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← JEE Main 2017 · 2 Apr · Shift 1
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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 70

lim⁡x→π2cot⁡x−cos⁡x(π−2x)3\displaystyle\lim_{x\to\frac\pi2}\frac{\cot x-\cos x}{(\pi-2x)^3} equals :

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Answer and worked solution

Official answer: A

Put x=π2−hx=\frac\pi2-h: the expression becomes tan⁡h−sin⁡h8h3→h3/28h3=116\dfrac{\tan h-\sin h}{8h^3}\to\dfrac{h^3/2}{8h^3}=\dfrac1{16}.

Topics:Limits
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