Chapter 5.1, Problem 54E

(a)

To determine

To show: The graph of the function $f\left(x\right)=\sqrt{1-x^2}$ represents an upper half of the circle of radius 1 centered at origin.

(b)

To determine

To estimate: The area of the region bounded by the graph of $f$ and the x-axis on the interval $\left[-1,1\right]$ using the midpoint Riemann sum with $n=25$ subintervals.

(c)

To determine

To estimate: The area of the region bounded by the graph of $f$ and the x-axis on the interval $\left[-1,1\right]$ using the midpoint Riemann sum with $n=75$ subintervals.

(d)

To determine

To find:  The midpoint Riemann sum on $\left[-1,1\right]$ as $n\to \infty$