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Thread: [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 $\displaystyle f'(3)$?

    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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