ering different paths of approach, show that the function has no limit as (x,y)-(0,0). f(x,y)=- Find the limit as (x,y)-(0,0) along the path y=x for x > 0. (Type an exact answer, using radicals as needed.) Find the limit as (x,y)-(0,0) along the path y = x for x <0. (Type an exact answer, using radicals as needed.) Why doesn't the limit exist? OA. The limit does not exist because f(x,y) has the same limits along two different paths in the domain of f as (x,y) approaches (0,0). OB. The limit does not exist because f(x,y) has different limits along two different paths in the domain of f as (x,y) approaches (0,0). OC. The limit does not exist because f(x,y) is not defined at the point (0,0). OD. The limit does not exist because f(x,y) is not continuous.
ering different paths of approach, show that the function has no limit as (x,y)-(0,0). f(x,y)=- Find the limit as (x,y)-(0,0) along the path y=x for x > 0. (Type an exact answer, using radicals as needed.) Find the limit as (x,y)-(0,0) along the path y = x for x <0. (Type an exact answer, using radicals as needed.) Why doesn't the limit exist? OA. The limit does not exist because f(x,y) has the same limits along two different paths in the domain of f as (x,y) approaches (0,0). OB. The limit does not exist because f(x,y) has different limits along two different paths in the domain of f as (x,y) approaches (0,0). OC. The limit does not exist because f(x,y) is not defined at the point (0,0). OD. The limit does not exist because f(x,y) is not continuous.
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:By considering different paths of approach, show that the function has no limit as (x,y)-(0,0).
f(x,y)=-- √2+
Find the limit as (x,y)-(0,0) along the path y=x for x > 0.
(Type an exact answer, using radicals as needed.)
Find the limit as (x,y)-(0,0) along the path y = x for x <0.
(Type an exact answer, using radicals as needed.)
Why doesn't the limit exist?
OA. The limit does not exist because f(x,y) has the same limits along two different paths in the domain of f as (x,y) approaches (0,0).
OB. The limit does not exist because f(x,y) has different limits along two different paths in the domain of f as (x,y) approaches (0,0).
OC. The limit does not exist because f(x,y) is not defined at the point (0,0).
D. The limit does not exist because f(x,y) is not continuous.
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