anonymous
  • anonymous
If the Limit of a function = L as x approaches c, does the f(c)= L? Explain?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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amistre64
  • amistre64
well, that IS the definition .... so yes.
amistre64
  • amistre64
If the limit if a function is the limit of a function; does the limit of the function exist? .... yes
anonymous
  • anonymous
heck no

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amistre64
  • amistre64
youve pretty much asked: I circle is round if a circle is round; is a circle round? if so, why?
anonymous
  • anonymous
if it did, why would you say limit?
amistre64
  • amistre64
i see it lol
anonymous
  • anonymous
you would just say \[f(c)\]
anonymous
  • anonymous
How about if f(c) = L, then the limit of f(x) as x approaches c = L?
amistre64
  • amistre64
f(c) doesnt HAVE to equal L; but that is the gist of it
amistre64
  • amistre64
semantics lol
anonymous
  • anonymous
right that is the whole point. if you could compute limits by evaluating functions we would never have heard of them.
anonymous
  • anonymous
Well, the book is telling me it is false.........
anonymous
  • anonymous
of course it is false!
anonymous
  • anonymous
that is the whole point. if the function is continuous then it is true.
amistre64
  • amistre64
the limit if a poly is L at c :)
anonymous
  • anonymous
here is the simplest example i can think of \[lim_{x->2}\frac{x^2-4}{x-2}\]
anonymous
  • anonymous
in this case \[f(x)=\frac{x^2-4}{x-2}\] and this limit is obviously 4 but \[f(4)\] is undefined.
amistre64
  • amistre64
oh that aint the simplest lol; how about: x^2 --- as x approaches 0 x
anonymous
  • anonymous
ok simpler still.
anonymous
  • anonymous
I think a piecewise function would be a better explanation....
anonymous
  • anonymous
matter of fact here is an even simpler one. \[f(x)=x\] if \[x\neq5\] \[f(5)=\pi\]
amistre64
  • amistre64
piecewise is better suited for continuity i think
anonymous
  • anonymous
then the limit as x->5 is 5, but \[f(5)=\pi\]
anonymous
  • anonymous
no i don't think piecewise is a better explanation at all.
anonymous
  • anonymous
well except that my example was a piecewise function.
anonymous
  • anonymous
Ok, it was a little tricky at first, but it is actually pretty simple..........thanks satellite

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