In the figure for Part II shown on previous page: Compute the area A of the rect

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In the figure for Part II shown on previous page: Compute the area A of the rectangles below the curve y = 1/x and express in terms of H_A(6) . Generalize to H_A(n). Note, x is the continuous variable and n only exists for whole numbers (1, 2, 3, etc). Compute the area B of the rectangles above the curve y = 1/x and express in terms of H_B(6). Generalize to H_B(n). Let C denote the area below the curve y = 1/x from 1 to n. It is obvious that A < C < B, i.e., A and B are lower and upper bounds for C respectively. Plug in your results from a) and b) to obtain lower and upper bound for C in terms of H(n). Rearrange your results from c) to obtain upper bounds for H(n) in terms of C. 2. Compute C using Calculus as follows. The area under the curve y = 1/x from 1 to n is called an integral and is denoted by . It can be computed using the Fundamental Theorem of Calculus, which says that C = F(n) – F(1) where F(x) is the antiderivative of f(x) = 1/x, i.e., F(x) = f(x), where F(x) is the derivative of f(x). What function F(x) has derivative 1/x? 3. Now plot H_A(n), H_B(n) and C(n) all on the same plot for n = 1:100. Don’t forget the axis labels and a title or legend

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