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Evaluate limit

  1. Sep 22, 2014 #1
    1. The problem statement, all variables and given/known data
    Evaluate lim h->0 ((8+h)^⅓ -2)/h.


    2. Relevant equations
    Hint: Let 8+h=x^3


    3. The attempt at a solution
    I've uploaded a picture of my calculation. But I am not sure if that is the final answer or is there a following step to get the answer.
     

    Attached Files:

  2. jcsd
  3. Sep 22, 2014 #2

    Dick

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    Why do you think that as h->0 with x^3=8+h that x->(-3)? And why do you think that (x^3)^(1/3)=x^3?
     
  4. Sep 22, 2014 #3

    Ray Vickson

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    Please do not post thumbnails; they cannot be viewed on some media! Just type out things directly.
     
  5. Sep 23, 2014 #4

    HallsofIvy

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    I don't know exactly which of many possible methods you are expected to use here, but did you notice that this limit is precisely that defining the derivative of f(x) at x= 8, with [itex]f(x)= x^{2/3}[/itex]?
     
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