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) =
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, x+ 0
O B. y= kx, x+ 0
OC. y= kx°, x+ 0
O D. y= kx + 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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F283b3a0d-0821-472c-a1ce-fcf162c3f2c6%2F8640a9a2-d538-4d28-b955-4fea2738520b%2F7a9hwy_processed.png&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) =
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, x+ 0
O B. y= kx, x+ 0
OC. y= kx°, x+ 0
O D. y= kx + 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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