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Math Help - [SOLVED] Instantaneous rate of change

  1. #1
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    [SOLVED] Instantaneous rate of change

    Which of the following will not give the instantaneous rate of change of h(x) with respect to x when x=3?

    1. lim x->3 (f(x)-f(3))/(x-3)
    2. lim h->0 (f(3+h)-f(3-h))/2h
    3. lim x->3 (f(3)-f(x))/(3-x)
    4. (f(3)-f(3-0.1))/0.1


    I know for sure the 1 will give the instantaneous rate of change. Not sure about 2,3 and 4. I guessing that 4 is the answer, because it gives what seems like an average value instead of an instantaneous value.
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  2. #2
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    Quote Originally Posted by solars View Post
    Which of the following will not give the instantaneous rate of change of h(x) with respect to x when x=3?

    1. lim x->3 (f(x)-f(3))/(x-3)
    2. lim h->0 (f(3+h)-f(3-h))/2h
    3. lim x->3 (f(3)-f(x))/(3-x)
    4. (f(3)-f(3-0.1))/0.1


    I know for sure the 1 will give the instantaneous rate of change. Not sure about 2,3 and 4. I guessing that 4 is the answer, because it gives what seems like an average value instead of an instantaneous value.
    4.

    An instantaneous rate of change is found using a limiting process.

    4. gives the approximate rate of change at x = 3.

    1., 2., and 3. are all equivalent and correct.
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  3. #3
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    Quote Originally Posted by solars View Post
    4. (f(3)-f(3-0.1))/0.1

    I know for sure the 1 will give the instantaneous rate of change. Not sure about 2,3 and 4. I guessing that 4 is the answer, because it gives what seems like an average value instead of an instantaneous value.



    Well done

    Now as an exercise, can you reason out why the others are f'(3)?

    P.S: There is an easy trick, do you know L'Hospital's rule?
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  4. #4
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    Yup!
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