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Math Help - L'Hospitals Rule ---- easy quick help

  1. #1
    Member mybrohshi5's Avatar
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    L'Hospitals Rule ---- easy quick help

    Find lim as n--> infinity of 2n/(1+3sqrt(n))

    since its infinity over infinity use L'Hospitals rule

    2 / (3/2 n^-1/2)

    2(3/2 sqrt(n))



    OK so i know this is wrong and i know it should be

    2sqrt(n) / (3/2)

    but i dont get why only the n^(-1/2) comes up to the top and the 3/2 stays in the denominator cause i thought the 3/2 and n^-1/2 should go up top since they are connected (multiplying).
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  2. #2
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    Quote Originally Posted by mybrohshi5 View Post
    Find lim as n--> infinity of 2n/(1+3sqrt(n))

    since its infinity over infinity use L'Hospitals rule

    2 / (3/2 n^-1/2)

    2(3/2 sqrt(n))



    OK so i know this is wrong and i know it should be

    2sqrt(n) / (3/2)

    but i dont get why only the n^(-1/2) comes up to the top and the 3/2 stays in the denominator cause i thought the 3/2 and n^-1/2 should go up top since they are connected (multiplying).
    2/(3/2)*n^-1/2
    = 2*(n^1/2)/(3/2)
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  3. #3
    Member mybrohshi5's Avatar
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    I understand that it is 2*(n^1/2)/(3/2) but i dont get why it is this. why doesnt the (3/2) go to the numerator along with the n^-1/2 since they are "attatched to one another"
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  4. #4
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    Quote Originally Posted by mybrohshi5 View Post
    I understand that it is 2*(n^1/2)/(3/2) but i dont get why it is this. why doesnt the (3/2) go to the numerator along with the n^-1/2 since they are "attatched to one another"
    When 3/2 goes to numerator it becomes (3/2)^-1 = 2/3
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