1, lim [ (n^2 + n )(2n -1)] / (- n^3 – 3n +1)

1, lim [ (n^2 + n )(2n -1)] / (- n^3 – 3n +1)

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  1. $\lim\dfrac{(n^2+n)(2n-1)}{-n^3-3n+1}$

    $=\lim\dfrac{n^2\Big(1+\dfrac{1}{n}\Big).n\Big(2-\dfrac{1}{n}\Big)}{-n^3-3n+1}$

    $=\lim\dfrac{\Big(1+\dfrac{1}{n}\Big)\Big(2-\dfrac{1}{n}\Big)}{-1-\dfrac{3}{n^2}+\dfrac{1}{n^3}}$

    $=\dfrac{1.2}{-1}=-2$

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