## Question

###### By considering different- paths of approach, show that the function below hlx,y) = has no limit as (xy)--(0,0)Examine the values of h along curves thatend at (0,0) Along which set of curves is h OA y=kx? constant value? X#0,k#0 0 B. y=kx + kx?,xFO,kf0 C. y=kx,X#0,k#0 0 D. y=k,XFO,kf0 If (X,y) approaches (0,0) along the curve when k = _ 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 =2 used in the set of curves f

By considering different- paths of approach, show that the function below hlx,y) = has no limit as (xy)--(0,0) Examine the values of h along curves thatend at (0,0) Along which set of curves is h OA y=kx? constant value? X#0,k#0 0 B. y=kx + kx?,xFO,kf0 C. y=kx,X#0,k#0 0 D. y=k,XFO,kf0 If (X,y) approaches (0,0) along the curve when k = _ 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 =2 used in the set of curves found above, what is the Iimit? (Simplify your answer:) What can you conclude? Since f has the same limit along two different paths to (0,0), by the two-F ~path test; has no limit as (x,Y) approaches (0,0}. has two different limits along two different paths to (0,0}, by the two-path test; f has no limit as (X,Y) approaches (0,01. Since different paths to (0,0), it cannot be determined whether or not / has limit as (x,y) approaches (0,0}. Since has the same limit along two has limit as (X,Y) approaches (0,0} paths to (0,0), it cannot be determined whether or not = Since has two different limits along two different