Limits and exponents

Question

If there is a limit function with $n\to infty$, but the limit function does have any term involving $n$, does the limit function tend to $0$?

e.g. for $$\lim_{n\to\infty} xe^{-x}.$$ Is the answer to this simply $0$?

Thank you

Answer 1

$xe^{-x}$ does not depend on $n$. So the limit is $xe^{-x}$.

Answer 2

If the function does not depend on $n $, then it will be considered as a constant.

$$\lim_{n\to+\infty}f (x)=f (x) $$