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Math Help - Please check my answers

  1. #1
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    Please check my answers

    determine if it exists Lim x^2-2x+1/sqrt(x+3)-2
    x->1

    Lim x^2-2x+1 *sqrt(x+3 ) +2 / (sqrt(x+3)-2)(sqrt(x+3)+2)
    x->1

    Lim (x-1)(x-1)*sqrt(x+3 ) +2 /(x-1)
    x->1

    Lim (x-1) sqrt(x+3 ) +2 = 0
    x->1
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  2. #2
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    Quote Originally Posted by bobby77
    determine if it exists Lim x^2-2x+1/sqrt(x+3)-2
    x->1

    Lim x^2-2x+1 *sqrt(x+3 ) +2 / (sqrt(x+3)-2)(sqrt(x+3)+2)
    x->1

    Lim (x-1)(x-1)*sqrt(x+3 ) +2 /(x-1)
    x->1

    Lim (x-1) sqrt(x+3 ) +2 = 0
    x->1
    Hello,

    please use brackets to determine numerator and denominator of fractions. Otherwise your terms are not clear enough to help you.

    Greetings

    EB
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  3. #3
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    please check my answer

    determine if it exists Lim (x^2-2x+1)/(sqrt(x+3)-2)
    x->1

    Lim (x^2-2x+1) *(sqrt(x+3 ) +2) /[ (sqrt(x+3)-2)(sqrt(x+3)+2) ]
    x->1

    Lim [(x-1)(x-1)]*(sqrt(x+3 ) +2) /(x-1)
    x->1

    Lim (x-1)*( sqrt(x+3 ) +2) = 0
    x->1
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  4. #4
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    Quote Originally Posted by bobby77
    determine if it exists Lim (x^2-2x+1)/(sqrt(x+3)-2)
    x->1

    Lim (x^2-2x+1) *(sqrt(x+3 ) +2) /[ (sqrt(x+3)-2)(sqrt(x+3)+2) ]
    x->1

    Lim [(x-1)(x-1)]*(sqrt(x+3 ) +2) /(x-1)
    x->1

    Lim (x-1)*( sqrt(x+3 ) +2) = 0
    x->1
    Or more simply ya got,
    \lim_{x\to 1}\frac{(x-1)^2}{\sqrt{x+3}-2}
    Rationalize,
    \frac{(x-1)^2}{\sqrt{x+3}-2}\cdot \frac{\sqrt{x+3}+2}{\sqrt{x+3}+2}
    Thus,
    \frac{(x-1)^2(\sqrt{x+3}+2)}{x-1}
    Thus,
    (x-1)(\sqrt{x+3}+2)
    As, x\to 1 you get 0.
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