Problems from Side limits

Calculate the limit of the following function in the point $x = 1$ :

$f (x) = {\begin{matrix} x si x < 1 \\ x + 1 si x \geq 1 \end{matrix}$

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In this case we must find the side limits, because they might not coincide

$lim_{x \to 1^{-}} f (x) = lim_{x \to 1^{-}} x = 1$ $lim_{x \to 1^{+}} f (x) = lim_{x \to 1^{+}} x + 1 = 1 + 1 = 2$

The limit from the left is $2$ and from the right is $0$ .

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