Find _ x 0 f(x) and _ x 1 f(x) where f(x) = * 20 c 2x + 3 & x 0 3… - Vidyadip

Question

Find $\mathop {\lim }\limits_{x \to 0} f(x)$ and $\mathop {\lim }\limits_{x \to 1} f(x)$ where $f(x) = \left\{ {\begin{array}{*{20}{c}} {2x + 3}&{x \le 0} \\ {3(x + 1)}&{x > 0} \end{array}} \right.$

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Answer

Here f(x) = $\left\{ {\begin{array}{*{20}{c}} {2x + 3}&{x \le 0} \\ {3(x + 1)}&{x > 0} \end{array}} \right.$
Now $\mathop {\lim }\limits_{x \to 0} f(x)$ = $\mathop {\lim }\limits_{x \to 0} 2x + 3$ = 2 $\times$ 0 + 3 = 3
$\mathop {\lim }\limits_{x \to 1} f(x)$ = $\mathop {\lim }\limits_{x \to 1} 3(x + 1) $ = 3(1 + 1) = 3 $\times$ 2 = 6

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