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Math Help - Determine the limit and where possible compute.

  1. #1
    cpj
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    Determine the limit and where possible compute.

    hi, the problem i have is i'm having trouble with how to determine the limit using first principles, any help would be appreciated. the problem is..

    lim (5x-2)^1/2 - 2(2^1/2)
    x->2 (x^2)-(3x)+2

    thanks for any help, i've never had much luck with limits
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  2. #2
    Flow Master
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    Quote Originally Posted by cpj View Post
    hi, the problem i have is i'm having trouble with how to determine the limit using first principles, any help would be appreciated. the problem is..

    lim (5x-2)^1/2 - 2(2^1/2)
    x->2 (x^2)-(3x)+2

    thanks for any help, i've never had much luck with limits
    Multiply numerator and denominator by the conjugate surd \sqrt{5x - 2} + \sqrt{8}, simplify the numerator, factorise the denominator, cancel the common factor and then take the limit. Please show your work if you need more help.
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  3. #3
    cpj
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    (5x-2)^1/2 - (8)^1/2
    x^2 - 3x + 2

    [(5x-2)^1/2 - (8)^1/2] * [(5x-2)^1/2 + (8)^1/2]
    [(5x-2)^1/2 + (8)^1/2]*[(x^2)-3x+2]


    (5x-2)-8
    [(5x-2)^1/2 + (8)^1/2]*(x-1)(x-2)


    5
    -2(2^1/2)

    this is my final limit, could you tell me if its correct please. i'm not sure..
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  4. #4
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    Quote Originally Posted by cpj View Post
    (5x-2)^1/2 - (8)^1/2
    x^2 - 3x + 2

    [(5x-2)^1/2 - (8)^1/2] * [(5x-2)^1/2 + (8)^1/2]
    [(5x-2)^1/2 + (8)^1/2]*[(x^2)-3x+2]


    (5x-2)-8
    [(5x-2)^1/2 + (8)^1/2]*(x-1)(x-2)


    5
    -2(2^1/2)

    this is my final limit, could you tell me if its correct please. i'm not sure..
    I get \frac{5}{2 \sqrt{8}}.
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