Question $1-(10$ points$)$ Prove each of the following without using limits$.$ Include all the details.

a$)n^3+3n^{2}in(n^2)$

b$)2^{(n-1)}in(2^{n-2})$

c$)(log{n}^2)ino(logn{)}^2$

d$)2^{(n+1)}inO(4^n)$

e$)2^{2n}!in(2^n)$