Question Video: Interpreting the Limit of a Function at a Point | Nagwa Question Video: Interpreting the Limit of a Function at a Point | Nagwa

# Question Video: Interpreting the Limit of a Function at a Point Mathematics • Second Year of Secondary School

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True or False: lim_(π₯ β π) π(π₯) = π means that as π₯ gets closer to π, π(π₯) gets closer to π.

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### Video Transcript

True or False: The limit as π₯ approaches π of π of π₯ is equal to π means that as π₯ gets closer to π, π of π₯ gets closer to π.

In this question, we need to determine whether a statement is true or false. We need to determine whether saying that the limit as π₯ approaches π of π of π₯ is equal to π means that as π₯ gets closer to π, π of π₯ gets closer to π. And to answer this question, letβs start by recalling what we mean by this limit notation. We can recall that we say if the values of π of π₯ approach some finite value of π as the values of π₯ approach π from either side, but not necessarily when π₯ is equal to π, then we say that the limit as π₯ approaches π of π of π₯ is equal to π. This is the definition of what this limit notation means. And we can rewrite and reorder this information slightly.

For example, saying that π₯ approaches π from either side but not necessarily when π₯ is equal to π is exactly the same as saying our values of π₯ are getting closer and closer to π. Similarly, saying that when this happens the values of π of π₯ are approaching some finite value of π is exactly the same as saying our values of π of π₯ are getting closer and closer to this value of π. So this statement is exactly the same as our definition; weβve just reordered the information slightly.

Therefore, we can say itβs true that saying the limit as π₯ approaches π of π of π₯ is equal to π means that as π₯ gets closer to π, π of π₯ gets closer to π.

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