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Dido525 Group Title

Find the values of a and b so that the following is true.

  • 2 years ago
  • 2 years ago

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  1. Dido525 Group Title
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    I am thinking about L'Hospital's rule but I am not sure how I would apply it...

    • 2 years ago
  2. Rezz5 Group Title
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    well, you can separate them, then solve them

    • 2 years ago
  3. Dido525 Group Title
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    Yeah.... But I have two variables then.

    • 2 years ago
  4. Rezz5 Group Title
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    are you sure it tends to infinity?

    • 2 years ago
  5. Dido525 Group Title
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    Yep.

    • 2 years ago
  6. Dido525 Group Title
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    0.

    • 2 years ago
  7. Dido525 Group Title
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    oops.

    • 2 years ago
  8. Rezz5 Group Title
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    why two variables?

    • 2 years ago
  9. Rezz5 Group Title
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    if you differentiate the variable you get nothing from a, but b will still be present, you can get b right?

    • 2 years ago
  10. Dido525 Group Title
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    \[\lim_{x \rightarrow 0} (\frac{ \sin(2x) }{ x^3 }+a+\frac{ b }{ x^2 })=0\]

    • 2 years ago
  11. Dido525 Group Title
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    Yeah. I think you are right.

    • 2 years ago
  12. Rezz5 Group Title
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    ahhh, so it tends to zero?

    • 2 years ago
  13. Dido525 Group Title
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    Yep :P . I typed wrong.

    • 2 years ago
  14. Rezz5 Group Title
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    no problem, you can separate them then do the limits, you can spot it by inspection, very easily

    • 2 years ago
  15. Dido525 Group Title
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    Hmm Let me try...

    • 2 years ago
  16. Rezz5 Group Title
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    have you done it?

    • 2 years ago
  17. Dido525 Group Title
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    I can't solve the limit of: \[\lim_{x \rightarrow 0}\frac{ \sin(2x) }{ x^3 }\]

    • 2 years ago
  18. Rezz5 Group Title
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    you can!! differentiate 3 times until the denominator is 1,

    • 2 years ago
  19. Rezz5 Group Title
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    not 1, differentiate until the denominator is a constant

    • 2 years ago
  20. Rezz5 Group Title
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    sin(2)=2sin(x)cos(x)

    • 2 years ago
  21. Dido525 Group Title
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    I got -4/3 .

    • 2 years ago
  22. Rezz5 Group Title
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    for?

    • 2 years ago
  23. Dido525 Group Title
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    The limit.

    • 2 years ago
  24. Rezz5 Group Title
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    sin(2x)/x^3 as x tends to infinity?

    • 2 years ago
  25. Rezz5 Group Title
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    how ?

    • 2 years ago
  26. Dido525 Group Title
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    To 0 :P .

    • 2 years ago
  27. Rezz5 Group Title
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    lol!!! im losing it today...

    • 2 years ago
  28. Rezz5 Group Title
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    but still, i would have thought it was zero

    • 2 years ago
  29. Dido525 Group Title
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    Waitt.

    • 2 years ago
  30. Dido525 Group Title
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    The Limit is infinity..... :( .

    • 2 years ago
  31. Rezz5 Group Title
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    yep,

    • 2 years ago
  32. Dido525 Group Title
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    We can't solve anything then.

    • 2 years ago
  33. Rezz5 Group Title
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    we could, i mean if one of the variables was infinity

    • 2 years ago
  34. Dido525 Group Title
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    But We can't do anything with infinity.... It's not a number.

    • 2 years ago
  35. Rezz5 Group Title
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    wait are you sure it should tend to 0?

    • 2 years ago
  36. Dido525 Group Title
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    Well I would assume it should tend to a finite value.

    • 2 years ago
  37. Rezz5 Group Title
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    i suspect the limit should tend to infinity then for it so satisfy the limit

    • 2 years ago
  38. Rezz5 Group Title
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    not necessarily, it can be infinity, let assume it was infinity, then we can do the question with ease. have you done analysis by any chance?

    • 2 years ago
  39. Dido525 Group Title
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    No.....

    • 2 years ago
  40. Dido525 Group Title
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    Here is the question.

    • 2 years ago
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  41. Rezz5 Group Title
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    okay, no problem, assume it is infinity because i think you were right the first time round, if it was infinity just plug in infinity to the differential you had computed

    • 2 years ago
  42. Dido525 Group Title
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    If we did that then a would be infinity and b would not exist.

    • 2 years ago
  43. Rezz5 Group Title
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    b would, it would be x^2,

    • 2 years ago
  44. Rezz5 Group Title
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    one moment,

    • 2 years ago
  45. Dido525 Group Title
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    but since b^2 tends to infinity the whole thing would be 0.

    • 2 years ago
  46. Dido525 Group Title
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    x^2 sorry not b^2.

    • 2 years ago
  47. Rezz5 Group Title
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    which would be 0, at when b/x^2 as x ->0

    • 2 years ago
  48. Dido525 Group Title
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    Exactly. We can't work with that.

    • 2 years ago
  49. Rezz5 Group Title
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    we could, if b = 0,

    • 2 years ago
  50. Rezz5 Group Title
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    0/anynumber = 0

    • 2 years ago
  51. Dido525 Group Title
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    But it's not. B/x^2 is zero, not b.

    • 2 years ago
  52. Dido525 Group Title
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    We don't know what b is.

    • 2 years ago
  53. Rezz5 Group Title
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    a could be -infinity, then this would satisfy the limit

    • 2 years ago
  54. Dido525 Group Title
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    But infinity- infinity is not 0.

    • 2 years ago
  55. Rezz5 Group Title
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    yes it is

    • 2 years ago
  56. Dido525 Group Title
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    No it's not. Infinity is not a number. It's a concept.

    • 2 years ago
  57. Rezz5 Group Title
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    that is true, i moment, i am trying to multi task, i jst remembered the proof that it isnt,

    • 2 years ago
  58. Dido525 Group Title
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    http://en.wikibooks.org/wiki/Calculus/Infinite_Limits/Infinity_is_not_a_number

    • 2 years ago
  59. Rezz5 Group Title
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    okay, you need to apply l'hpitals rule over and over again, i would recon, but first you need to put all the equation under one common factor so \[=\frac{\sin(2x) + ax^{3} + bx}{x^{3}}\]

    • 2 years ago
  60. Rezz5 Group Title
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    http://answers.yahoo.com/question/index?qid=20110406112720AARpKn1 here is a better and easier way of doing it the sint is taylor expansion i think, the rest is pretty self explanatory

    • 2 years ago
  61. Dido525 Group Title
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    Lol. THanks :P .

    • 2 years ago
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