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onegirl

  • 2 years ago

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.

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

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

  3. UnkleRhaukus
    • 2 years ago
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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

  4. onegirl
    • 2 years ago
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    hmm its becomes 0/3?

  5. UnkleRhaukus
    • 2 years ago
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    yeah, do you know what that simplifies to ?

  6. onegirl
    • 2 years ago
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    umm 0?

  7. UnkleRhaukus
    • 2 years ago
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    correct,

  8. onegirl
    • 2 years ago
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    okay so how would i describe it?

  9. UnkleRhaukus
    • 2 years ago
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    can you fill in the table |dw:1359329822568:dw|

  10. onegirl
    • 2 years ago
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    yes i can

  11. onegirl
    • 2 years ago
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    okay let me try this

  12. onegirl
    • 2 years ago
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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?

  13. onegirl
    • 2 years ago
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    ok so i got |dw:1359330562610:dw|

  14. onegirl
    • 2 years ago
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    so did i get it?

  15. UnkleRhaukus
    • 2 years ago
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    |dw:1359330502446:dw|

  16. onegirl
    • 2 years ago
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    are u there?

  17. onegirl
    • 2 years ago
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    ok

  18. onegirl
    • 2 years ago
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    how about now? |dw:1359331215777:dw|

  19. onegirl
    • 2 years ago
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    umm are u there?

  20. UnkleRhaukus
    • 2 years ago
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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|

  21. onegirl
    • 2 years ago
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    okay

  22. onegirl
    • 2 years ago
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    so then i draw the graph? right ?

  23. UnkleRhaukus
    • 2 years ago
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    yeah not plot those points |dw:1359331297137:dw|

  24. UnkleRhaukus
    • 2 years ago
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    not*now

  25. onegirl
    • 2 years ago
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    ok

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

  27. onegirl
    • 2 years ago
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    what are the question marks and the lines?

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

  29. onegirl
    • 2 years ago
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    ohh okay

  30. UnkleRhaukus
    • 2 years ago
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    |dw:1359331760380:dw|

  31. onegirl
    • 2 years ago
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    so its a curve?

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

  33. onegirl
    • 2 years ago
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    okay

  34. onegirl
    • 2 years ago
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    so that will be the end of the problem?

  35. UnkleRhaukus
    • 2 years ago
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    |dw:1359332271558:dw|

  36. UnkleRhaukus
    • 2 years ago
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    |dw:1359332425565:dw|

  37. UnkleRhaukus
    • 2 years ago
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    |dw:1359332578040:dw|

  38. onegirl
    • 2 years ago
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    ok so this is the final graph?

  39. UnkleRhaukus
    • 2 years ago
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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

  40. onegirl
    • 2 years ago
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    okay

  41. UnkleRhaukus
    • 2 years ago
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    |dw:1359332784659:dw|

  42. onegirl
    • 2 years ago
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    ohh ok i get it

  43. UnkleRhaukus
    • 2 years ago
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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

  44. UnkleRhaukus
    • 2 years ago
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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

  45. onegirl
    • 2 years ago
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    okay

  46. UnkleRhaukus
    • 2 years ago
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    i hope i haven't confused you too much

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

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

  49. onegirl
    • 2 years ago
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    okay

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

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

  52. onegirl
    • 2 years ago
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    ok thanks!! :)

  53. UnkleRhaukus
    • 2 years ago
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    ok im off, good luck

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

  55. onegirl
    • 2 years ago
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    @satellite73 can u help with this?

  56. onegirl
    • 2 years ago
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    @zepdrix ??

  57. onegirl
    • 2 years ago
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    @jim_thompson5910 ??

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