
Re: Does this imply that lim x > oo f'(x) = 0?
Posted:
May 23, 2013 2:55 PM


steinerartur@gmail.com wrote in news:287a9b1037904437aa0a39f1e0d3cca3@googlegroups.com:
> Suppose f:[0, oo) > R is increasing, differentiable and has a finite > limit as x > oo. Then, must we have lim x > oo f'(x) = 0? I guess > not, but couldn't find a counter example. > > Thank you
Something like f(x) = sum_1^infinity arctan(2^n ( x2^n) )/2^n should
work. f'(x) is a sum of terms like 1/(1 + (2^n x 2^(2n))^2. f'(2^n)=1 plus some small positive terms. But f'(2^n+2^(n1)) should be pretty close to zero.

