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Evaluate the Limit (just confirmation)

  1. Mar 20, 2013 #1
    1. The problem statement, all variables and given/known data

    lim (cubicsquareroot(x) - 2)/(x-8)
    x→8



    2. Relevant equations



    3. The attempt at a solution

    I obtained 1/12 as my final answer, after changing the variable since its in indeterminate form.
    ..let p=cubicsquareroot(x), then as x→8, p→2
    then, p^3=x

    Using this logic I obtained 1/12.

    Is this correct ?
     
  2. jcsd
  3. Mar 20, 2013 #2
    Precisely, Although It'd be nicer if you had done some substitutions.. Yeah is correct!
     
  4. Mar 20, 2013 #3
    My bad! you have! And when you reach L'Hopital's rule, revisit these questions..
     
  5. Mar 20, 2013 #4

    SammyS

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    What's a "cubicsquareroot" ?
     
  6. Mar 20, 2013 #5
    Assumed he meant x^(1/3) *kids today*
     
  7. Mar 20, 2013 #6
    lol Yeah I mean't x^(1/3). And thanks.
     
  8. Mar 20, 2013 #7

    Mark44

    Staff: Mentor

    L' Hopital's Rule is not needed in this problem.

    The OP apparently revised the original problem to this form:
    $$ \lim_{p \to 2} \frac{p - 2}{p^3 - 8}$$

    and then factored the denominator to (p - 2)(p2 + 2p + 4), and then took the limit.
     
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