lim⁡z→∞∫1/2z[cot⁡−1x]dx∫1/2z[1+1x]dx\lim_{z \to \infty} \frac{\int_{1/2}^{z} [\cot^{-1} x] dx}{\int_{1/2}^{z} \left[ 1 + \frac{1}{x} \right] dx}…

Problem

lim⁡z→∞∫1/2z[cot⁡−1x]dx∫1/2z[1+1x]dx\lim_{z \to \infty} \frac{\int_{1/2}^{z} [\cot^{-1} x] dx}{\int_{1/2}^{z} \left[ 1 + \frac{1}{x} \right] dx} , where [⋅][\cdot] denotes the greatest integer function, equals a. 0 b. 1 c. cot⁡1\cot 1 d. not defined

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