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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)= x² + y² 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? OA. 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). OB. 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). OC. 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 (( O D. 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). 1

By considering different paths of approach, show that the function below has no limit as (x,y)-(0,0). f(x,y)= x² + y² 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? OA. 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). OB. 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). OC. 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 (( O D. 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). 1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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 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 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). OB. 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). OC. 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 O D. 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).
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 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 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). OB. 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). OC. 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 O D. 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).
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