You are given $\lim _ { x \rightarrow a } f ( x ) = L$ and a tolerance $\varepsilon$. Find a number $\delta$ such that $| f ( x ) - L |

Question

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 $0 < | x - a | < \delta$.
$$\lim _ { x \rightarrow 3 } 4 x = 12 ; \quad \varepsilon = 0.01$$

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The Answer of 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 $0 < | x - a | < \delta$.
$$\lim _ { x \rightarrow 3 } 4 x = 12 ; \quad \varepsilon = 0.01$$

You Are Given lim⁡x→af(x)=L\lim _ { x \rightarrow a } f ( x ) = Llimx→a​f(x)=L

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