(a) Is f continuous at the point (0,0)? Justify your answer. (b) Does the equality lim lim f(x, y) = lim lim f(x, y) hold? Justify your answer. y 0 x 0 x→0 y 0
(a) Is f continuous at the point (0,0)? Justify your answer. (b) Does the equality lim lim f(x, y) = lim lim f(x, y) hold? Justify your answer. y 0 x 0 x→0 y 0
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:Let the function f : R² → R be defined by
{
f(x, y) =
=
y+xsin () if y # 0
0
if y = 0.
Transcribed Image Text:(a) Is f continuous at the point (0,0)? Justify your answer.
(b) Does the equality lim lim f(x, y) = lim lim f(x, y) hold? Justify your answer.
y 0 x 0
x→0 y 0
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