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Math Help - Limits of function

  1. #1
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    Limits of function

    Please give me some tips on how to solve this..

    f: (1,∞) -> IR


    f(x) = (1/6)((√x)-1)------(√7x) +√7--- (x/6)(√(x-1))
    -------------------- + ------------- + -------------
    -------√(x-1) 3 ----------√(x+3)--------√(x-1)

    find exact value of

    lim f(x)
    x->1+


    Thanks.
    Last edited by Sasuke12; March 10th 2007 at 09:16 PM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Sasuke12 View Post
    Please give me some tips on how to solve this..

    f: (1,∞) -> IR


    f(x) = (1/6)((√x)-1)------(√7x) +√7--- (x/6)(√(x-1))
    -------------------- + ------------- + -------------
    -------√(x-1) 3 ----------√(x+3)--------√(x-1)

    find exact value of

    lim f(x)
    x->1+


    Thanks.
    Consider the terms separately. Look at the last one:

    (x/6) sqrt(x-1) / sqrt(x^2 - 1)

    divide top and bottom by x:

    (x/6) sqrt(x-1) / sqrt(x^2 - 1) = (1/6) sqrt(x-1) / sqrt(1 - 1/x^2)

    Now as x -> inft the denominator goes to 1, and the numerator goes to infty.
    Therefore the limit of this term is +infty.

    The other terms are all positive for large x, so it does not matter how they
    behave for large x we still have:

    lim(x->infty) f(x) = infty

    RonL
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