Question

\(lim\sqrt[3]{n^2+n^3}+n.\) B))lim\(\frac{n^2+2\sqrt{n}+3}{2n^2+n-\sqrt{n}}\)

C))\(\frac{2n\sqrt{n}+3}{n^2+n+1}\) Đ)) lim \(\frac{\left(3+\sqrt{n}\right)\left(2n\sqrt{n}\right)}{\left(n+1\right)\left(n+2\right)}\)

Answer 1

\(a=\lim\limits n\left(\sqrt[3]{\frac{1}{n}+1}+1\right)=+\infty.2=+\infty\)

\(b=\lim\limits\frac{n^2+2\sqrt{n}+3}{2n^2+n-\sqrt{n}}=\lim\limits\frac{1+\frac{2}{n\sqrt{n}}+\frac{3}{n^2}}{2+\frac{1}{n}-\frac{1}{n\sqrt{n}}}=\frac{1}{2}\)

\(c=\lim\limits\frac{2n\sqrt{n}+3}{n^2+n+1}=\frac{\frac{2}{\sqrt{n}}+\frac{3}{n^2}}{1+\frac{1}{n}+\frac{1}{n^2}}=\frac{0}{1}=0\)

\(d=\lim\limits\frac{2n^2+6n\sqrt{n}}{n^2+3n+2}=\lim\limits\frac{2+\frac{6}{\sqrt{n}}}{1+\frac{3}{n}+\frac{2}{n^2}}=\frac{2}{1}=2\)