Chapter 7.1, Problem 74E

a.

To determine

To explain: The reason of the area of the region bounded by the graph of the function $f\left(x\right)=\frac{1}{x}$ on the interval [1,2] and the x-axis is $\ln 2$.

b.

To determine

To construct: The rectangle over the interval $\left[1,2\right]$ with height $\frac{1}{2}$.

c.

To determine

To show: The statement $2^n>\frac{n}{2}$ and $2^{-n}>-\frac{n}{2}$.

d.

To determine

To conclude: The statements $\underset{x\to \infty }{\lim }\ln x=\infty$ and $\underset{x\to 0^{+}}{\lim }\ln x=-\infty$.