The image contains a question asking for the meaning of the mathematical expression:

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

This notation refers to the concept of a limit in calculus. Specifically, it means that as the variable $x$ approaches the value $c$, the function $f(x)$ approaches the value $L$. In other words, no matter how close $x$ gets to $c$, $f(x)$ will get arbitrarily close to $L$.

Explanation:

• $\lim$ means "the limit of."
• $x \to c$ means that $x$ is approaching the value $c$.
• $f(x)$ is the function we are examining.
• $L$ is the value that $f(x)$ approaches as $x$ gets closer to $c$.

For a limit to exist, the function $f(x)$ must approach the same value $L$ from both sides of $c$ (from the left and right of $c$).

Would you like further details or have any questions?

Here are five questions related to this concept:

1. What are left-hand and right-hand limits, and how do they relate to the overall limit?
2. Can the limit of $f(x)$ exist if $f(x)$ is not defined at $x = c$?
3. What happens if the limit from the left and right are not equal?
4. How do you compute limits of more complex functions?
5. How does continuity relate to the existence of a limit?

Tip: When calculating limits, always check if the function behaves similarly from both directions as $x$ approaches the target value!