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Math Help - linear density

  1. #1
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    Question linear density

    The mass of a part of a metal rod that lies between its left and a point x meters to the right is 3x^2 kg. Find the linear density when x is:

    (a) 1 m

    (b) 2 m

    (c) 3 m

    Also, where is the density the highest? The lowest?

    If anyone could help me out with this one that would be great! maybe show me how to do a,b or c and then I can try the rest? thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by thecount View Post
    The mass of a part of a metal rod that lies between its left and a point x meters to the right is 3x^2 kg. Find the linear density when x is:

    (a) 1 m

    (b) 2 m

    (c) 3 m

    Also, where is the density the highest? The lowest?

    If anyone could help me out with this one that would be great! maybe show me how to do a,b or c and then I can try the rest? thanks!
    Let the mass to the right of a point x be F(x)

    The linear density at x is the limit of the mass in a small element of the rod near x divided by the length of the element, so:

    f(x)=\lim_{\delta \to 0} \frac{F(x+\delta/2)-F(x-\delta/2)}{\delta}=F'(x)

    In this case F(x)=3x^2

    RonL
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