## anonymous 5 years ago If the Limit of a function = L as x approaches c, does the f(c)= L? Explain?

1. amistre64

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

2. amistre64

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

3. anonymous

heck no

4. amistre64

youve pretty much asked: I circle is round if a circle is round; is a circle round? if so, why?

5. anonymous

if it did, why would you say limit?

6. amistre64

i see it lol

7. anonymous

you would just say $f(c)$

8. anonymous

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

9. amistre64

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

10. amistre64

semantics lol

11. anonymous

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

12. anonymous

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

13. anonymous

of course it is false!

14. anonymous

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

15. amistre64

the limit if a poly is L at c :)

16. anonymous

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

17. anonymous

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

18. amistre64

oh that aint the simplest lol; how about: x^2 --- as x approaches 0 x

19. anonymous

ok simpler still.

20. anonymous

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

21. anonymous

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

22. amistre64

piecewise is better suited for continuity i think

23. anonymous

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

24. anonymous

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

25. anonymous

well except that my example was a piecewise function.

26. anonymous

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