## anonymous 5 years ago need help with continuity of limits graph posted

1. anonymous

top one is question below one is example

2. anonymous

hello

3. watchmath

It seems you didn't understand what I said earlier :). All the limits and f(2)=4 in this case. So the function is continuous.

4. anonymous

well here are the tougher q's i dont know if she wants us to graph or not

5. anonymous

4. Find where the Functions are discontinuous. a. F(x) = x + 3/ x2 – 9 b. F(x) = x + 6/ x2 + 36 c. F(x) = 3x - 6

6. watchmath

Well you can try by sketching the graphs and see where the function has a hole, jump or asymptote.

7. anonymous

i was thinking factoring the denominator

8. anonymous

for a)

9. watchmath

yes that's good

10. anonymous

then it comes out to 0/x-3

11. anonymous

i am horrible at math i will admit i dont know what to do next

12. watchmath

when you factor you have $$\frac{x+3}{(x+3)(x-3)}$$. Remember we can't divide by zero. So the function is undefined at x=-3 and x=3. Then at those points the function is discontinuous.

13. anonymous

F(x) = x + 6/ x2 + 36 so for this its at x+6 and x-6

14. anonymous

so at 6 and -6

15. watchmath

But if you plug in x=-6 or 6 to x^2+6 you won't get zero.

16. anonymous

wait its x^2 + 6

17. anonymous

so graph is continous eveywhere

18. watchmath

yes

19. anonymous

its a straight line

20. watchmath

good

21. anonymous

F(x) = 3x - 6

22. anonymous

same with this one?

23. watchmath

yup

24. anonymous

have a good one bro