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SMT 2022 Calculus #3

Source:

March 29, 2023

Problem Statement

For k=1,2,…k=1,2,\dots, let fkf_k be the number of times sin⁡(kπx2)\sin\left(\frac{k\pi x}{2}\right) attains its maximum value on the interval x∈[0,1]x\in[0,1]. Compute lim⁡k→∞fkk.\lim_{k\rightarrow\infty}\frac{f_k}{k}.
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