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# Find $\lim\limits_{x \to 0} f(x)$ and $\lim\limits_{x \to 1} f(x)$ where $f(x)=\left\{\begin{array}{1 1}2x+3, &x \leq 0\\ 3(x+1),& x > o\end{array}\right.$

The given function is
$f(x)=\left\{\begin{array}{1 1}(2x+3), &x \leq 0\\ 3(x+1),& x > o\end{array}\right.$
$\lim\limits_{x \to 0^-} f(x) = \lim\limits_{x \to 0} [2x+3]= 2(0)+3 = 3$
$\lim\limits_{x \to 0^+} f(x) = \lim\limits_{x \to 0}3(x+1) = 3( 0+1) =3$
$\therefore \lim\limits_{x \to 0^-} f(x) = \lim\limits_{x \to 0^+} f(x) = \lim\limits_{x \to 0} f(x) = 3$
$\lim\limits_{x \to 1^-} f(x) = \lim\limits_{x \to 1}3(x+1) = 3(1+1) = 6$
$\lim\limits_{x \to 1^+} f(x) = \lim\limits_{x \to 1}3(x+1) = 3(1+1) = 6$
$\therefore \lim\limits_{x \to 1^-} f(x) = \lim\limits_{x \to 1^+} f(x) = \lim\limits_{x \to 1} f(x) = 6$