By considering different paths of approach, show that the function below has no limit as (x,y) → (0,0). f(x,y)= X 4 X + Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? O A. y=kx³, x#0 OB. y = kx + kx², x O c. y=kx, x#0 OD. y=kx², x 0 , *#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? 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). OB. 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), by the two-path test, f has no limit as (x,y) approaches (0,0). OD. 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). f(x,y)= X 4 X + Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value? O A. y=kx³, x#0 OB. y = kx + kx², x O c. y=kx, x#0 OD. y=kx², x 0 , *#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? 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). OB. 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), by the two-path test, f has no limit as (x,y) approaches (0,0). OD. 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).
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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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
X +
Examine the values of f along curves that end at (0,0). Along which set of curves is f a constant value?
O A. y = kx³, x#0
B. y = kx + kx², x#0
O c. y = kx, x #0
OD. 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?
(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).
OC. 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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