$2)a)\displaystyle\lim_{x \to 2^+} \left(\dfrac{1}{x^2-4}-\dfrac{1}{x-2}\right)\\ =\displaystyle\lim_{x \to 2^+} \left(\dfrac{1}{x^2-4}-\dfrac{x+2}{x^2-4}\right)\\ =\displaystyle\lim_{x \to 2^+} -\dfrac{x+1}{x^2-4}\\ =-\dfrac{3}{0}\\ =-\infty\\ b)f(x)=\dfrac{8}{x}\\ f'(x)=-\dfrac{8}{x^2}\\ f'(2)=-\dfrac{8}{2^2}=-2\\ f'(-2)=-\dfrac{8}{(-2)^2}=-2\\ \Rightarrow f'(2)=f'(-2)$
