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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
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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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)!
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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