Giải thích các bước giải:
$\lim\dfrac{(2n^2+1)^4(n+2)^9}{n^{17}+1}$
$=\lim\dfrac{(n^2(2+\dfrac{1}{n^2}))^4(n(1+\dfrac{2}{n})^9}{n^{17}+1}$
$=\lim\dfrac{n^8(2+\dfrac{1}{n^2})^4.n^9(1+\dfrac{2}{n})^9}{n^{17}+1}$
$=\lim\dfrac{n^{17}(2+\dfrac{1}{n^2})^4(1+\dfrac{2}{n})^9}{n^{17}+1}$
$=\lim\dfrac{(2+\dfrac{1}{n^2})^4(1+\dfrac{2}{n})^9}{1+\dfrac{1}{n^{17}}}$
$=\dfrac{(2+0)^4(1+0)^9}{1+0}$
$=16$