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Math Help - Completely lost, someone please help. Limits and derivatives.

  1. #1
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    Completely lost, someone please help. Limits and derivatives.

    Alright, the question is:
    By identifying each of the following limits as a derivative, find the value of the limit.

    lim h->0 (((27+h)^1/3)-3)/h

    I see how this fits into the definition of a derivative

    f'(a) = lim h->0 (f(a+h) - f(a))/h, but I don't understand how I'm supposed to use this information to evaluate the limit.

    I see that the f(x) = cuberoot (x) and a=27 so f(a) = 3

    Any instruction would be highly appreciated. I'm taking an online calculus course so can only correspond with my tutor via email and am finding her to be extremely unhelpful.

    Thanks!
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  2. #2
    Member Miss's Avatar
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    Quote Originally Posted by shelter22 View Post
    I see that the f(x) = cuberoot (x) and a=27 so f(a) = 3
    You almost done!
    So the limit = f'(27).
    Find the derivative of f and substitute x=27 to get the value of the limit.

    Spoiler:

    Your answer should be \frac{1}{27}
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