Please explain and faster By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0).x? +yh(x,y) =yExamine the values of h along curves that end at (0,0). Along which set of curves is ha constant value?O A. y= kx?, x+0, k 0O B. y= kx, x#0, k #0OC. y= kx°, x ± 0, k ± 0O D. y= kx + kx?, x 0, k 0If (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 = 2 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 two different limits along two different paths to (0,0), it cannot be determined whether or not f has a 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).O D. Since f has the same limit along two different paths to (0.0), it cannot be determined whether or not f has a limit as (x,y) approaches (0,0).

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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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Question

Please explain and faster

By considering different paths of approach, show that the function below has no limit as (x,y)→(0,0).
x? +y
h(x,y) =
y
Examine the values of h along curves that end at (0,0). Along which set of curves is ha constant value?
O A. y= kx?, x+0, k 0
O B. y= kx, x#0, k #0
OC. y= kx°, x ± 0, k ± 0
O D. y= kx + kx?, x 0, k 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 = 2 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 two different limits along two different paths to (0,0), it cannot be determined whether or not f has a 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).
O D. Since f has the same limit along two different paths to (0.0), it cannot be determined whether or not f has a limit as (x,y) approaches (0,0).

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