Question

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

Answer 1

well, that IS the definition .... so yes.

Answer 2

If the limit if a function is the limit of a function; does the limit of the function exist? .... yes

Answer 3

heck no

Answer 4

youve pretty much asked:

I circle is round if a circle is round; is a circle round? if so, why?

Answer 5

if it did, why would you say limit?

Answer 6

i see it lol

Answer 7

you would just say \[f(c)\]

Answer 8

How about if f(c) = L, then the limit of f(x) as x approaches c = L?

Answer 9

f(c) doesnt HAVE to equal L; but that is the gist of it

Answer 10

semantics lol

Answer 11

right that is the whole point. if you could compute limits by evaluating functions we would never have heard of them.

Answer 12

Well, the book is telling me it is false.........

Answer 13

of course it is false!

Answer 14

that is the whole point. if the function is continuous then it is true.

Answer 15

the limit if a poly is L at c :)

Answer 16

here is the simplest example i can think of
\[lim_{x->2}\frac{x^2-4}{x-2}\]

Answer 17

in this case \[f(x)=\frac{x^2-4}{x-2}\] and this limit is obviously 4 but \[f(4)\] is undefined.

Answer 18

oh that aint the simplest lol; how about:

x^2
--- as x approaches 0
x

Answer 19

ok simpler still.

Answer 20

I think a piecewise function would be a better explanation....

Answer 21

matter of fact here is an even simpler one.
\[f(x)=x\] if \[x\neq5\]
\[f(5)=\pi\]

Answer 22

piecewise is better suited for continuity i think

Answer 23

then the limit as x->5 is 5, but \[f(5)=\pi\]

Answer 24

no i don't think piecewise is a better explanation at all.

Answer 25

well except that my example was a piecewise function.

Answer 26

Ok, it was a little tricky at first, but it is actually pretty simple..........thanks satellite