> [!summary] A limit is a notion to describe how a function behaves as it approaches a certain value. > **Key equations:** > General limit notion: $\displaystyle\lim_{ x \to n } f (x)$ >[!info]+ Read Time **⏱ 2 min** # Definition A limit tells you the value of a function as it **[[Epsilon-Delta Definition of a Limit|approaches]]** a certain point. Formally this is the limit of a function ($f(x)$) as it approaches a point $n$ as shown below. $ \displaystyle\lim_{ x \to n } f(x) $ Limits can also have directions, and is denote as: $ \begin{array}{c} \text{Limit as x approaches n from the left} \\ \displaystyle \lim_{ x \to n^+ } f(x)\\ \\ \text{Limit x approaches n from the right} \\\displaystyle \lim_{ x \to n^-} f(x) \end{array} $ > [!note] To solve limits analytically, knowledge of [[Analytical Limits Rules|analytical limit rules]] are needed. # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/kfF40MiS7zA?si=2SoB-YypfOummvGh" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe> --- > 🧠 Enjoy this walkthrough? [Support Math & Matter](https://github.com/rajeevphysics/Obsidan-MathMatter) with a star and help others learn more easily. ---