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Question Number 73570 by Rio Michael last updated on 13/Nov/19

$$f:x\to \{\begin{array}{l}1+x,ifx<1\\ 2x-1,ifx>1\end{array}$$$$investigatetheexistenceandnonexistenceofthe$$$$limitoffatthepointx=1$$

Commented by kaivan.ahmadi last updated on 13/Nov/19

$${lim}_{x\to 1^{-}}f\left(x\right)={lim}_{x\to 1^{-}}(1+x)=2$$$${lim}_{x\to 1^{+}}f\left(x\right)={lim}_{x\to 1^{+}}(2x-1)=1$$$$\Rightarrow {lim}_{x\to 1^{-}}f\left(x\right)\ne {lim}_{x\to 1^{+}}f\left(x\right)\Rightarrow$$$${lim}_{x\to 1}f\left(x\right)isnotexist.$$

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