What is a simple example of a limit in the real world?

This morning, I read Wikipedia's informal definition of a limit:

Informally, a function f assigns an output $f(x)$ to every input $x$. The function has a limit $L$ at an input $p$ if $f(x)$ is "close" to $L$ whenever $x$ is "close" to $p$. In other words, $f(x)$ becomes closer and closer to $L$ as $x$ moves closer and closer to $p$.

To me that sounds like something that might be better described as a 'target'.

If I take a simple function, say one that only multiplies the input by $2$; and if my limit is $10$ at an input $5$: then I've described something that seems to match the elements contained in Wikipedia's definition. I don't believe that that's right. To me it looks like an elementary-algebra problem ($2p = 10$). To make it more calculusy, I could graph the function's output when I use inputs other than $p$, but that really wouldn't give me anything but an illustration of the fact that one's answer moves farther from the right answer as it becomes more wrong (go figure).

So limits are important; what I've just described is trivial. I do not understand them. I know calculus is often used for solving real-world challenges, and that limits are an important element of calculus, so I assume there must be some simple real-world examples of what it is that limits describe.

What is a simple example of a limit in the real world?

Thank you

-Hal.

Your example of a limit is of a limit which is easy to evaluate, but it's still a perfectly reasonable example!

Here's another fairly easy to grasp example of a limit which avoids triviality.

If I keep tossing a coin as long as it takes, how likely am I to never toss a head?

Rephrased as a limit problem, we might say

If I toss a coin $N$ times, what is the probability $p(N)$ that I have not yet tossed a head? Now what is the limit as $N\to\infty$ of $p(N)$?

The mathematical answer to this is $p(N)=\left(\frac{1}{2}\right)^N$. Then $$\lim_{N\to\infty}p(N) = 0$$ because $p=\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \ldots$ gets closer and closer to zero as $N$ gets "closer to $\infty$".

The reading of your speedometer (e.g., 85 km/h) is a limit in the real world. Maybe you think speed is speed, why not 85 km/h. But in fact your speed is changing continuously during time, and the only "solid", i.e., "limitless" data you have is that it took you exactly 2 hours to drive the 150 km from A to B. The figure your speedometer gives you is at each instant $t_0$ of your travel the limit $$v(t_0):=\lim_{\Delta t\to0}{s(t_0)-s(t_0-\Delta t)\over\Delta t}\ ,$$ where $s(t)$ denotes the distance travelled up to time $t$.