$\displaystyle\lim_{x\to\pi/3}\frac{\sin(\pi/3-x)}{2\cos x-1}$ is equal to
Step-by-Step Solution
Key Concept: Let $t=x-\pi/3\to0$. Denominator: $2\cos(t+\pi/3)-1\approx-\sqrt3\,t$. Numerator: $\sin(-t)\approx-t$. Ratio $=1/\sqrt3$.
$\lim=\dfrac{-t}{-\sqrt3\,t}=\dfrac{1}{\sqrt3}$.
Correct Answer: 2