Consider the following functions and their given complexities. Find the n$0$ and c values that will

prove that f$($n$)$ is asymptotically bounded by the given complexity. $(15$ pts$)$

a$.$ f$($n$)=$ n$3/1000+100$n$2100$n $+3.$ Prove that f$($n$)=\backslash$Theta $($n$3)$

b$.$ T$($n$)=5$n$2+17$n $-4$ is O$($n$2)$

c$.$ Prove that T$($n$)=6$n$3+18$n$2-3$n $+6$ is $\backslash$Theta $($n$3)$

d$.$ Prove that T$($n$)=8$ lg$($ n $/4)=\backslash$Omega $($ lg n $)$

e$.$ Prove that T$($n$)=6$n$3-8$n$2+500$n $+6$ is O$($n$3)$