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Question Number 184239 by mathlove last updated on 04/Jan/23

$$f\left(x\right)=\{\begin{array}{l}x-2ifx>3\\ 3ifx=3\\ -x+4if1⩽x<3\\ 1if1<x\end{array}$$$$faind\underset{x\to 1}{\lim }f\left(x\right)=?and\underset{x\to 3}{\lim }f\left(x\right)=?$$

Answered by SEKRET last updated on 04/Jan/23

$${\mathbf{lim}}_{\mathbf{x}\to 1^{-}}\mathbf{f}\left(\mathbf{x}\right)=1{\mathbf{lim}}_{\mathbf{x}\to 1^{+}}\mathbf{f}\left(\mathbf{x}\right)=3$$$${\mathbf{lim}}_{\mathbf{x}\to 3^{-}}\mathbf{f}\left(\mathbf{x}\right)=1{\mathbf{lim}}_{\mathbf{x}\to 3^{+}}\mathbf{f}\left(\mathbf{x}\right)=1$$$${\mathbf{lim}}_{\mathbf{x}\to 3}\mathbf{f}\left(\mathbf{x}\right)=3$$

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