## onegirl Group Title Use numerical and graphical evidence to conjecture value(s) for the limits, if they exist. If not, describe what is happening at x = a graphically. one year ago one year ago

1. onegirl Group Title

1) lim x-> 1 (x^2 - 1)/(x + 2) 2) lim x-> 1 (x^2 + 1)/(x - 1)

2. onegirl Group Title

@UnkleRhaukus umm can u help?

3. UnkleRhaukus Group Title

1) $\lim\limits_ {x\to1}\frac{ x^2 - 1}{x + 2}$ what happens when we put x=1 into the fraction

4. onegirl Group Title

hmm its becomes 0/3?

5. UnkleRhaukus Group Title

yeah, do you know what that simplifies to ?

6. onegirl Group Title

umm 0?

7. UnkleRhaukus Group Title

correct,

8. onegirl Group Title

okay so how would i describe it?

9. UnkleRhaukus Group Title

can you fill in the table |dw:1359329822568:dw|

10. onegirl Group Title

yes i can

11. onegirl Group Title

okay let me try this

12. onegirl Group Title

so for the -2 one i'm dividing -5 to 0 so will it be -5/0 since i cant divide that?

13. onegirl Group Title

ok so i got |dw:1359330562610:dw|

14. onegirl Group Title

so did i get it?

15. UnkleRhaukus Group Title

|dw:1359330502446:dw|

16. onegirl Group Title

are u there?

17. onegirl Group Title

ok

18. onegirl Group Title

19. onegirl Group Title

umm are u there?

20. UnkleRhaukus Group Title

(sorry my internet cut out for a moment there) um you got most of them right the first time but check the case when x=-1 agian |dw:1359331049113:dw|

21. onegirl Group Title

okay

22. onegirl Group Title

so then i draw the graph? right ?

23. UnkleRhaukus Group Title

yeah not plot those points |dw:1359331297137:dw|

24. UnkleRhaukus Group Title

not*now

25. onegirl Group Title

ok

26. UnkleRhaukus Group Title

|dw:1359331448238:dw| maybe i should have chosen some better x points

27. onegirl Group Title

what are the question marks and the lines?

28. UnkleRhaukus Group Title

ive put question marks for for the x=-2, y=-5/0 bit

29. onegirl Group Title

ohh okay

30. UnkleRhaukus Group Title

|dw:1359331760380:dw|

31. onegirl Group Title

so its a curve?

32. UnkleRhaukus Group Title

if i chose better x values we would have got something like this

33. onegirl Group Title

okay

34. onegirl Group Title

so that will be the end of the problem?

35. UnkleRhaukus Group Title

|dw:1359332271558:dw|

36. UnkleRhaukus Group Title

|dw:1359332425565:dw|

37. UnkleRhaukus Group Title

|dw:1359332578040:dw|

38. onegirl Group Title

ok so this is the final graph?

39. UnkleRhaukus Group Title

this shape is called a hyperbola at x=-2 y is undefined, this is because if we look at the graph is should be +∞ and also -∞  but it can't be more than one point we call this a vertical Asymptote

40. onegirl Group Title

okay

41. UnkleRhaukus Group Title

|dw:1359332784659:dw|

42. onegirl Group Title

ohh ok i get it

43. UnkleRhaukus Group Title

to describe what is happening at x=a if $$a < -2$$ the value will be on the bottom curve if $$a = -2$$ the value is undefined if $$a >2$$ the value will be on the top curve

44. UnkleRhaukus Group Title

__________ for 2) $\lim\limits_{x\to 1} \frac{x^2 + 1}{x - 1}$ the value is undefined as we are trying to taking the limit at the asymptote

45. onegirl Group Title

okay

46. UnkleRhaukus Group Title

i hope i haven't confused you too much

47. onegirl Group Title

noo u havent so i'll do the same this with lim x-> 1 (x^2 + 1)/(x -1)

48. UnkleRhaukus Group Title

another way of saying the value is undefined is to say the limit does not exist

49. onegirl Group Title

okay

50. onegirl Group Title

so i'll do the same for lim x-> 1 (x^2 + 1)/(x -1)?

51. UnkleRhaukus Group Title

yeah, i would use x =-5,-4,-3,-2,-1,0,2,3,4,5 this time

52. onegirl Group Title

ok thanks!! :)

53. UnkleRhaukus Group Title

ok im off, good luck

54. onegirl Group Title

hey so i did it is this correct? |dw:1359335654116:dw| |dw:1359335759751:dw|

55. onegirl Group Title

@satellite73 can u help with this?

56. onegirl Group Title

@zepdrix ??

57. onegirl Group Title

@jim_thompson5910 ??