For a continuous function (let's say f(x)) at a point x=c, is f(c) the limit of the function as x tends to c? Please explain.

1 Answer
sente
Oct 13, 2016

Yes, by definition

Explanation:

One commonly used definition for a function #f# being continuous at a point #c# is that #f# is continuous at #c# if

#lim_(x->c)f(x) = f(c)#

(note that this definition implicitly requires #lim_(x->c)f(x)# and #f(c)# to exist)

As the question #f(x)# being continuous at #c# as a given, that means all necessary conditions for #f(x)# being continuous at #c# must be true, in particular, #lim_(x->c)f(x) = f(c)#.

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