Chapter 7.8, Problem 47E

To determine

( a);

To make:

A table of approximate values of ${\displaystyle {\int }_1^{t}g\left(x\right)dx}$ using calculator or computer and state if it appear convergent.

To determine

(b)

To show:

that the integral ${\displaystyle {\int }_1^{\infty }g\left(x\right)dx}$ is convergent using comparison theorem.

To determine

(c)

To illustrate:

 Part (b) by graphing  f and g on the same screen for $1\le x\le 10$ and explain intuitively why ${\displaystyle {\int }_1^{\infty }g\left(x\right)dx}$ is convergent.