x,y) lim 0-1 in terms of the partial derivatives of f.
Exercise 8.6.5: Suppose f: R² → R is a C² function. For all (x, y) = R², compute ƒ(x+t,y)+ƒ(x−t,y)+ƒ(x,y+t) + f(x,y—t) — 4ƒ(x,y) lim 0-1 in terms of the partial derivatives of f.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Exercise 8.6.5: Suppose f: R² → R is a C² function. For all (x,y) = R², compute
f(x+t,y)+ƒf(x−t,y) + f(x,y+t) + f(x,y−t) — 4ƒ(x,y)
lim
t→0
in terms of the partial derivatives of f.
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