Chapter 3, Problem 25P

Show that $\underset{x\to \pi /3}{\lim }\frac{\sin (x-\pi /3)}{4{\cos }^{2}x-1}=\frac{-\sqrt{3}}{6}$ . Do this by first creating a vector x that has the elements $\pi /\text{3}-0.\text{1},\pi /\text{3}-0.000\text{1},\pi /\text{3}+0.000\text{1},\pi /\text{3}+0.0\text{1}$ , and $\pi /\text{3}+0.\text{1}$ . Then, create a new vector y in which each element is determine from the elements of x by $\frac{\sin (x-\pi /3)}{4{\cos }^{2}x-1}$ . Comoare the elementd of y with the value $\frac{-\sqrt{3}}{6}$ . Use formatlong to display the numbers.