By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). 4 f(х,у) - Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value? O A. y=kx+ kx2, x#0 O B. y=kx°, x#0 OC. y= kx, 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 the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approache 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). 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) approa
By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). 4 f(х,у) - Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value? O A. y=kx+ kx2, x#0 O B. y=kx°, x#0 OC. y= kx, 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 the same limit along two different paths to (0,0), in cannot be determined whether or not f has a limit as (x,y) approache 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). 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) approa
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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Question
![By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0).
f(x,y) =
十
...
Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value?
O A. y= kx + kx², x+0
O B. y= kx', x# 0
С. у3Кx, х#0
O D. y= 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?
O(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).
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).
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).
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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F08f364a7-58c9-40cd-a04d-83636aa816ab%2Fdd811b4f-b317-47a8-a7c0-193fe629dbfd%2F3plh2cu_processed.jpeg&w=3840&q=75)
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) =
十
...
Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value?
O A. y= kx + kx², x+0
O B. y= kx', x# 0
С. у3Кx, х#0
O D. y= 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?
O(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).
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).
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).
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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