Chapter 5.8, Problem 14ES

In parts (a)-(d), let $f\left(x\right)=1+\left(1/x\right)$ .

(a) Find the arithmetic average of the values $f\left(\frac{6}{5}\right),f\left(\frac{7}{5}\right),f\left(\frac{8}{5}\right),f\left(\frac{9}{5}\right),$ and $f\left(2\right)$ .

(b) Find the arithmetic average of the values $f\left(1.1\right),f\left(1.2\right),f\left(1.3\right),\dots ,f\left(2\right)$ .

(c) Find the average value of $f$ on $\left[1,2\right]$ .

(d) Explain why the answer to part (c) is greater than the answers to parts (a) and (b).