Chapter 11.2, Problem 11ES

To determine

(a)

To prove:

The function $23n^4+8n^2+4n$ is greater than or equal $0$ and less than or equal $35n^4$ for $n\ge 1$.

To determine

(b)

To prove:

The function $23n^4+8n^2+4n$ is greater than or equal $23n^4$ for $n\ge 1$.

To determine

(c)

To graph:

An illustration about the variation of the functions in previous part(a.) and party(b.)

( $0\le 23n^4+8n^2+4n\le 35n^4$ and $23n^4+8n^2+4n\ge 23n^4$ )

To determine

(d)

The relationship between the functions $23n^4+8n^2+4n$, $35n^4$ and $23n^4$ in the notations of $O-$ and $\Omega -$.

To determine

(e)

The order of the functions $23n^4+8n^2+4n$