a) $lim\frac{3n^4+1}{(n+1)(n-2)(n^2+1)} =\lim \dfrac{3+\dfrac{1}{n^4}}{(1+\dfrac{1}{n})(1-\dfrac{2}{n})(1+\dfrac{1}{n^2})}=3$
b) $lim (\sqrt{n^2+1}-\sqrt{n^3-1})=\lim \dfrac{n^2-n^3+2}{\sqrt{n^2+1}+\sqrt{n^3-1}}=\lim \dfrac{\dfrac{1}{n}-1+\dfrac{2}{n^3}}{\sqrt{\dfrac{1}{n^3}+\dfrac{1}{n^6}}+\sqrt{\dfrac{1}{n^2}-\dfrac{1}{n^6}}} =\infty$
(nếu e đa học giới hạn vô cùng thì cụ thể nó ra $=-\infty$)