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onegirl

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

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

    • one year ago
  2. onegirl
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    @UnkleRhaukus umm can u help?

    • one year ago
  3. UnkleRhaukus
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    1) \[\lim\limits_ {x\to1}\frac{ x^2 - 1}{x + 2}\] what happens when we put x=1 into the fraction

    • one year ago
  4. onegirl
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    hmm its becomes 0/3?

    • one year ago
  5. UnkleRhaukus
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    yeah, do you know what that simplifies to ?

    • one year ago
  6. onegirl
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    umm 0?

    • one year ago
  7. UnkleRhaukus
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    correct,

    • one year ago
  8. onegirl
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    okay so how would i describe it?

    • one year ago
  9. UnkleRhaukus
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    can you fill in the table |dw:1359329822568:dw|

    • one year ago
  10. onegirl
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    yes i can

    • one year ago
  11. onegirl
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    okay let me try this

    • one year ago
  12. onegirl
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    so for the -2 one i'm dividing -5 to 0 so will it be -5/0 since i cant divide that?

    • one year ago
  13. onegirl
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    ok so i got |dw:1359330562610:dw|

    • one year ago
  14. onegirl
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    so did i get it?

    • one year ago
  15. UnkleRhaukus
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    |dw:1359330502446:dw|

    • one year ago
  16. onegirl
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    are u there?

    • one year ago
  17. onegirl
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    ok

    • one year ago
  18. onegirl
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    how about now? |dw:1359331215777:dw|

    • one year ago
  19. onegirl
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    umm are u there?

    • one year ago
  20. UnkleRhaukus
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    (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|

    • one year ago
  21. onegirl
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    okay

    • one year ago
  22. onegirl
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    so then i draw the graph? right ?

    • one year ago
  23. UnkleRhaukus
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    yeah not plot those points |dw:1359331297137:dw|

    • one year ago
  24. UnkleRhaukus
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    not*now

    • one year ago
  25. onegirl
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    ok

    • one year ago
  26. UnkleRhaukus
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    |dw:1359331448238:dw| maybe i should have chosen some better x points

    • one year ago
  27. onegirl
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    what are the question marks and the lines?

    • one year ago
  28. UnkleRhaukus
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    ive put question marks for for the x=-2, y=-5/0 bit

    • one year ago
  29. onegirl
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    ohh okay

    • one year ago
  30. UnkleRhaukus
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    |dw:1359331760380:dw|

    • one year ago
  31. onegirl
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    so its a curve?

    • one year ago
  32. UnkleRhaukus
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    if i chose better x values we would have got something like this

    • one year ago
  33. onegirl
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    okay

    • one year ago
  34. onegirl
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    so that will be the end of the problem?

    • one year ago
  35. UnkleRhaukus
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    |dw:1359332271558:dw|

    • one year ago
  36. UnkleRhaukus
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    |dw:1359332425565:dw|

    • one year ago
  37. UnkleRhaukus
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    |dw:1359332578040:dw|

    • one year ago
  38. onegirl
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    ok so this is the final graph?

    • one year ago
  39. UnkleRhaukus
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    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

    • one year ago
  40. onegirl
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    okay

    • one year ago
  41. UnkleRhaukus
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    |dw:1359332784659:dw|

    • one year ago
  42. onegirl
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    ohh ok i get it

    • one year ago
  43. UnkleRhaukus
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    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

    • one year ago
  44. UnkleRhaukus
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    __________ 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

    • one year ago
  45. onegirl
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    okay

    • one year ago
  46. UnkleRhaukus
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    i hope i haven't confused you too much

    • one year ago
  47. onegirl
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    noo u havent so i'll do the same this with lim x-> 1 (x^2 + 1)/(x -1)

    • one year ago
  48. UnkleRhaukus
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    another way of saying the value is undefined is to say the limit does not exist

    • one year ago
  49. onegirl
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    okay

    • one year ago
  50. onegirl
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    so i'll do the same for lim x-> 1 (x^2 + 1)/(x -1)?

    • one year ago
  51. UnkleRhaukus
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    yeah, i would use x =-5,-4,-3,-2,-1,0,2,3,4,5 this time

    • one year ago
  52. onegirl
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    ok thanks!! :)

    • one year ago
  53. UnkleRhaukus
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    ok im off, good luck

    • one year ago
  54. onegirl
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    hey so i did it is this correct? |dw:1359335654116:dw| |dw:1359335759751:dw|

    • one year ago
  55. onegirl
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    @satellite73 can u help with this?

    • one year ago
  56. onegirl
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    @zepdrix ??

    • one year ago
  57. onegirl
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    @jim_thompson5910 ??

    • one year ago
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