Another limit with two variables

[oahsen]

consider the limit
when lim x,y goes to 0,0 (x*(|y|^k))/(x^2+y^4)
a-) find all values of k where the limit does not exist
b-)find all value of k where the liğmit exist..

I tried to write epsilon-delta method but I could not go further...
Which method should I use in order to show the limit is exist/does not exist?

 

[oahsen]

consider the limit
when lim x,y goes to 0,0 (x*(|y|^k))/(x^2+y^4)
a-) find all values of k where the limit does not exist
b-)find all value of k where the limit exist..

I tried to write epsilon-delta method but I could not go further...
Which method should I use in order to show the limit is exist/does not exist?

After very intense struggling, I found that if k>2 the limit exist. (I used the sandwich theorem and showed that the function is less than |y|^(k-2) and greater than 0; hence if k-2>0 (by sandwich theorem) then the value goes to 0). However, in the question it also asks to show the existence of the limit by the epsilon-delta method. Do you have any advice to show it with epsilon-delta method? Please help me, I am trying to solve this problem almost for 2 days...