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sam0004

  • one year ago

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

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  1. myininaya
    • one year ago
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    compare to definition of derivative

  2. myininaya
    • one year ago
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    \[\lim_{x \rightarrow a}\frac{f(x)-f(a)}{x-a}=f'(a)\]

  3. sam0004
    • one year ago
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    So the limit would = 1?

  4. myininaya
    • one year ago
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    no

  5. myininaya
    • one year ago
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    what is f?

  6. sam0004
    • one year ago
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    ...?

  7. myininaya
    • one year ago
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    what is f(x) and what is a?

  8. sam0004
    • one year ago
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    F(x)=sin(x), f(a)=sin(pi/6)

  9. myininaya
    • one year ago
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    so what is f'?

  10. sam0004
    • one year ago
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    Cos(x)-cos(pi/6)?

  11. myininaya
    • one year ago
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    :( if f=sin(x), then f'=?

  12. sam0004
    • one year ago
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    Cos(x)

  13. myininaya
    • one year ago
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    right now plug in a to get your answer

  14. sam0004
    • one year ago
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    A=sin(pi/6)?

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

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

  17. myininaya
    • one year ago
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    do you see all i'm trying to get you to do is use the definition of derivative

  18. myininaya
    • one year ago
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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

  19. sam0004
    • one year ago
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    Sqrt(3)/2?

  20. myininaya
    • one year ago
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    yep

  21. sam0004
    • one year ago
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    Thank you

  22. sam0004
    • one year ago
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    Any chance you can help with critical numbers?

  23. myininaya
    • one year ago
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    sure

  24. sam0004
    • one year ago
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    F(x)=4x/x^2+1

  25. sam0004
    • one year ago
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    I know i need the derivative

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

  27. sam0004
    • one year ago
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    Yes. F'(x)=(-4x^2+4)/(x^2+1)^2

  28. myininaya
    • one year ago
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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

  29. sam0004
    • one year ago
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    Sqrt(-1)

  30. myininaya
    • one year ago
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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)

  31. sam0004
    • one year ago
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    ...+or-sqrt(-1)

  32. sam0004
    • one year ago
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    +or-sqrt(1)

  33. myininaya
    • one year ago
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    right sqrt(1)=1 so x=1 or x=-1

  34. myininaya
    • one year ago
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    those are the critical numbers for F.

  35. sam0004
    • one year ago
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    Wow...

  36. sam0004
    • one year ago
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    Find the intervals where f(x)=4/(x^+1) is increasing or decreasing.

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

  38. sam0004
    • one year ago
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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?

  39. sam0004
    • one year ago
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    I was writing an exponent

  40. sam0004
    • one year ago
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    I apologize for missing the exponent

  41. sam0004
    • one year ago
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    It should have said 4/(x^2+1)

  42. myininaya
    • one year ago
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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

  43. myininaya
    • one year ago
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    so what is f' first?

  44. sam0004
    • one year ago
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    -8x/(x^4+1)

  45. sam0004
    • one year ago
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    X=-1 and x=1

  46. myininaya
    • one year ago
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    (x^2+1)^2 does not equal x^4+1

  47. myininaya
    • one year ago
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    just leave is at (x^2+1)^2

  48. sam0004
    • one year ago
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    Increasing from negative infinity to 0 and decreasing from 0 to positive infinity

  49. myininaya
    • one year ago
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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=?

  50. myininaya
    • one year ago
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    ok yep

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

  52. sam0004
    • one year ago
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    Do i again begin with taking the derivative?

  53. myininaya
    • one year ago
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    see if there any critical numbers between 0 and 3 first

  54. myininaya
    • one year ago
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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

  55. sam0004
    • one year ago
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    X=2

  56. myininaya
    • one year ago
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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

  57. sam0004
    • one year ago
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    Ok so you use the tow numbers in the interval and the critical number?

  58. myininaya
    • one year ago
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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

  59. myininaya
    • one year ago
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    you have two equal signs

  60. myininaya
    • one year ago
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    i'm guessing that second equal sign is a + or a -

  61. myininaya
    • one year ago
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    can't decide which one

  62. sam0004
    • one year ago
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    Should be +5

  63. myininaya
    • one year ago
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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

  64. myininaya
    • one year ago
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    like it seems like you are studying

  65. sam0004
    • one year ago
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    I just need ideas on how to pass my final...i struggle with a few areas.

  66. myininaya
    • one year ago
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    i would like to help you more but...

  67. myininaya
    • one year ago
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    I have to go do some house stuff good luck on your final

  68. myininaya
    • one year ago
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    i hope i was helpful

  69. sam0004
    • one year ago
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    Ok thanks

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