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sam0004 Group Title

Lim as x approaches pi/6 of (sin(x)-sin(pi/6))/x-pi/6

  • 6 months ago
  • 6 months ago

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  1. myininaya Group Title
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    compare to definition of derivative

    • 6 months ago
  2. myininaya Group Title
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    \[\lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a}=f'(a)\]

    • 6 months ago
  3. sam0004 Group Title
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    So the limit would = 1?

    • 6 months ago
  4. myininaya Group Title
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    no

    • 6 months ago
  5. myininaya Group Title
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    what is f?

    • 6 months ago
  6. sam0004 Group Title
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    ...?

    • 6 months ago
  7. myininaya Group Title
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    what is f(x) and what is a?

    • 6 months ago
  8. sam0004 Group Title
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    F(x)=sin(x), f(a)=sin(pi/6)

    • 6 months ago
  9. myininaya Group Title
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    so what is f'?

    • 6 months ago
  10. sam0004 Group Title
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    Cos(x)-cos(pi/6)?

    • 6 months ago
  11. myininaya Group Title
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    :( if f=sin(x), then f'=?

    • 6 months ago
  12. sam0004 Group Title
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    Cos(x)

    • 6 months ago
  13. myininaya Group Title
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    right now plug in a to get your answer

    • 6 months ago
  14. sam0004 Group Title
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    A=sin(pi/6)?

    • 6 months ago
  15. myininaya Group Title
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    \[\lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a}=f'(a) \text{ or we could say it equals } =(f(x))'|_{x=a}\]

    • 6 months ago
  16. myininaya Group Title
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    \[\lim_{x \rightarrow \frac{\pi}{6}}\frac{\sin(x)-\sin(\frac{\pi}{6})}{x-\frac{\pi}{6}}=(\sin(x))'|_{x=\frac{\pi}{6}} \]

    • 6 months ago
  17. myininaya Group Title
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    do you see all i'm trying to get you to do is use the definition of derivative

    • 6 months ago
  18. myininaya Group Title
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    you are suppose to determine f and a then find f' then plug a into f' to get the result you are searching for

    • 6 months ago
  19. sam0004 Group Title
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    Sqrt(3)/2?

    • 6 months ago
  20. myininaya Group Title
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    yep

    • 6 months ago
  21. sam0004 Group Title
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    Thank you

    • 6 months ago
  22. sam0004 Group Title
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    Any chance you can help with critical numbers?

    • 6 months ago
  23. myininaya Group Title
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    sure

    • 6 months ago
  24. sam0004 Group Title
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    F(x)=4x/x^2+1

    • 6 months ago
  25. sam0004 Group Title
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    I know i need the derivative

    • 6 months ago
  26. myininaya Group Title
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    do you mean 4x/(x^2+1)? Also what did you get for the derivative?

    • 6 months ago
  27. sam0004 Group Title
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    Yes. F'(x)=(-4x^2+4)/(x^2+1)^2

    • 6 months ago
  28. myininaya Group Title
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    thats great now find when F'=0 Also we don't have to worry when F' DNE because x^2+1 is always positive. so F'=0 when top=0 so when -4x^2+4=0 solve for x now

    • 6 months ago
  29. sam0004 Group Title
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    Sqrt(-1)

    • 6 months ago
  30. myininaya Group Title
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    I think you should retry solving -4x^2+4=0 I will give you a (you will get two real solutions)

    • 6 months ago
  31. sam0004 Group Title
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    ...+or-sqrt(-1)

    • 6 months ago
  32. sam0004 Group Title
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    +or-sqrt(1)

    • 6 months ago
  33. myininaya Group Title
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    right sqrt(1)=1 so x=1 or x=-1

    • 6 months ago
  34. myininaya Group Title
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    those are the critical numbers for F.

    • 6 months ago
  35. sam0004 Group Title
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    Wow...

    • 6 months ago
  36. sam0004 Group Title
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    Find the intervals where f(x)=4/(x^+1) is increasing or decreasing.

    • 6 months ago
  37. myininaya Group Title
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    is that f(x)=4/(x+1)? like you weren't trying to write an exponent right?

    • 6 months ago
  38. sam0004 Group Title
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    I Find the derivative...then set the denominator equal to zero...put those numbers on a number line and plug in numbers to find the intervals?

    • 6 months ago
  39. sam0004 Group Title
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    I was writing an exponent

    • 6 months ago
  40. sam0004 Group Title
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    I apologize for missing the exponent

    • 6 months ago
  41. sam0004 Group Title
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    It should have said 4/(x^2+1)

    • 6 months ago
  42. myininaya Group Title
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    well I don't know what f you are looking at exactly. but yeah you definitely need to find f' because f' tells you if f is decreasing or increasing or neither f'=0 means the function is resting f'>0 means f is increasing f'<0 means f is decreasing I first find when f' =0 and when f' does not exist and then test each interval around those numbers to see if the function is increasing there or decreasing there

    • 6 months ago
  43. myininaya Group Title
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    so what is f' first?

    • 6 months ago
  44. sam0004 Group Title
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    -8x/(x^4+1)

    • 6 months ago
  45. sam0004 Group Title
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    X=-1 and x=1

    • 6 months ago
  46. myininaya Group Title
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    (x^2+1)^2 does not equal x^4+1

    • 6 months ago
  47. myininaya Group Title
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    just leave is at (x^2+1)^2

    • 6 months ago
  48. sam0004 Group Title
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    Increasing from negative infinity to 0 and decreasing from 0 to positive infinity

    • 6 months ago
  49. myininaya Group Title
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    also x^2+1 is always positive so f' and f exist everywhere so you just need to find when f'=0 which is when -8x=0 which is when x=?

    • 6 months ago
  50. myininaya Group Title
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    ok yep

    • 6 months ago
  51. sam0004 Group Title
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    F(x)=3x^2-12x=5 over the closed interval 0,3. Find absolute extrema.

    • 6 months ago
  52. sam0004 Group Title
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    Do i again begin with taking the derivative?

    • 6 months ago
  53. myininaya Group Title
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    see if there any critical numbers between 0 and 3 first

    • 6 months ago
  54. myininaya Group Title
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    which means you need to find f' which all means you need find when f'=0 this looks like you meant to write a polynomial so we don't need to worry when f' dne

    • 6 months ago
  55. sam0004 Group Title
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    X=2

    • 6 months ago
  56. myininaya Group Title
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    ok do F(0) and F(2) and F(3) which ever one of these are the lowest value is the absolute min value which ever one of these are the highest value is the absolute max value

    • 6 months ago
  57. sam0004 Group Title
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    Ok so you use the tow numbers in the interval and the critical number?

    • 6 months ago
  58. myininaya Group Title
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    also I don't know what your function is exactly critical numbers in between the critical numbers and any included endpoints just plug them back into the original function

    • 6 months ago
  59. myininaya Group Title
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    you have two equal signs

    • 6 months ago
  60. myininaya Group Title
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    i'm guessing that second equal sign is a + or a -

    • 6 months ago
  61. myininaya Group Title
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    can't decide which one

    • 6 months ago
  62. sam0004 Group Title
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    Should be +5

    • 6 months ago
  63. myininaya Group Title
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    ok do you want me to check your answers for this one or are you just going through problems and getting ideas on how to do them so you can pass your final

    • 6 months ago
  64. myininaya Group Title
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    like it seems like you are studying

    • 6 months ago
  65. sam0004 Group Title
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    I just need ideas on how to pass my final...i struggle with a few areas.

    • 6 months ago
  66. myininaya Group Title
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    i would like to help you more but...

    • 6 months ago
  67. myininaya Group Title
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    I have to go do some house stuff good luck on your final

    • 6 months ago
  68. myininaya Group Title
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    i hope i was helpful

    • 6 months ago
  69. sam0004 Group Title
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    Ok thanks

    • 6 months ago
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