The arithemtic mean, in the infinite case, is also an integral. Namely you have:
F(b) - F(a) AM = -----------, where F(x) = integ f(x) dx b - a
AM was used by Newton to derive the e^x formula. AM has a nice property, you can estimate:
AM = f(c) for some c in (b,a)
Which gives further bounds, for example for a montonic funtion that we have:
f(a) =< AM =< f(b)
But this still no way to get rid of limit or infinite series.
Am Mittwoch, 8. November 2017 13:59:18 UTC+1 schrieb John Gabriel: > Read the second New Calculus abstract and take the quiz: > > https://drive.google.com/open?id=0B-mOEooW03iLdnljbmJkc0t0RWc > > Quiz: > > Which of the following statements are TRUE? > > [A] The Ancient Greeks foresaw John Gabriel's genius but only got as far as defining plane number and solid number. > [B] Area is properly defined as square units. > [C] Area is properly defined as the product of arithmetic means. > [D] Area is properly defined as triangular units. > [E] Area can't be properly defined without the arithmetic mean.