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Recall the definition of a limit: ![\[\lim_{x\to c} f(x) = L\]](AdminLatexEx9a.gif)
means
given any positive real number, ε, there
exists a positive real number, δ, such that
![\[ 0 < |x-c| < \delta \Rightarrow |f(x) - L| < \varepsilon \]](AdminLatexEx9b.gif)
A function, f, is continuous on the open interval (a,b) means ![\[\lim_{x\to c} f(x) = f(c)\]](AdminLatexEx9c.gif)
for all c in (a,b).
A function, f, is continuous on the closed interval [a,b] means f is
continuous on (a,b) and ![\[\lim_{x\to a+} f(x) = f(a)\]](AdminLatexEx9d.gif)
,
and ![\[\lim_{x\to b-} f(x) = f(b)\]](AdminLatexEx9e.gif)
.
Calculus Theorems -- important facts about continuous functions
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