Problem: Let $F$ and $G$ be functions such that $0\leq F(x)\leq G(x)$ for all $x$ near $c$, except possibly at $c$. Show that if $\lim_{x\rightarrow c} G(x)=0$, then $\lim_{x\rightarrow c} F(x)=0$.
I really don't know how to use the formal definition in this demonstration.
This is the solution but I can't understand (https://i.stack.imgur.com/CdxTr.jpg)
I am not sure what if what you mean is the Squeeze Theorem. That is: let F1, F2, G be functions such that $$ F_1\left( x \right) \leqslant \,\,G\left( x \right) \leqslant F_2\left( x \right) $$
when x -> x0, lim F1 = lim F2 define = C so that lim x -> x0 G = C