Question

Lim x→π​​/6 {x^2/tanx}

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Answer 1

The limand is continuous at x = π/6, so by direct substitution

`\displaystyle \lim_(x\to\pi/6) (x^2)/(\tan(x)) = (\left(\frac\pi6\right)^2)/(\tan\left(\frac\pi6\right)) = \frac{\pi^2}{36*\frac1{\sqrt3}} = \boxed{(\pi^2)/(12\sqrt3)}`