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sam0004

  • 7 months ago

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

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  1. myininaya
    • 7 months ago
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    compare to definition of derivative

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

  3. sam0004
    • 7 months ago
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    So the limit would = 1?

  4. myininaya
    • 7 months ago
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    no

  5. myininaya
    • 7 months ago
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    what is f?

  6. sam0004
    • 7 months ago
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    ...?

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

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

  9. myininaya
    • 7 months ago
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    so what is f'?

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

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

  12. sam0004
    • 7 months ago
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    Cos(x)

  13. myininaya
    • 7 months ago
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    right now plug in a to get your answer

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

  15. myininaya
    • 7 months 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
    • 7 months 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
    • 7 months 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
    • 7 months 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
    • 7 months ago
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    Sqrt(3)/2?

  20. myininaya
    • 7 months ago
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    yep

  21. sam0004
    • 7 months ago
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    Thank you

  22. sam0004
    • 7 months ago
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    Any chance you can help with critical numbers?

  23. myininaya
    • 7 months ago
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    sure

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

  25. sam0004
    • 7 months ago
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    I know i need the derivative

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

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

  28. myininaya
    • 7 months 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
    • 7 months ago
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    Sqrt(-1)

  30. myininaya
    • 7 months 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
    • 7 months ago
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    ...+or-sqrt(-1)

  32. sam0004
    • 7 months ago
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    +or-sqrt(1)

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

  34. myininaya
    • 7 months ago
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    those are the critical numbers for F.

  35. sam0004
    • 7 months ago
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    Wow...

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

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

  38. sam0004
    • 7 months 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
    • 7 months ago
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    I was writing an exponent

  40. sam0004
    • 7 months ago
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    I apologize for missing the exponent

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

  42. myininaya
    • 7 months 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
    • 7 months ago
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    so what is f' first?

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

  45. sam0004
    • 7 months ago
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    X=-1 and x=1

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

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

  48. sam0004
    • 7 months ago
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    Increasing from negative infinity to 0 and decreasing from 0 to positive infinity

  49. myininaya
    • 7 months 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
    • 7 months ago
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    ok yep

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

  52. sam0004
    • 7 months ago
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    Do i again begin with taking the derivative?

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

  54. myininaya
    • 7 months 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
    • 7 months ago
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    X=2

  56. myininaya
    • 7 months 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
    • 7 months ago
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    Ok so you use the tow numbers in the interval and the critical number?

  58. myininaya
    • 7 months 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
    • 7 months ago
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    you have two equal signs

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

  61. myininaya
    • 7 months ago
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    can't decide which one

  62. sam0004
    • 7 months ago
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    Should be +5

  63. myininaya
    • 7 months 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
    • 7 months ago
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    like it seems like you are studying

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

  66. myininaya
    • 7 months ago
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    i would like to help you more but...

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

  68. myininaya
    • 7 months ago
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    i hope i was helpful

  69. sam0004
    • 7 months ago
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    Ok thanks

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