By considering different paths of approach, show that the function below has no limit as (x,y) -> (0,0). 4 f(x, y) = 2 4 X + Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value? 1 y = kx + kx, x+0 2 y = kx", x#0 3 y= kx, x#0 4 4 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? If (x,y) approaches (0,0) along the curve when k=0 used in the set of curves found above, what is the limit? What can you conclude? 1 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). 2 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). 3 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). 4 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).
By considering different paths of approach, show that the function below has no limit as (x,y) -> (0,0). 4 f(x, y) = 2 4 X + Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value? 1 y = kx + kx, x+0 2 y = kx", x#0 3 y= kx, x#0 4 4 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? If (x,y) approaches (0,0) along the curve when k=0 used in the set of curves found above, what is the limit? What can you conclude? 1 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). 2 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). 3 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). 4 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).
Chapter1: Equations, Inequalities, And Mathematical Modeling
Section1.1: Graphs Of Equations
Problem 9ECP
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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).
4
f(x, y) =
2
4
X +
Examine the values of f along curves that end at (0,0). Along which set of curves is fa constant value?
1
y = kx + kx, x+0
2
y = kx", x#0
3 y= kx, x#0
4
4 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?
If (x,y) approaches (0,0) along the curve when k=0 used in the set of curves found above, what is the limit?
What can you conclude?
1 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).
2 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).
3 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).
4
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).
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