PUTNAM EXAM CHALLENGE
Let k be a fixed positive integer. The n th derivative of has the form where is a polynomial. Find .
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Let , where are real numbers and where n is a positive integer. Given that for all real x prove that .
Find all the continuous positive functions f(x), for , such that
where is a given real number.
Let f be a twice-differentiable real-valued function satisfying where for all real x. Prove that is bounded.