Homework Help is Here – Start Your Trial Now!
Math
Calculus
By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). 4 f(x,y) = 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+ kx?, 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 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), 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 (0,0), in cannot be determined whether or not f has a 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). 4 f(x,y) = 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+ kx?, 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 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), 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 (0,0), in cannot be determined whether or not f has a 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).

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...
See similar textbooks
icon
Related questions
Question
By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). 4 X f(x,y) = 2 4 X' +y Examine the values of f along curves that end at (0,0). Along which set of curves isfa 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 whenk=0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? 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). B. 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). C. 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). 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). 4 X f(x,y) = 2 4 X' +y Examine the values of f along curves that end at (0,0). Along which set of curves isfa 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 whenk=0 used in the set of curves found above, what is the limit? (Simplify your answer.) What can you conclude? 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). B. 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). C. 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). 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).
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS