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If
is continuous at
and
, then:
- The limit of
as approaches 4 is 3. - The function approaches 3 from both sides as
gets close to 4. - There are no jumps or breaks at
.
In other words,
smoothly reaches 3 when
is near 4.
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Bonus Knowledge
If
is continuous at
and
, it implies that the limit of
as
approaches 4 must equal
. In mathematical terms, this means:
This tells us that as we get closer and closer to the value
, the function
will also get closer and closer to the value 3.
Moreover, this consistency at the point
indicates that there are no unexpected jumps or breaks in the graph of
at this point, ensuring a smooth transition through this value.
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