If the Limit of a function = L as x approaches c, does the f(c)= L? Explain?

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If the Limit of a function = L as x approaches c, does the f(c)= L? Explain?

Mathematics
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well, that IS the definition .... so yes.
If the limit if a function is the limit of a function; does the limit of the function exist? .... yes
heck no

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youve pretty much asked: I circle is round if a circle is round; is a circle round? if so, why?
if it did, why would you say limit?
i see it lol
you would just say \[f(c)\]
How about if f(c) = L, then the limit of f(x) as x approaches c = L?
f(c) doesnt HAVE to equal L; but that is the gist of it
semantics lol
right that is the whole point. if you could compute limits by evaluating functions we would never have heard of them.
Well, the book is telling me it is false.........
of course it is false!
that is the whole point. if the function is continuous then it is true.
the limit if a poly is L at c :)
here is the simplest example i can think of \[lim_{x->2}\frac{x^2-4}{x-2}\]
in this case \[f(x)=\frac{x^2-4}{x-2}\] and this limit is obviously 4 but \[f(4)\] is undefined.
oh that aint the simplest lol; how about: x^2 --- as x approaches 0 x
ok simpler still.
I think a piecewise function would be a better explanation....
matter of fact here is an even simpler one. \[f(x)=x\] if \[x\neq5\] \[f(5)=\pi\]
piecewise is better suited for continuity i think
then the limit as x->5 is 5, but \[f(5)=\pi\]
no i don't think piecewise is a better explanation at all.
well except that my example was a piecewise function.
Ok, it was a little tricky at first, but it is actually pretty simple..........thanks satellite

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