=\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