Problem $1-4.$ Using the definitions of $O(n)$ and $(n),$

$($a$)[5$ points$]$ show that $f(n)=2n^2+3n+5$ is $f(n)=O(n^2).$

$($b$)$ points$]$ Also, show that $f(n)=(n^2).$

$($c$)[5$ points$]$ Once you show that $f(n)=O(n^2)$ and $f(n)=(n^2),$ use the definition of

$(n)$ to show that $f(n)=(n^2).$