Another limit with two variables

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The limit of the function (x^3*y)/(x^5+2*y^3) as (x,y) approaches (0,0) is confirmed to be 0 using the epsilon-delta method and the sandwich theorem. The discussion highlights that the limit does not exist when contrasting parameterizations such as y=x^2 and y=0. The conclusion emphasizes the importance of method selection in limit evaluation.

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how can I show that
lim of (x^3*y)/(x^5+2*y^3) when (x,y) goes to (0,0) is 0.
I tried to solve with epsilon-delta method and with sandwich method. however, all of my attempts resulted withous sucess? Which method should I use and how should ı start?
 
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The limit is not 0. It does not exist. Contrast the parameterizations y=x^2 and y=0.
 
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