There are two situations in which a function has no limit at all. One is that the limit of that point is infinite, and the other is infinitesimal. Then, the answer came out. If the limit of these two functions is infinite, then the limit of their difference must exist, and so must the infinitesimal difference. If the limits of these two functions are infinitesimal and infinitesimal, their sum limit must exist, so in any case, their sum or difference limit must exist. Get a license.
Remember to adopt it when you are satisfied.