Question

In calculus limits, what does it mean for one value to approach another?

Answer 1

In calculus, when we say that one value approaches another, we are referring to the concept of a limit. More specifically, it means that as the input of a function gets closer and closer to a certain value, the output of the function approaches a specific value as well. The limit notation using LaTeX would look like this:

$$\lim_{x \to a} f(x) = L$$

Here, the limit of the function $f(x)$ approaches the value $L$ as $x$ approaches $a$. This means that as $x$ gets arbitrarily close to $a$, the function's output, $f(x)$, gets arbitrarily close to $L$.