8 Feb
2008
8 Feb
'08
12:38 p.m.
<< Jim asked about the integrability of 2 x sin(1/x) - cos(1/x) if x is not zero, f(x) = 0 if x is zero. The function is Riemann integrable on [0,1]. Consider the intervals from 0 to \eps, and from \eps to 1. By uniform continuity, there is some \delta such that on the larger interval, any partitions of mesh \delta, on a subinterval of \eps to 1, with any associated Riemann sums, will yield values within \eps of one another. . . . . . .
Huh? Uniform continuuity of what? Because of the cos(1/x) term, f is not continuous on [0,1]. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele