Question

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

Answer 1

plz reply karo plzzzzzzzzzz

Answer 2

{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

Answer 3

i got a value of c

Answer 4

ok cool!

Answer 5

i got !
4sin2c+(1\90)=cosc
now how can be find value of c

Answer 6

4sin(2c)+cos(c)=2/pi

Answer 7

plz reply fast myninaya............

Answer 8

-0.04535615498 is what I got using a calculator
so the problem says to use the mean value thm?

Answer 9

how can you find the value of c . give me the method?

Answer 10

\[Average = \frac{1}{b-a}\int\limits_{a}^{b}2\cos 2x +\sin x dx\]

Answer 11

dumcow i don't understand this method . give me another method?

Answer 12

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

Answer 13

but my teacher says that u can use mean value theorm

Answer 14

http://www.eldamar.org.uk/maths/calculus/node17.html

Answer 15

m(b-a)=int(f(x),a..b)
m is the mean value

Answer 16

cow has already said this though

Answer 17

do you know how to integrate?

Answer 18

no i don't know?

Answer 19

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

Answer 20

Therefore,
\[{f(b)-f(a) \over b-a}={-1-(-3) \over {\pi \over 2}-{-\pi \over 2}}={2 \over \pi}\]

Answer 21

Does that help?

Answer 22

its right but how we can find the value of c?

Answer 23

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

Answer 24

f`c= -4sin2c+cosc

Answer 25

-4sin2c+cosc=pi\2
so how we can find C?

Answer 26

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).

Answer 27

how can it solve the equa? i don't understand this equation to find the value for C

Answer 28

i would graph it and approximate the solution

Answer 29

you could also use newton's method

Answer 30

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.

Answer 31

Just gimme a minute.

Answer 32

BRB

Answer 33

BRB what?

Answer 34

means be right back

Answer 35

ok

Answer 36

no body can solve this question?

Answer 37

oops myininaya has already solved the problem. Sorry I didn't see that.

Answer 38

lol

Answer 39

you are give my proper metjhod to find the valuc of C?

Answer 40

as myininaya, we can estimate the value by graphing.

Answer 41

c will be around 1.66

Answer 42

you said that C1.66 . how you can find tell me?

Answer 43

Wait. this value of c is out side our interval. The value of c, that's in the interval is around 0.045

Answer 44

look for x intercepts of f'(c)=2/pi

Answer 45

\[f'(c)={f(b)-f(a) \over b-a}\] this is the formula.

Answer 46

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

Answer 47

this is what I got when I used newton's method to find c

Answer 48

f(x)=2cos2x+sinx
andf`(x)=-4sin2x+cosx

Answer 49

oops i forgot about the 2/pi
you try
i have to go

Answer 50

ok thanks!