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Math Help - Instantaneous rate of change of a sphere

  1. #1
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    Instantaneous rate of change of a sphere

    Hi, I need help finding the final answer of this, I know how to do it, but i'm not sure what the final answer should be:

    The volume, V, of a sphere of radius r is given by V = f(r) = 4pi(r^3) / 3. Calculate the instantaneous rate of chnage of the volume, V, with respect to the change of the radius, r, at r = 15.1.

    (doing this without derivatives)

    We calculate the instantaneous rate of change of the volume, V, with the respect to change of the radius, r, at r = 15.1, as

    lim r->15.1 ( f(r) - f(15.1) ) / (r - 15.1)
    =
    lim r->15.1 ( (4pi(r^3)/3) - (4pi(15.1^3)/3) ) / (r - 15.1)
    =
    4pi/3 * lim r->15.1 (r^3 - 15.1^3) / (r - 15.1)
    = ___

    I know to use the difference of cubes formula so I get:

    4pi/3 * lim x->r (r + 15.1r + 15.1)

    Thanks!
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  2. #2
    MHF Contributor kalagota's Avatar
    Joined
    Oct 2007
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    Taguig City, Philippines
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    Quote Originally Posted by coldfire View Post
    Hi, I need help finding the final answer of this, I know how to do it, but i'm not sure what the final answer should be:

    The volume, V, of a sphere of radius r is given by V = f(r) = 4pi(r^3) / 3. Calculate the instantaneous rate of chnage of the volume, V, with respect to the change of the radius, r, at r = 15.1.

    (doing this without derivatives)

    We calculate the instantaneous rate of change of the volume, V, with the respect to change of the radius, r, at r = 15.1, as

    lim r->15.1 ( f(r) - f(15.1) ) / (r - 15.1)
    =
    lim r->15.1 ( (4pi(r^3)/3) - (4pi(15.1^3)/3) ) / (r - 15.1)
    =
    4pi/3 * lim r->15.1 (r^3 - 15.1^3) / (r - 15.1)
    = ___

    I know to use the difference of cubes formula so I get:

    4pi/3 * lim x->r (r + 15.1r + 15.1)

    Thanks!
    what happened to that red thing? it should be r->15.1 and do limit thing..
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  3. #3
    Junior Member
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    Yeah sorry my mistake, it should be:

    4pi/3 * lim r->15.1 (r + 15.1r + 15.1)

    Can anyone help me out?
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  4. #4
    MHF Contributor kalagota's Avatar
    Joined
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    Taguig City, Philippines
    Posts
    1,026
    from there, you can just substitute 15.1 to the remaining function since it is now defined there..
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