This problem was given in one of these math contests my school had and that no one was able to prove it (in extreem detail).(adsbygoogle = window.adsbygoogle || []).push({});

Problem: Suppose that f is a function with the property that

lim f(x) exists for all real c

x->c

Define a new function g this way:

g(x) = lim f(t)

x->t

Prove in hideous detail that g is continuous everywhere, (i.e. continuous at every real number).

As far as i can tell you, i m not at this level of proving such a problem, but it would be helpful if someone could explain it to me on doing this problem. As it would help me understand my class related topics better. This is was a contest question, so I dont expect everyone being able to do it, as even my teacher said it is difficult.

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# Homework Help: Hard limit problem

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