The correct option is:

|f(x) − L| < ε

This inequality represents the formal definition of a limit in calculus. It expresses that the function $f(x)$ is within an $\epsilon$-neighborhood of $L$ when the distance between $f(x)$ and $L$ is less than $\epsilon$.

Would you like a detailed explanation of the limit definition or its application in this context?

Here are 5 related questions you might find helpful:

1. What is the formal definition of a limit?
2. How is the $\epsilon-\delta$ definition of a limit applied in proofs?
3. What are some examples of using $|f(x) - L| < \epsilon$ in practical scenarios?
4. How does the definition change for one-sided limits?
5. What does it mean when $|f(x) - L| > \epsilon$ instead?

Tip: Always pay attention to the absolute value inequalities in limit problems—they directly represent distance and tolerance.