lim_x→π31 2cos xπ 3x 00 formUsing L'Hospital's rule we get, =lim_x→π32sin x 3 =2√(3) 6 = 1√(3) ...

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Limit

limx →π3 1-2...

Question

$lim x \to \frac{π}{3}$ $\frac{1 - 2 cos x}{π - 3 x}$

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Solution

$lim x \to \frac{π}{3} \frac{1 - 2 cos x}{π - 3 x}$ $\frac{0}{0}$ form
Using L'Hospital's rule we get,
$= lim x \to \frac{π}{3} \frac{2 sin x}{- 3}$

$= \frac{2 \sqrt{3}}{- 6}$

$= - \frac{1}{\sqrt{3}}$

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