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anonymous

  • 5 years ago

find mean value? 2cos2x+sinx=0 a= -pi\2, b=pi\2

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  1. anonymous
    • 5 years ago
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    plz reply karo plzzzzzzzzzz

  2. myininaya
    • 5 years ago
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    {f(b)-f(a)}/{b-a}={f(pi/2)-f(-pi/2)}/{pi}={[2cos(pi)+sin(pi/2)]-[2cos(-pi)+sin(-pi/2)]}/{pi} ={2(-1)+1-2(-1)-(-1)}/pi=(-2+1+2+1)/pi=2/pi but f'(x)=4sin(2x)+cosx f'(c)=4sin(2c)+cos(c) set f'(c)=2/pi and solve for c

  3. anonymous
    • 5 years ago
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    i got a value of c

  4. myininaya
    • 5 years ago
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    ok cool!

  5. anonymous
    • 5 years ago
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    i got ! 4sin2c+(1\90)=cosc now how can be find value of c

  6. myininaya
    • 5 years ago
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    4sin(2c)+cos(c)=2/pi

  7. anonymous
    • 5 years ago
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    plz reply fast myninaya............

  8. myininaya
    • 5 years ago
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    -0.04535615498 is what I got using a calculator so the problem says to use the mean value thm?

  9. anonymous
    • 5 years ago
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    how can you find the value of c . give me the method?

  10. dumbcow
    • 5 years ago
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    \[Average = \frac{1}{b-a}\int\limits_{a}^{b}2\cos 2x +\sin x dx\]

  11. anonymous
    • 5 years ago
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    dumcow i don't understand this method . give me another method?

  12. dumbcow
    • 5 years ago
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    are you looking for the mean value of the function from a to b or does it say to use mean value theorem to find point that equals avg rate of change

  13. anonymous
    • 5 years ago
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    but my teacher says that u can use mean value theorm

  14. myininaya
    • 5 years ago
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    http://www.eldamar.org.uk/maths/calculus/node17.html

  15. myininaya
    • 5 years ago
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    m(b-a)=int(f(x),a..b) m is the mean value

  16. myininaya
    • 5 years ago
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    cow has already said this though

  17. myininaya
    • 5 years ago
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    do you know how to integrate?

  18. anonymous
    • 5 years ago
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    no i don't know?

  19. anonymous
    • 5 years ago
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    Okay, By the mean value theorem. The mean value is [f(b)-f(a)]/[b-a]. \[f(b)=f(\pi/2)=2\cos \pi +\sin(\pi/2)=-2+1=-1\] \[f(a)=f(-{\pi \over 2})=2\cos (-\pi)+\sin (-\pi/2)=-2-1=-3\]

  20. anonymous
    • 5 years ago
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    Therefore, \[{f(b)-f(a) \over b-a}={-1-(-3) \over {\pi \over 2}-{-\pi \over 2}}={2 \over \pi}\]

  21. anonymous
    • 5 years ago
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    Does that help?

  22. anonymous
    • 5 years ago
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    its right but how we can find the value of c?

  23. anonymous
    • 5 years ago
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    This value, we just found (2/pi) is equal to f'(c). You can use this relation to find c.

  24. anonymous
    • 5 years ago
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    f`c= -4sin2c+cosc

  25. anonymous
    • 5 years ago
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    -4sin2c+cosc=pi\2 so how we can find C?

  26. anonymous
    • 5 years ago
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    Solve the equation, you may get more than one value for c. Take only the value that is in the given interval (-pi/2,pi/2).

  27. anonymous
    • 5 years ago
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    how can it solve the equa? i don't understand this equation to find the value for C

  28. myininaya
    • 5 years ago
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    i would graph it and approximate the solution

  29. myininaya
    • 5 years ago
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    you could also use newton's method

  30. anonymous
    • 5 years ago
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    You never solved quadratic equation?! Hmm I think myininaya got a point. It's difficult to solve it using identities. Probably graphing is a good method.

  31. anonymous
    • 5 years ago
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    Just gimme a minute.

  32. anonymous
    • 5 years ago
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    BRB

  33. anonymous
    • 5 years ago
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    BRB what?

  34. myininaya
    • 5 years ago
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    means be right back

  35. anonymous
    • 5 years ago
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    ok

  36. anonymous
    • 5 years ago
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    no body can solve this question?

  37. anonymous
    • 5 years ago
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    oops myininaya has already solved the problem. Sorry I didn't see that.

  38. myininaya
    • 5 years ago
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    lol

  39. anonymous
    • 5 years ago
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    you are give my proper metjhod to find the valuc of C?

  40. anonymous
    • 5 years ago
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    as myininaya, we can estimate the value by graphing.

  41. anonymous
    • 5 years ago
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    c will be around 1.66

  42. anonymous
    • 5 years ago
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    you said that C1.66 . how you can find tell me?

  43. anonymous
    • 5 years ago
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    Wait. this value of c is out side our interval. The value of c, that's in the interval is around 0.045

  44. myininaya
    • 5 years ago
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    look for x intercepts of f'(c)=2/pi

  45. anonymous
    • 5 years ago
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    \[f'(c)={f(b)-f(a) \over b-a}\] this is the formula.

  46. anonymous
    • 5 years ago
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    ok i know thic formula i completed.. -4sin2c+cosx=2\pi after what can i do i don't understand?

  47. myininaya
    • 5 years ago
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  48. myininaya
    • 5 years ago
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    this is what I got when I used newton's method to find c

  49. anonymous
    • 5 years ago
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    f(x)=2cos2x+sinx andf`(x)=-4sin2x+cosx

  50. myininaya
    • 5 years ago
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    oops i forgot about the 2/pi you try i have to go

  51. anonymous
    • 5 years ago
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    ok thanks!

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