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Help please...Riemann sum problem and what is a rectangular hyperbola?
Posted:
Jul 15, 1996 12:48 AM


Am having trouble with a Riemann sum for the problem f(x) = x^2 + 2x over [1,4]; n=6. Can someone help?? So far what I have is:
R = (summation from i=1 to n of x superscript star and subscript i) times (delta x)
Where:
delta x = (b  a)/n = (4  1)/6 = 1/2
x superscript star and subscript i = (i) times (delta x)
Which gives:
R = [summation from i=1 to n of f(x superscript star and subscript i)^2] times [delta x]
R = {[summation from i=1 to n of (i/2)^2] + [2 (summation from i=1 to n of i/2]} times (1/2)
R = (1/2) times {[1/4 times summation from i=1 to n of i^2] + [(2)(1/2) times the summation from i=1 to n of (i)]}
R = (1/2) times [1/4 (n^3/3 + n^2/2 +n/6) + (n^2/2 + n/2)]
substituting 6 for n I get 32.375 which is wrong according to my text and TI82. Answer should be 41.375.
If you can show me where I am going wrong I would be very much appreciative.
Second question is one that I ran across in reading Keith Taylor's The Logic of Limits. In it are several references to rectangular hyperbolas. These were in regards to the topics of cooperatvity and anticooperativity, convergence and divergence, and saturation and threshold. What is a rectangular hyperbola?
Again, many thanks
Steph in Arizona, USA



