You Are Given $\lim _ { x \rightarrow a } f ( x ) = L$

Short Answer

You are given $\lim _ { x \rightarrow a } f ( x ) = L$ and a tolerance $\varepsilon$ . Find a number $\delta$ such that $| f ( x ) - L | < \varepsilon$ whenever $0 < | x - a | < \delta$ .
$$\lim _ { x \rightarrow 3 } 4 x = 12 ; \quad \varepsilon = 0.01$$