Giải thích các bước giải:
$\lim \sqrt[3]{2n-n^3}+(n-1)$
$=\lim \sqrt[3]{2n-n^3}+n-1$
$=\lim\dfrac{2n-n^3+n^3}{ \sqrt[3]{2n-n^3}^2-n\sqrt[3]{2n-n^3}+n^2}-1$
$=\lim\dfrac{2n-n^3+n^3}{ \sqrt[3]{2n-n^3}^2-n\sqrt[3]{2n-n^3}+n^2}-1$
$=\lim\dfrac{2n}{ \sqrt[3]{2n-n^3}^2-n\sqrt[3]{2n-n^3}+n^2}-1$
$=\lim\dfrac{\dfrac 2n}{ \sqrt[3]{\dfrac{2}{n^2}-1}^2-\sqrt[3]{\dfrac{2}{n^2}-1}+1}-1$
$=\dfrac{0}{1-1.1+1}-1$
$=-1$
$\lim\dfrac{\sqrt[3]{n^3-3n^2+7n-9}-(n+2)}{\sqrt{4n^2-1}-2n+3}$
$=\lim\dfrac{\dfrac{n^3-3n^2+7n-9-(n+2)^3}{\sqrt[3]{n^3-3n^2+7n-9}^2+(n+2)\sqrt[3]{n^3-3n^2+7n-9}+(n+2)^2}}{\dfrac{4n^2-1-(2n-3)^2}{\sqrt{4n^2-1}+2n-3}}$
$=\lim\dfrac{\dfrac{-9n^2-5n-17}{\sqrt[3]{n^3-3n^2+7n-9}^2+(n+2)\sqrt[3]{n^3-3n^2+7n-9}+(n+2)^2}}{\dfrac{12n-10}{\sqrt{4n^2-1}+2n-3}}$
$=\lim\dfrac{(-9n^2-5n-17)(\sqrt{4n^2-1}+2n-3)}{(\sqrt[3]{n^3-3n^2+7n-9}^2+(n+2)\sqrt[3]{n^3-3n^2+7n-9}+(n+2)^2)(12n-10)}$
$=\lim\dfrac{(-9-\dfrac 5n-\dfrac{17}{n^2})(\sqrt{4-\dfrac1{n^2}}+2-\dfrac 3n)}{(\sqrt[3]{1-\dfrac 3{n^2}+\dfrac{7}{n^2}-\dfrac 9{n^3}}^2+(1+\dfrac 2n)\sqrt[3]{1-\dfrac 3{n^2}+\dfrac{7}{n^2}-\dfrac 9{n^3}}+(1+\dfrac 2n)^2)(12-\dfrac{10}n)}$
$=\dfrac{-9.(2+2)}{(1+1.1+1).12}=-1$
