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schmidtdancer Group Title

FIND the limit!!

  • 2 years ago
  • 2 years ago

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  1. schmidtdancer Group Title
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    |dw:1343661876978:dw|

    • 2 years ago
  2. agentx5 Group Title
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    Ah! This is one best though of visually, let me make you a graph:

    • 2 years ago
  3. schmidtdancer Group Title
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    ok

    • 2 years ago
  4. ParthKohli Group Title
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    If you find the function continuous, then you may just plug 3 for \(x\) by the way.

    • 2 years ago
  5. ParthKohli Group Title
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    Let's see how the graph is..

    • 2 years ago
  6. schmidtdancer Group Title
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    Ok. If I plug in 3, I get 3 sqrt(0)

    • 2 years ago
  7. ParthKohli Group Title
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    Don't do that now.

    • 2 years ago
  8. agentx5 Group Title
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    What you need are numbers slightly less than 3, like 2.9999999999999

    • 2 years ago
  9. ParthKohli Group Title
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    Looks like we can plug in values less than \(3\).

    • 2 years ago
  10. schmidtdancer Group Title
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    Ok

    • 2 years ago
  11. ParthKohli Group Title
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    Because it is a left handed limit, we may plug numbers like agentx5 said :)

    • 2 years ago
  12. agentx5 Group Title
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    That - sign above the limit means "numbers from the left hand side limit" or the number slightly less than 3 (but as close as you can get)

    • 2 years ago
  13. schmidtdancer Group Title
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    ok! can you show how I would solve it

    • 2 years ago
  14. schmidtdancer Group Title
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    Ok i understand that

    • 2 years ago
  15. telliott99 Group Title
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    About your graph, notice what happens to the function for x > 3

    • 2 years ago
  16. schmidtdancer Group Title
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    So how would I solve the limit?

    • 2 years ago
  17. ParthKohli Group Title
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    By plugging numbers slightly less than 3.

    • 2 years ago
  18. agentx5 Group Title
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    @telliott99 , I know... look at the notation for imaginary and real...

    • 2 years ago
  19. telliott99 Group Title
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    Just saying the graph is not correct. It doesn't have a hole in it. And do what @ParthKohli says

    • 2 years ago
  20. schmidtdancer Group Title
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    2.99(9-2.99^2)

    • 2 years ago
  21. ParthKohli Group Title
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    \[ \begin{array}{l|r} x & f(x) \\ \hline 2.5 & \\ 2.9 \\ 2.999 \\ 2.99999\end{array} \] Fill the f(x)'s.

    • 2 years ago
  22. schmidtdancer Group Title
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    for 2.5, f(x) would be 4.145

    • 2 years ago
  23. ParthKohli Group Title
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    Find them for all.

    • 2 years ago
  24. agentx5 Group Title
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    And and as you get closer and closer to 2.999999999999? Every closer to 3 from the "just under" side and you'll approach some limit.

    • 2 years ago
  25. schmidtdancer Group Title
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    Ok can you help find the limit now? Like I understand how to find that, i just dont haeve time to find them all

    • 2 years ago
  26. ParthKohli Group Title
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    Calculator, Schmidt.

    • 2 years ago
  27. schmidtdancer Group Title
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    so agentx5, I should just use 2.999999 to find the limit?

    • 2 years ago
  28. agentx5 Group Title
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    Or if you prefer, 2.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999... Get the point? :P

    • 2 years ago
  29. schmidtdancer Group Title
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    I got 7.3484

    • 2 years ago
  30. ParthKohli Group Title
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    Just not 3.

    • 2 years ago
  31. ParthKohli Group Title
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    Looks like its getting closer to 7.5, but let's see it for more values.

    • 2 years ago
  32. schmidtdancer Group Title
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    Ok! I think its going to be 7.5

    • 2 years ago
  33. ParthKohli Group Title
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    Are you sure? Try for 2.9999999 and 2.999999999999999. So on.

    • 2 years ago
  34. schmidtdancer Group Title
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    I just tried for that

    • 2 years ago
  35. schmidtdancer Group Title
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    can someone tell me if im right

    • 2 years ago
  36. ParthKohli Group Title
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    I am too lazy to do so :/

    • 2 years ago
  37. schmidtdancer Group Title
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    come onnn lol

    • 2 years ago
  38. schmidtdancer Group Title
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    plz! i really need your help..

    • 2 years ago
  39. ParthKohli Group Title
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    All right :) let me check it out on Wolfram.

    • 2 years ago
  40. schmidtdancer Group Title
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    OK

    • 2 years ago
  41. ParthKohli Group Title
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    @agentx5 Where is the graph?

    • 2 years ago
  42. agentx5 Group Title
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    Here's the algebra trick, you need to find what y would be when x=3. You can't do this normally but... \(x\sqrt{(3+x)(3-x)}\) , For what solutions does y = 0? Well, 0, +3 and -3. So... ;-) Replacing with a better graph (more accurate, real #'s only): |dw:1343662913297:dw|

    • 2 years ago
  43. schmidtdancer Group Title
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    ok thx @agentx5 so what would the limit be for this probb?

    • 2 years ago
  44. ParthKohli Group Title
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    I was actually surprised how I was plugging values and getting it approaching something else. Hence, I asked.

    • 2 years ago
  45. ParthKohli Group Title
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    The limit was getting smaller and smaller. ;)

    • 2 years ago
  46. ParthKohli Group Title
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    You may find from the graph, actually.|dw:1343663313029:dw|

    • 2 years ago
  47. ParthKohli Group Title
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    What is \(y\) approaching in the graph? ^

    • 2 years ago
  48. agentx5 Group Title
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    With the limit shown... |dw:1343663226621:dw|

    • 2 years ago
  49. schmidtdancer Group Title
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    like 2 or 3 right?

    • 2 years ago
  50. agentx5 Group Title
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    I actually had my imaginary lines going the wrong way @telliott99 and the circles were too high in the original sketch (they're on the x-axis), I stand corrected. Although I'm not sure that's what you meant. ;-)

    • 2 years ago
  51. schmidtdancer Group Title
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    Guys do you know the actual limit?

    • 2 years ago
  52. agentx5 Group Title
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    Yes.

    • 2 years ago
  53. agentx5 Group Title
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    And I'm trying to help you learn visually what's going on so you're not lost here

    • 2 years ago
  54. schmidtdancer Group Title
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    Yeah I do see it visually,

    • 2 years ago
  55. schmidtdancer Group Title
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    is the limit around 2 or 3

    • 2 years ago
  56. schmidtdancer Group Title
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    wait it looks around 0

    • 2 years ago
  57. agentx5 Group Title
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    \[\lim_{x \rightarrow 3^-}\] What is the output of the function approaching? The input gets closer to 3 from the "slightly less" side.

    • 2 years ago
  58. schmidtdancer Group Title
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    as 3 approaches 3 from the left, the y value is 0, right?

    • 2 years ago
  59. schmidtdancer Group Title
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    sorry i meant, as x approaches 3

    • 2 years ago
  60. agentx5 Group Title
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    Or using the analytical method, as you plug in larger and larger 2.9999999999999999...'s you get smaller and smaller numbers. Infinitesimally small. To the point gets damned close to zero. Thus the limit is zero, correct.

    • 2 years ago
  61. schmidtdancer Group Title
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    ok so the limit for this function is 0? :D

    • 2 years ago
  62. agentx5 Group Title
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    The reason you can't just substitute 3 in place of x, officially is because you might have one like this: \[\lim_{x \rightarrow 1} = \frac{1}{1-x}\] Look what happens if you plug in 1?

    • 2 years ago
  63. schmidtdancer Group Title
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    But, limit is 0 right? and yes the ddenominator bneomes 0.. not possible

    • 2 years ago
  64. agentx5 Group Title
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    In this case your left and your right hand limits are going in opposite directions, and the limit doesn't exist. |dw:1343663845294:dw| And yes, twice to the above post. :-)

    • 2 years ago
  65. schmidtdancer Group Title
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    wait so the limit is DNE? or zero!?!

    • 2 years ago
  66. agentx5 Group Title
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    For your original problem, Zero. For the one I just asked you, trying to get you to learn, Does Not Exist.

    • 2 years ago
  67. agentx5 Group Title
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    You will see DNE problems, I can guarantee you.

    • 2 years ago
  68. schmidtdancer Group Title
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    Oh yeah, I know!:)

    • 2 years ago
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