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 + 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), in cannot be determined whether or not f has a 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 (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).
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 + 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), in cannot be determined whether or not f has a 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 (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).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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) =
4
2
X' +
...
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), in cannot be determined whether or not f has a 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 (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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