anonymous
  • anonymous
find mean value? 2cos2x+sinx=0 a= -pi\2, b=pi\2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
plz reply karo plzzzzzzzzzz
myininaya
  • myininaya
{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
anonymous
  • anonymous
i got a value of c

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myininaya
  • myininaya
ok cool!
anonymous
  • anonymous
i got ! 4sin2c+(1\90)=cosc now how can be find value of c
myininaya
  • myininaya
4sin(2c)+cos(c)=2/pi
anonymous
  • anonymous
plz reply fast myninaya............
myininaya
  • myininaya
-0.04535615498 is what I got using a calculator so the problem says to use the mean value thm?
anonymous
  • anonymous
how can you find the value of c . give me the method?
dumbcow
  • dumbcow
\[Average = \frac{1}{b-a}\int\limits_{a}^{b}2\cos 2x +\sin x dx\]
anonymous
  • anonymous
dumcow i don't understand this method . give me another method?
dumbcow
  • dumbcow
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
anonymous
  • anonymous
but my teacher says that u can use mean value theorm
myininaya
  • myininaya
http://www.eldamar.org.uk/maths/calculus/node17.html
myininaya
  • myininaya
m(b-a)=int(f(x),a..b) m is the mean value
myininaya
  • myininaya
cow has already said this though
myininaya
  • myininaya
do you know how to integrate?
anonymous
  • anonymous
no i don't know?
anonymous
  • anonymous
Okay, By the mean value theorem. The mean value is [f(b)-f(a)]/[b-a]. \[f(b)=f(\pi/2)=2\cos \pi +\sin(\pi/2)=-2+1=-1\] \[f(a)=f(-{\pi \over 2})=2\cos (-\pi)+\sin (-\pi/2)=-2-1=-3\]
anonymous
  • anonymous
Therefore, \[{f(b)-f(a) \over b-a}={-1-(-3) \over {\pi \over 2}-{-\pi \over 2}}={2 \over \pi}\]
anonymous
  • anonymous
Does that help?
anonymous
  • anonymous
its right but how we can find the value of c?
anonymous
  • anonymous
This value, we just found (2/pi) is equal to f'(c). You can use this relation to find c.
anonymous
  • anonymous
f`c= -4sin2c+cosc
anonymous
  • anonymous
-4sin2c+cosc=pi\2 so how we can find C?
anonymous
  • anonymous
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).
anonymous
  • anonymous
how can it solve the equa? i don't understand this equation to find the value for C
myininaya
  • myininaya
i would graph it and approximate the solution
myininaya
  • myininaya
you could also use newton's method
anonymous
  • anonymous
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.
anonymous
  • anonymous
Just gimme a minute.
anonymous
  • anonymous
BRB
anonymous
  • anonymous
BRB what?
myininaya
  • myininaya
means be right back
anonymous
  • anonymous
ok
anonymous
  • anonymous
no body can solve this question?
anonymous
  • anonymous
oops myininaya has already solved the problem. Sorry I didn't see that.
myininaya
  • myininaya
lol
anonymous
  • anonymous
you are give my proper metjhod to find the valuc of C?
anonymous
  • anonymous
as myininaya, we can estimate the value by graphing.
anonymous
  • anonymous
c will be around 1.66
anonymous
  • anonymous
you said that C1.66 . how you can find tell me?
anonymous
  • anonymous
Wait. this value of c is out side our interval. The value of c, that's in the interval is around 0.045
myininaya
  • myininaya
look for x intercepts of f'(c)=2/pi
anonymous
  • anonymous
\[f'(c)={f(b)-f(a) \over b-a}\] this is the formula.
anonymous
  • anonymous
ok i know thic formula i completed.. -4sin2c+cosx=2\pi after what can i do i don't understand?
myininaya
  • myininaya
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myininaya
  • myininaya
this is what I got when I used newton's method to find c
anonymous
  • anonymous
f(x)=2cos2x+sinx andf`(x)=-4sin2x+cosx
myininaya
  • myininaya
oops i forgot about the 2/pi you try i have to go
anonymous
  • anonymous
ok thanks!

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