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Chapter 3 – Continuous Functions and Limits
Section 3.1 – Continuity
Pg 43, Definition – A function is said to be
continuous
at the point x
o
in D provided that whenever
is a sequence in
D that converges to x
o
, the image sequence
converges to f(x
o
). The function
is said to be
continuous
at every point
in D.
Pg 44, Theorem 3.1 – Suppose that the functions
and
are continuous at the point x
o
in D. Then the sum
the product
and, if
for all x in D, the quotient
Pg 45, Corollary 3.2 – Let
be a polynomial. Then
is continuous. Moreover, if
is also a polynomial and , then the
quotient
is continuous.
Pg 45, Definition – For functions
and
such that f(D) is contained in U, we define the
composition
of
with ,
denoted by , by the formula
Pg 45, Theorem 3.3 – For functions
and
such that f(D) is contained in U, suppose that
is continuous at the point x
o
in D and
is continuous at the point f(x
o
). Then the composition
is continuous at x
o
.
Section 3.2 – The Extreme Value Theorem
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 Spring '11
 Higdon
 Continuity, Limits

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