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is convergent and $\underset{n\to \mathrm{\infty }}{lim}\frac{12n^3+5n+1}{2n^3-6}=6$.

is convergent and $\underset{n\to \mathrm{\infty }}{lim}\frac{12n^3+5n+1}{2n^3-6}=0$.

is convergent and $\underset{n\to \mathrm{\infty }}{lim}\frac{12n^3+5n+1}{2n^3-6}=12$.

is divergent and $\underset{n\to \mathrm{\infty }}{lim}\frac{12n^3+5n+1}{2n^3-6}=\mathrm{\infty }$.

has no limit.