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Limit with a constant

  1. Sep 4, 2012 #1
    1. The problem statement, all variables and given/known data

    Find in terms of constant a

    lim (√6(a+h) - √6a) / h
    h→0





    3. The attempt at a solution

    I've tried multiplying by the conjugate [√6(a+h) + √6a] but I still can't seem to get the right answer.

    Any help would be appreciated.
     
    Last edited: Sep 4, 2012
  2. jcsd
  3. Sep 4, 2012 #2

    Mark44

    Staff: Mentor

    Show us what you tried. You can't just multiply by the conjugate - you have to multiply by the conjugate over itself. Show us what you did and we can steer you in the right direction.
     
  4. Sep 4, 2012 #3

    Mark44

    Staff: Mentor

    Also, don't post a problem in more than one forum section. This is the right place - I deleted your other post of this problem.
     
  5. Sep 4, 2012 #4
    well,

    I've multiplied both the top and bottom by the conjugate which would then equal,
    6(a+h)-6a / h(√6(a+h) + √6a)

    which i then get,
    6a+6h-6a/ h(√6(a+h) + √6a)

    but then the whole thing just equals 0 and I'm lost.

    am i correct or wrong so far?
     
  6. Sep 4, 2012 #5

    Mark44

    Staff: Mentor

    No, the whole thing doesn't equal 0.

    What do you get when you simplify this? (6a+6h-6a)/ [h(√6(a+h) + √6a)]
    Note the added parentheses and brackets.

    After you simplify it as much as possible, then take the limit as h → 0.
     
  7. Sep 4, 2012 #6
    so,

    (6a+6h-6a)= 0a+6h= 6h

    and

    [h(√6(a+h) + √6a)]= (h√6(a+h)) + (h√6a)

    which would mean,

    6h / [(h√6(a+h)) + (h√6a)]


    Should I separate (h√6(a+h)) into [h√6a + h√6h] or no?
     
  8. Sep 4, 2012 #7
    i ended up doing,

    6h / h (2√6a) + (√6h) and than cancel out the h

    = 6 / (2√6a) + (√6h) and then multiplying (2√6a) + (√6h) to top and bottom to get rid of sqrts

    = 6 [(2√6a) + (√6h)] / 12a+6h = 12(√6a)+6(√6h) / 12a + 6h

    if i plug in 0 for h i get,

    12(√6a)+6(√6(0)) / 12a + 6(0)
    = 12(√6a) + 0 / 12a + 0 = 12(√6a) / 12a

    now i simplify the 12/12 into 1/1 = (√6a) / a

    however when i plug in (√6a) / a as my answer, it is incorrect.

    am I still wrong?


    wait a minute i figured my mistake,

    2(√6a)*2(√6a) = 24a not 12a...

    after transferring 24a for 12a and re-doing my work the answer i come up with is,

    6(2(√6a)+(√6h)) / 24a + 6h = 12√6a + 6√6h / 24a + 6h

    substituting 0 for h i get,

    12√6a + 6√6(0) / 24a + 6(0) = 12√6a / 24a

    simplifying gives me,

    √6a / 2a
     
    Last edited: Sep 4, 2012
  9. Sep 4, 2012 #8

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    So far, you are correct with 6h / [(h√6(a+h)) + (h√6a)]. Now what do you get when you cancel the factor of h in the numerator and denominator? You are making a lot of algebraic mistakes.
     
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