$$\lim_{x\rightarrow x_0}{(f)}$$

$$\lim_{x\rightarrow 0}{(0)}=0$$

\[\lim_{x\rightarrow x_0}{(f)}=\lim_{x\rightarrow x_0}{(\frac{f(x)-f(x_0)}{x-x_0})}\] The limit (lim) function in mathematics is used to determine the value that a function approaches as its input approaches a particular value or infinity. It's denoted as: \[\lim_{x → a}(f(x))\] This notation represents the limit of the function \(f(x)\) as the variable x approaches the value a. It helps us understand the behavior of a function near a specific point or as it extends to infinity, providing insights into continuity, asymptotes, and convergence. Essentially, it helps us analyze how a function behaves as its input gets closer and closer to a certain value or infinity.