Let f (x, y) = {*, (x, y) = 0. / 0, (x, y) = ( 0, 0) }. x+y Show that lim (x, y) → ( 0, 0 ) exists along any path y = mx but lim (x,y) → (0, 0) does not exist.
Let f (x, y) = {*, (x, y) = 0. / 0, (x, y) = ( 0, 0) }. x+y Show that lim (x, y) → ( 0, 0 ) exists along any path y = mx but lim (x,y) → (0, 0) does not exist.
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 f (x, y) = {
, (x, y) = 0. / 0, (x, y) = (0, 0) 3.
x'+y
Show that lim (x, y) → ( 0, 0 ) exists along any path y = mx
but lim (x, y) → (0, 0) does not exist.
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