Please help me solve these in very detailed just like the exaples given on the second picture below as detailed as that please so i understand

Make sure you show all your work and be as detailed as possible.

$(10$ points$)$ Determine the big$-$O for each of the following functions.

a$.f(n)=1$

b$.f(n)=100n+2n!$

c$.f(n)=n^{2}log(n)+n^3$

d$.f(n)=2^n+3^n$

e$.f(n)=9n^3+n^{3}log(n)$

f$.f(n)=n^{4}log(n)+9n^n+4n!+7$

g$.f(n)=(nlog(n)+n^2)(3^n+2^n)$

ine the big$-$O for each of the following functions.

$f(n)=100$ constant $O(100)harr10(1)$

$f(n)=7n,O(7n)longleftrightarrowO(n)$

$f(n)=n^2+n^{2}log(n)+n0(n!)$

$f(n)=5n^3+3nlog(n),n^3>nlog(n)=>O(n^3),nlog$

$f(n)=n^5+n^{3}n!+,n!>n^5=>0(n^{3}n!),n^8>nlog$

$f(n)=(n{2}^n+3n^5)(2n^7+2log(n))=2n^4{2}^n+2n{2}^{n}log(n)+6n^{12}+6n^{5}log(n)$

hine $T(n)$ relationship between processing time and $n.$ Then determine a big$-$O estin number of operations $($a Simple Statement takes one unit of time$)$ used in this segn gorithm.

$j=0$;$j$

Simole Statement