What is the value of [math] \displaystyle \lim_{x \to \tfrac{\pi}{3}} \frac{\sin\left(x-\tfrac{\pi}{3}\right)}{1 - 2 \cos x} [/math]?
What are the value of [math]x[/math] and [math]y[/math] in [math]\dfrac{x}{y}+\dfrac{x^2}{y^2}+\dfrac{x^3}{y^3}=14[/math] and [math]x+y=3[/math]?