Show that the function does not have a limit at (0,0) by examining the following limits. (a) Find the limit of f as (x,y) → (0,0) along the line y = x. 9- lim f(x, y) = (z.y)-(0,0) f(x, y) = = ysz x5y +y5 10 (b) Find the limit of f as (x, y) → (0,0) along the curve y = 25. lim f(x,y) = (2.0) (0,0) v=z5 (Be sure that you are able to explain why the results in (a) and (b) indicate that f does not have a limit at (0,0)!
Show that the function does not have a limit at (0,0) by examining the following limits. (a) Find the limit of f as (x,y) → (0,0) along the line y = x. 9- lim f(x, y) = (z.y)-(0,0) f(x, y) = = ysz x5y +y5 10 (b) Find the limit of f as (x, y) → (0,0) along the curve y = 25. lim f(x,y) = (2.0) (0,0) v=z5 (Be sure that you are able to explain why the results in (a) and (b) indicate that f does not have a limit at (0,0)!
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:Show that the function
f(x, y)
lim f(x, y) =
(z.y)→(0,0)
y=z
(b) Find the limit of f as (x, y) -
lim f(x, y) =
(2,y) (0,0)
y=25
does not have a limit at (0,0) by examining the following limits.
(a) Find the limit of f a (x, y) → (0,0) along the line y = x.
x5y
x 10+y5
(0,0) along the curve y = x5.
(Be sure that you are able to explain why the results in (a) and (b) indicate that f does not have a limit at (0,0)!
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