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2-40.

Recall problem 2-17:

i. For left-endpoint and midpoint rectangles, let the index start at 0 and end at n-1.
For right-endpoint rectangles, let the index start at 1 and end at n.
n = number of rectangles.

To determine the width of each rectangle, divide the domain by the number of rectangles:

iii. The transformed function represents the HEIGHT of each rectangle.
For left- and right-endpoint rectangles, the heights are represented by f(a + Δxi).
For midpoint rectangles, the heights are represented by

a = starting value
Δx = width of each rectangle.