=$\mathop {\lim }\limits_{\ }\frac{3n^{2}+1-3n^2}{\sqrt{3n^{2}+1}+\sqrt{3}n}$ =$\mathop {\lim }\limits_{\ }\frac{1}{\sqrt{3n^{2}+1}+\sqrt{3}n}$ =$\mathop {\lim }\limits_{\ }\frac{\frac{1}{n}}{\sqrt{3+\frac{1}{n^{2}}}+\sqrt{3}}$ =$\frac{0}{2\sqrt{3}}$=0
b)=$\mathop {\lim }\limits_{\ }\frac{3n^{2}+1-3n^2}{\sqrt{3n^{2}+1}+\sqrt{3}n}$ =$\mathop {\lim }\limits_{\ }\frac{1}{\sqrt{3n^{2}+1}+\sqrt{3}n}$ =$\mathop {\lim }\limits_{\ }\frac{\frac{1}{n}}{\sqrt{3+\frac{1}{n^{2}}}+\sqrt{3}}$ =$\frac{0}{2\sqrt{3}}$=0