I have a question for determining the limit of a function with two variables. My textbook says that the limit (x,y)->(0,0) of 4xy^2/(x^2+y^2)=0. This is true if we evaluate the limit if it approaches along the x-axis (y=0) or the y-axis (x=0) or any line on the plane y=kx. I am wondering if this is sufficient to prove the limit=0 if we only need approach with lines.(adsbygoogle = window.adsbygoogle || []).push({});

If for example we let y=x^(1/3) then the limit does not equal zero.

I am just starting multivariable calculus so the idea of multivariable limits is new to me, so I am not sure if the direction we choose has to be a straight line or if it can be along any path like y=x^(1/3)

THanks

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# Limit of function with two variables

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