Asked • 03/15/19

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.

2 Answers By Expert Tutors

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Justin P. answered • 03/15/19

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