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By considering different paths of approach, show that the function below has no limit as (x,y) →(0,0). f(x,y)= Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? OA. y=kx², x*0 OB. y=kx³, x*0 OC. y=kx, x*0 OD. y=kx+kx².x#0 If (x,y) approaches (0,0) along the curve when k= 1 used in the set of curves found above, what is the limit? (Simplify your answer.) If (x,y) approaches (0,0) along the curve when k=0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? O A. Since f has two different limits along two different paths to (0.0), by the two-path test, f has no limit as (x,y) approaches (0,0). O B. Since f has the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). OC. Since f has the same limit along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). O D. Since f has two different limits along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0).

By considering different paths of approach, show that the function below has no limit as (x,y) →(0,0). f(x,y)= Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? OA. y=kx², x*0 OB. y=kx³, x*0 OC. y=kx, x*0 OD. y=kx+kx².x#0 If (x,y) approaches (0,0) along the curve when k= 1 used in the set of curves found above, what is the limit? (Simplify your answer.) If (x,y) approaches (0,0) along the curve when k=0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? O A. Since f has two different limits along two different paths to (0.0), by the two-path test, f has no limit as (x,y) approaches (0,0). O B. Since f has the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). OC. Since f has the same limit along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). O D. Since f has two different limits along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (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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By considering different paths of approach, show that the function below has no limit as (x,y) →(0,0). f(x,y)= x4 x +y Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? O A. y=kx², x#0 O B. y=kx³, x#0 OC. y = kx, x#0 O D. y=kx+kx², x#0 If (x,y) approaches (0,0) along the curve when k = 1 used in the set of curves found above, what is the limit? (Simplify your answer.) If (x,y) approaches (0,0) along the curve when k = 0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? O A. Since f has two different limits along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). O B. Since f has the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). O C. Since f has the same limit along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). O D. Since f has two different limits along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0).
Transcribed Image Text:By considering different paths of approach, show that the function below has no limit as (x,y) →(0,0). f(x,y)= x4 x +y Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? O A. y=kx², x#0 O B. y=kx³, x#0 OC. y = kx, x#0 O D. y=kx+kx², x#0 If (x,y) approaches (0,0) along the curve when k = 1 used in the set of curves found above, what is the limit? (Simplify your answer.) If (x,y) approaches (0,0) along the curve when k = 0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? O A. Since f has two different limits along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). O B. Since f has the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). O C. Since f has the same limit along two different paths to (0,0), by the two-path test, f has no limit as (x,y) approaches (0,0). O D. Since f has two different limits along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0).
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