# Using epsilon delta to prove $\lim_{x\to 1}(x^3-5x)(2+\cos(\frac{1}{x-1}))$ does not exist

How would I use the epsilon-delta definition to show that the limit $$\lim_{x\to 1}(x^3-5x)\left(2+\cos\left(\frac{1}{x-1}\right)\right)$$ does not exist?

• How epsilon-delta definition shows that a limit does not exist? – Nosrati Oct 16 '17 at 2:47