For , let . Then…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

For n∈Nn\in\mathbb{N}, let fn(x)=tan⁡x2(1+sec⁡x)(1+sec⁡2x)(1+sec⁡4x)…(1+sec⁡2nx)f_n(x)=\tan\frac{x}{2}(1+\sec x)(1+\sec 2x)(1+\sec 4x)\dots(1+\sec 2^n x). Then lim⁡x→0fn(x)2x\lim_{x\to0}\frac{f_n(x)}{2x} is (1) 00 (2) 2n2^n (3) 2n−12^{n-1} (4) 2n+12^{n+1}

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