## anonymous 4 years ago find the limit of (x+7)/(x^2 -6x + 9) as x approaches 3. please show all calc involved

1. amistre64

is 3 a bad value for x?

2. anonymous

what do you mean?

3. amistre64

4. anonymous

when i plug in 3, i get 10/0...thats not good according to my teacheelser but dont know what else to do

5. amistre64

right, /0 is a bad fraction so x=3 makes this go bad

6. amistre64

can we undo the offending part with algebra?$\frac{(x+7)}{(x-3)^2}$ prolly not

7. myininaya

lol i love your definition of the term bad fraction i like to say discontinuous at such and such but bad fraction is a good term

8. amistre64
9. myininaya

So anyways since there is no way to force this fraction to be continuous at x=3 then the limit does not exist

10. amistre64

inf aint a good answer then is it :)

11. amistre64

it aint a real number so ....

12. myininaya

does not exist is fine but saying it approaches infinity gives a little more info on that "does not exist" phrase

13. anonymous

Infinty and does exists are not same right?

14. amistre64

exist means a definitive value; infinity is more a direction than a value i believe

15. myininaya

right amistre

16. anonymous

This limit exists and it is infinity...

17. anonymous

what about x^2-x-20/2x^2-32, as x approaches -4

18. anonymous

happy birthday myininaya

19. myininaya

infinity is not a number

20. anonymous

Right hand limit =left hand limit = infinity

21. myininaya

so it does not exist

22. anonymous

I know but infinity is not same as undefined.

23. amistre64

24. myininaya

infinity is fine to say when both sides are approaching infinity (same for negative infinity) but i feel it is also okay to say it dne since infinity is not a number

25. anonymous

amistre whats the screenshot for

26. anonymous

but can anyone help with the last question i posted please

27. myininaya

hes just saying the question in the window thingy is not the same as the question you asked

28. anonymous

For this question I would say that the limit is infinity, but if for the purposes of some questions where only finite limits are applicable then an infinite limit might be considered DNE.

29. Zarkon

I'd probably say infinity too, but with the understanding that the limit really does not exist...infinity is just the direction that the function is going.

30. anonymous

Myin, this is interesting: http://math.stackexchange.com/questions/36289/