If , then is equal…

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

If f(x)=lim⁡t→0tan⁡−1(ext−1t)f(x)=\lim_{t\to0}\tan^{-1}\left(\frac{e^{xt}-1}{t}\right), then lim⁡x→0f(x)−xx3\lim_{x\to0}\frac{f(x)-x}{x^3} is equal to (a) 12\frac{1}{2} (b) −12-\frac{1}{2} (c) 13\frac{1}{3} (d) −13-\frac{1}{3}

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