I would like to know if there is any non trivial function $f(x)$ and a $x_0$ such that $$\lim_{x\to\ x_0} f(x)$$
is currently not known, with $x_0 \in \mathbb{R}\cup \{-\infty, +\infty \}$.
An example of a "trivial" function is $A(x)$ where $A(x)$ denotes the number of perfect numbers not greater than $x$. It is an open problem to find the value of $\lim_{x\to\infty} A(x)$, since we don't know if there are infinitely many perfect numbers.
I would prefer a limit which can be recognized by a high school student.
2026-03-25 09:23:01.1774430581
Is there any function whose limit at $x_0$ is unknown?
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Brun's theorem states that the sum of reciprocals of twin primes is convergent, but there is no other known expression for the limit.