Question: Let f(x) = 1 - x 2 . a. Show that the graph of f is the upper half of a circle of radius 1

Let f(x) = √1 - x2.

a. Show that the graph of f is the upper half of a circle of radius 1 centered at the origin.

b. Estimate the area between the graph of f and the x-axis on the interval [-1, 1] using a midpoint Riemann sum with n = 25.

c. Repeat part (b) using n = 75 rectangles. 

d. What happens to the midpoint Riemann sums on [-1, 1] as n →∞?

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