21/08/31 10:18:58.82 k5ZVRW0j.net
>>170
The 80th William Lowell Putnam mathematical competition
Saturday, December 7, 2019
〔A6〕 Let g be a real-valued function that is continuous on the closed interval [0,1] and twice differentiable on the open interval (0,1).
Suppose that for some number r>1,
lim_{x→+0} g(x)/(x^r) = 0.
Prove that either
lim_{x→+0} g '(x) = 0
or
limsup_{x→+0} (x^r)|g "(x)| = ∞.