How would I approach a question such as:
find the limits:
1-lim{ (x^4 + y^4) / (x^2+ y^2)} as (x,y) tends to (0,0)
2-lim{ xy^2 / (x^2 + y^4)} as (x,y) tends to (0,0)
Thanks
Hi
It tells me there is no limit at the origin since there are points close to the origin which the function takes the value 1/2 and not 0 ?
Why use polar coordinates on the first one?
Also, are there any pointers you can advise on how to approach these questions, i.e. finding the value of a limit at a point(for vector valued fns)?
hi
I used polar coordinates because I find it convenient and relatively easy here to show that no matter what angle we approach by, the function tends to zero.
I´m not that familiar with vector valued functions to be honest, I have only done these types of limits when .
But I would imagnine that both limits have to exist for a vector to approach some point so to speak.