Chapter 11.2, Problem 12ES

To determine

(a)

To prove:

The function $7n^3+10n^2+3$ is greater than or equal $0$ and less than or equal $20n^3$ for $n\ge 1$.

To determine

(b)

To prove:

The function $7n^3+10n^2+3$ is greater than or equal $7n^3$ for $n\ge 1$.

To determine

(c)

To graph:

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

( $0\le 7n^3+10n^2+3\le 20n^3$ and $7n^3+10n^2+3\ge 7n^3$ )

To determine

(d)

The relationship between the functions $7n^3+10n^2+3$, $20n^3$ and $7n^3$ in the notations of $O-$ and $\Omega -$.

To determine

(e)

The order of the functions $7n^3+10n^2+3$.