$a)\underset{n\to \infty }{\lim }\left(5n^2+n-1\right)=\underset{n\to \infty }{\lim }{n}^2\left(5+\frac{1}{n}-\frac{1}{n^2}\right)=\infty$

 

$b)\underset{n\to \infty }{\lim }\left(-n^3+2n+3\right)=\underset{n\to \infty }{\lim }-n^3\left(1-\frac{2}{n^2}-\frac{3}{n^3}\right)=-\infty$

 

$c)\underset{n\to \infty }{\lim }{\left(1-n\right)}^2\left(2n-1\right)=\underset{n\to \infty }{\lim }\left(1-2n+n^2\right)n\left(2-\frac{1}{n}\right)=\underset{n\to \infty }{\lim }{n}^3\left(1-\frac{2}{n}+\frac{1}{n^2}\right)\left(2-\frac{1}{n}\right)=\infty$