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Continuity:
A function f is continuos at x = a if f is
defined at x = a and either ; f is not defined anywhere
near a; or f is defined arbitrarily near x = a
and limx®a
f(x)=f(a).
Conversely, A function f is discontinuous at x = a if
f is defined at x = a and f is not continuos at
x = a.
Addition, Subtraction, Multiplication and Division of
Continuity:
If f and g are continuos functions at x = a
then; f + g, f - g, f · g and f/g;
where g(a) ¹ 0; are also
continuous at x = a.
If the function f is a polynomial or a rational
function then f is continuos wherever it is defined.
Given f(g(x)), where g is continuos
at x = a , and f is continuos at x = g(a) then f(g(x))
is continuos at x = a.
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