By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). f(x,y)= X4 O B. y = kx³, x#0 O c. 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 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). 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 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).
By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0). f(x,y)= X4 O B. y = kx³, x#0 O c. 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 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). 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 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).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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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)=
X4
O B. y = kx³, x#0
O c. 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 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).
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 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).
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