Question 624103
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Let *[tex \LARGE a] be a point in the domain of the function *[tex \LARGE f].  Then *[tex \LARGE f] is continuous at *[tex \LARGE a] if and only if:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\rightarrow{a}}f(x)\ =\ f(a)]


So, the statement that *[tex \LARGE f] is continuous at *[tex \LARGE x\ =\ 1] means two things.  1: The value *[tex \LARGE 1] is an element of the domain set of *[tex \LARGE f] and 2: *[tex \LARGE \lim_{x\rightarrow{1}}f(x)\ =\ f(1)].  The existence of the limit being implied by the fact that it equals something.


The statement that *[tex \LARGE f] is discontinuous at *[tex \LARGE x\ =\ 1] means that either the value *[tex \LARGE 1] is not in the domain set of *[tex \LARGE f] or *[tex \LARGE \lim_{x\rightarrow{1}}f(x)\ \neq\ f(1)] (which could be a consequence of the non-existence of the limit).


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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