- #1
member 508213
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.
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
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