- #1

mathmari

Gold Member

MHB

- 5,049

- 7

I want to check the existence of the limit $\lim_{x\to 0}\frac{x}{x} $ using the definition.

For that do we use the epsilon delta definition?

If yes, I have done the following:

Let $\epsilon>0$. We want to show that there is a $\delta>0$ s.t. if $0<|x-0|<\delta$ then $|f(x)-1|<\epsilon$.

We have that $\left |f(x)-1\right |=\left |\frac{x}{x}-1\right |=\left |\frac{x-1}{x}\right |=\frac{|x-1|}{|x|}$.

How can we continue? (Wondering)