How to solve this definition of limit proof?

Question

Let $s: \mathbb{R} \to \mathbb{R}$ be defined by $$s(x)=\frac{x}{2^x+1}.$$

Prove that

$$\lim_{x\to 0} s(x) = 0$$

I am having trouble using the delta-epsilon definition.

Answer 1

Observe that for $x\in \Bbb R $,

$$\Bigl| \frac {x}{2^x+1} \Bigr| <|x|$$

so you can take $$\delta=\epsilon $$