### 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, letβs
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; weβve just reordered the information slightly.

Therefore, we can say itβs 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.