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Math Help - [SOLVED] Rates of change formula?

  1. #1
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    [SOLVED] Rates of change formula?

    I'm trying to solve the question for f(x)= x + sin x find the average rate of change of f(x) for

    i) [0, pi / 2]

    I think the formula is f(b)-f(a) / b-a

    in which this case we would have

    pi/2 + sin pi/2 - sin0 / pi/2 - 0

    I'm not sure if I got this right though.

    Edit: Okay so I got my formula:

    change over y / change over x

    f(x2) - f(x1) / fx2 - fx1

    In the above scenario I think we have to factor out something to eliminate the denominator but I'm not sure how to do it.
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  2. #2
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    Simplify \frac{\frac{\pi}{2} + \sin \left(\frac{\pi}{2}\right)}{\frac{\pi}{2}}
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  3. #3
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    Quote Originally Posted by thekrown View Post
    I think the formula is f(b)-f(a) / b-a
    correct \frac{f(b)-f(a)}{ b-a}
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  4. #4
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    Okay so I can factor out pi/2 and end up with

    pi/2 (sin 1) / pi/2

    I can then cross out pi/2 from the numerator and denominator. This leaves us with sin 1.

    I remember some problems where I would turn to the unit circle, find the location and then find sin by finding y/r or something similar.

    However, in this case I don't really know what sin 1 is since usually there is a pi somewhere.
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  5. #5
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    Quote Originally Posted by thekrown View Post
    Okay so I can factor out pi/2 and end up with

    pi/2 (sin 1) / pi/2

    I can then cross out pi/2 from the numerator and denominator. This leaves us with sin 1.
    That is all wrong.

     <br />
\sin \left(\frac{\pi}{2}\right)=1 <br />
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  6. #6
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    I see, so in this case we have pi/2 + 1/2 divided by pi/2

    I think this is equal to 2pi/2 divided by pi/2 which should be 2 right?
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     <br />
\frac{\frac{\pi}{2} + \sin \left(\frac{\pi}{2}\right)}{\frac{\pi}{2}}= \frac{\frac{\pi}{2} + 1}{\frac{\pi}{2}} = \frac{2}{\pi}\left(\frac{\pi}{2} + 1\right) = 1+\frac{2}{\pi}<br />
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  8. #8
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    Quote Originally Posted by thekrown View Post
    I see, so in this case we have pi/2 + 1/2 divided by pi/2

    I think this is equal to 2pi/2 divided by pi/2 which should be 2 right?
    (pi/2 + 1/2) divided by pi/2 = (pi/2 + 1/2) times 2/pi
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