Thoughts on riemman approximations.

read moreSurely you can’t approximate the integral of a function on the interval negative to positive infinity that diverges using reimman sums.

I mean, reimman sums can evaluate to infinity, no? If you take the limit of some sum as it goes to infinity, such as summation of lim as t-> infinity of (1/x) from 0 to infinity.

Think about its rate of escape? How fast does it go to infinity.

We take it to be true that the integral 1/x over the interval negative to positive infinity diverges. But, what can we say about how

Comparison of the rate at which arctan(x) approaches y=pi/2 with the rate at which tan(x) approaches the line x=pi/2.

They’re inverse functions, so the line they approach is inverse.