Chapter 11.2, Problem 10ES

To determine

(a)

To prove:

The function $2n^2+15n+4$ is greater than or equal $0$ and less than or equal $21n^2$ for $n\ge 1$.

To determine

(b)

To prove:

The function $2n^2+15n+4$ is greater than or equal $2n^2$ for $n\ge 1$.

To determine

(c)

To graph:

The relationships we have obtained in part (a.) and part (b.)

( $0\le 2n^2+15n+4\le 21n^2$ and $2n^2\le 2n^2+15n+4$ )

To determine

(d)

The relationship between the functions $2n^2+15n+4$, $21n^2$ and $2n^2$ in the notations of $O-$ and $\Omega -$.

To determine

(e)

The order of the functions $2n^2+15n+4$.