## anonymous 5 years ago Prove that the graph is continuous or not continuous at x = 2.

1. anonymous

i have attached the graph

2. amistre64

its an empty graph

3. anonymous

one sec

4. amistre64

and a picture is better, since not everyone has microsoft office

5. anonymous

sure one sec

6. anonymous

there the pic is attached

7. anonymous

Or even if they do have office, opening docs from unknown sources can sometimes be problematic.

8. anonymous

f(2) exists (infact f(2) = 4

9. amistre64

to prove: the lefthand limit has to equal the right hand limit at x = 2

10. amistre64

how to prive that without actual functions? my best guess is just to point to it on the graph and say, "see! right there"

11. anonymous

do you have pdf

12. amistre64

no

13. anonymous

i can send you a similar graph which the teacher gave us to review with

14. amistre64

i got the picture of the graph now; its just that there is no peicewise function defining the curves

15. anonymous

You can see what the left and right hand limits are by looking at the graph.

16. anonymous

And they aren't both f(-2)

17. anonymous

err f(2)

18. anonymous

$\lim_{x \rightarrow 2^+}f (x)=5\neq \lim_{x \rightarrow 2^-}f(x)=2$ Hence f is not continuous at $$x=2$$.

19. anonymous

k thats one

20. anonymous

A function is continuous about a point p if and only if p in in the domain of f, and the limit from the left = the limit from the right = f(p)

21. anonymous

f(2) exists (in fact f(2) = 4 is this correct

22. amistre64

sprinkle in some epsilons and deltas for good effect :)

23. anonymous

one second i will attach the sample graph she provided i think thats how she wants the answers

24. amistre64

we can see that there for every epsilon in the neighborhood of L can be produced by a delta such that 0<|x-c|<d in the neightborhood of 2

25. anonymous

forget this problem adding a new one