Question

Compute \lim_{x \rightarrow 6} \frac{\frac{2}{x} - \frac{1}{3}}{x-6}

Answer 1

A Course by simpler methods involving .

PS: The answer is 1/18 and can be easily verified by a calculator by putting x=0.01

Answer 2

This is a problem from "A Course of Pure Mathematics" by G H Hardy. Find the limit $$\lim_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$$ I had solved ...