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Math Help - Confused with example for textbook, Dividing sqrt help pleaseee

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    Confused with example for textbook, Dividing sqrt help pleaseee

    k so in my textbook i see this example
    lim as x approaches infinity sqrt(2x^2+1)/(3x-5)
    and it explains how u divide the numerator and denominator by the highest power of x in the denominator. Everything i understood until it showed:

    lim x approaches infinity sqrt(2x^2+1)/(3x-5) =lim x approaches infinity sqrt(2+(1/x^2))/(3-5/x)

    So the denominator i understand, simple cancelling of the x, but how did we go from sqwrt(2x^2+1) to sqrt (2+(1/x^2)) just by dividing by x? So confused
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    Quote Originally Posted by kensington View Post
    k so in my textbook i see this example
    lim as x approaches infinity sqrt(2x^2+1)/(3x-5)
    and it explains how u divide the numerator and denominator by the highest power of x in the denominator. Everything i understood until it showed:

    lim x approaches infinity sqrt(2x^2+1)/(3x-5) =lim x approaches infinity sqrt(2+(1/x^2))/(3-5/x)

    So the denominator i understand, simple cancelling of the x, but how did we go from sqwrt(2x^2+1) to sqrt (2+(1/x^2)) just by dividing by x? So confused
    since x > 0, each term in the the numerator was divided by x = \sqrt{x^2}
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    Quote Originally Posted by kensington View Post
    k so in my textbook i see this example
    lim as x approaches infinity sqrt(2x^2+1)/(3x-5)
    and it explains how u divide the numerator and denominator by the highest power of x in the denominator. Everything i understood until it showed:

    lim x approaches infinity sqrt(2x^2+1)/(3x-5) =lim x approaches infinity sqrt(2+(1/x^2))/(3-5/x)

    So the denominator i understand, simple cancelling of the x, but how did we go from sqwrt(2x^2+1) to sqrt (2+(1/x^2)) just by dividing by x? So confused

    For positive x, you have x\sqrt{a}=\sqrt{x^2a}, so \frac{1}{x}\,\sqrt{2x^2+1}=\sqrt{\frac{2x^2+1}{x^2  }}=\sqrt{2+\frac{1}{x^2}}

    Tonio
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