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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) = x x ... Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? OA. y = kx + kx², x*0 B. y=kx³, x #0 O C. y = kx², x#0 O D. y=kx, 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), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). OB. 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).

By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). f(x,y) = x x ... Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? OA. y = kx + kx², x*0 B. y=kx³, x #0 O C. y = kx², x#0 O D. y=kx, 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), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). OB. 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).

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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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) = x x ... 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 = kx + kx², x*0 B. y=kx³, x #0 O C. y = kx², x#0 O D. y=kx, 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), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). O B. 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). OC. 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 D. 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).
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) = x x ... 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 = kx + kx², x*0 B. y=kx³, x #0 O C. y = kx², x#0 O D. y=kx, 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), in cannot be determined whether or not f has a limit as (x,y) approaches (0,0). O B. 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). OC. 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 D. 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).
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