What are some real life applications of limits? I have been recently taught limits  in calculus but I don't see any real life applications. Are there any? Thanks.

Example:
Let $X$ denote a random variable that can take any positive integer value.
Given the probability function $P(X=k)=\frac{1}{2^k}$, find the expected value of $X$.
The solution is $\lim\limits_{n\to\infty}\left(\sum\limits_{k=1}^{n}\frac{k}{2^k}\right)=2$.
