Then xnyn and xn/yn may or may not be limited.

Such as xn = 1/n, yn = n,

Then xnyn and xn/yn have limits,

Another example is xn = 1, yn = (- 1)? ,

Xnyn and xn/yn are not limited.

But yn/xn must have no limit, because if there is a limit, then xn * (yn/xn) = yn also has a limit, which obviously does not meet the conditions.