\(\lim\limits\dfrac{2n^2-n+3}{3n^2+2n+1}=\lim\dfrac{2-\dfrac{1}{n}+\dfrac{3}{n^2}}{3+\dfrac{2}{n}+\dfrac{1}{n^2}}=\dfrac{2-0+0}{3+0+0}=\dfrac{2}{3}\)
\(\lim\dfrac{2n+1}{n^3+4n^2+3}=\dfrac{\dfrac{2}{n^2}+\dfrac{1}{n^3}}{1+\dfrac{4}{n}+\dfrac{3}{n^3}}=\dfrac{0+0}{1+0+0}=0\)
\(\lim\dfrac{3n^3+2n^2+n}{n^3+4}=\lim\dfrac{3+\dfrac{2}{n}+\dfrac{1}{n^2}}{1+\dfrac{4}{n^3}}=\dfrac{3+0+0}{1+0}=3\)
\(\lim\dfrac{n^4}{\left(n+1\right)\left(2+n\right)\left(n^2+1\right)}=\lim\dfrac{1}{\left(1+\dfrac{1}{n}\right)\left(\dfrac{2}{n}+1\right)\left(1+\dfrac{1}{n^2}\right)}=\dfrac{1}{\left(1+0\right)\left(0+1\right)\left(1+0\right)}=1\)
\(\lim\dfrac{n^2+1}{2n^4+n+1}=\lim\dfrac{\dfrac{1}{n^2}+\dfrac{1}{n^4}}{2+\dfrac{1}{n^3}+\dfrac{1}{n^4}}=\dfrac{0+0}{2+0+0}=\dfrac{0}{2}\)
\(\lim\dfrac{2n^4+n^2-3}{3n^3-2n^2+1}=\lim\dfrac{2n+\dfrac{1}{n}-\dfrac{3}{n^3}}{3-\dfrac{2}{n}+\dfrac{1}{n^3}}=\dfrac{+\infty}{3}=+\infty\)
