Continuity
Continuity lintels many different aspects of mathematics, One of the aspects that
we feel is most important is limits. We will briefly explain what limits are and how they
are directly linked to continuity. A limit is the intended height of a function. This means
that when
x
approaches a specific number on the xaxis the height will approach a
specific number on the yaxis. Here is an example that may help to better understand
what the limit of a function is.
f
(
x
) =
x
² (let say
x
approaches 2, so we plug in 2 for
x
)
f
(2) = 2² (as
x
approaches 2 the height approaches 2²)
f
(2) = 4 (so when
x
approaches 2 the height approaches 4)
As
x
approaches 2 the intended height must be 4. This means that when
x
approaches 2
the limit must be 4. The mathematical way to write this is lim
f
(
x
) = 4.
x
→
2
Whenever limits of a function is used the notation must always look like the that of the
Notation above, which is based upon the definition lim
f
(
x
) = L.
x
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '10
 Staff
 Math, Continuity, Limits, Continuous function, Classification of discontinuities

Click to edit the document details