How do limits work intuitively?

Problem Statement

How do limits work intuitively?

Step-by-Step Explanation

Intuitively, a limit follows where function values are heading, even if the function is not defined at that point.

1. Identify what the question is asking. In Calculus, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

Intuitively, a limit follows where function values are heading, even if the function is not defined at that point. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.