Đáp án:
12. $1$
13. $\dfrac43$
Giải thích các bước giải:
12. $\lim\dfrac{n\sqrt{n^2 +1} + 2n^2 +3}{3n^2 + n +1}$
$= \lim\dfrac{\sqrt{1 +\dfrac{1}{n^2}} + 2 + \dfrac{3}{n^2}}{3 + \dfrac1n +\dfrac{1}{n^2}}$
$=\dfrac{\sqrt{1 + 0} + 2 + 3.0}{3 + 0 + 0}$
$= 1$
13. $\lim\dfrac{\sqrt[3]{8n^3 + n} + 2n +5}{3n+4}$
$=\lim\dfrac{\sqrt[3]{8 +\dfrac{1}{n^2}} + 2 + \dfrac{5}{n}}{3 +\dfrac4n}$
$= \dfrac{\sqrt[3]{8+0} + 2 + 5.0}{3 + 4.0}$
$= \dfrac43$